A Superior Atheist (allegedly)

An Apologist asks me to comment on a quote that he attributes to Kevin Harris. The Apologist has a habit of copying quotes from websites without checking the provenance and this is another example. The quote is obviously written by someone claiming to be an atheist. Kevin Harris is a Christian Apologist – he’s the sidekick on William Lane Craig’s apologist podcast.  In fact the text is an anonymous comment that was allegedly posted on a blog, but cannot be seen. So the quote should be attributed to “anonymous” and not poor Kevin Harris. Using an anonymous (possibly non-existent) comment as the basis of an argument is somewhat pathetic. It’s the easiest thing in the world to find an opinion on a website that coincides with one’s own opinion. But that doesn’t make it right. Surely it saves time and effort to express and defend one’s own opinion? That would also avoid the embarrassment of misquoting.

Ironically, the text makes a series of spurious arguments, which are the same as those made by Evangelicals and Creationists when they rail against atheism. Whoever created this anonymous text was probably trying to be funny, or contentious, or was trolling. Or is genuinely ignorant. And it certainly fits the criteria of Poe’s Law. 

But let’s take it at face value…

#	What the alleged atheist allegedly said	My Opinion
1	We deride the Theists for having created myths and holy books.	Who is “we”? Maybe you do, but you seem unaware of the origin of those myths and holy books.  It’s fair to deride the beliefs – but it’s not fair to deride “the theists”. Those myths and holy books were created thousands of years ago. You should not deride people who are indoctrinated. Your target should be the indoctrinators.
2	We imagine ourselves superior.	Again… “we”.  You imagine yourself to be superior. That’s likely to be a psychological defence mechanism for an inherent feeling of inferiority. Ironically, it’s a trait exploited by religion.  Seems to me you are someone who needs religion.
3	But we too imagine there are reasons to obey laws, be polite, protect the weak etc.	We don’t imagine reasons – there are actual reasons to obey laws, be polite and protect the weak and usually we are not consciously aware of those reasons. Have you done any research?
4	Rubbish.	Your previous statement was indeed, rubbish.
5	We are nurturing a new religion, one where we imagine that such conventions have any basis in reality.	Again… who is “we”?  And again… have you done any research on the basis of those “conventions”? If you do you will find they do have a basis in reality.  But now that you mention it… you do seem to have a religious mentality.
6	Have they allowed life to exist? Absolutely.	“Allowed” is the wrong word. The “conventions” you allude to are a key evolutionary reason that human life exists (and other species too).  You don’t appear to know much about evolution. Are you not even curious?
7	But who cares?	Well, apparently you do!
8	Outside of my greedy little gene’s need to reproduce, there is nothing in my world that stops me from killing you and reproducing with your wife.	There obviously is something stopping you doing those things, because you don’t do them.
9	Only the fear that I might be incarcerated and thus be deprived of the opportunity to do the same with the next guy’s wife stops me.	It’s good to know the law is a deterrent in your case. You might want to ask yourself why that works for you and not for other people, when most of them are not atheists.  It’s obvious you live in the USA, and the last time I checked (2013) the incarceration rate in your country was the highest in the world (716 per 100,000 of the population). The USA has 4% of the world's population, but it has 22% of the world's prisoners.
10	Some of my Atheist friends have fooled themselves into acting like the general population. They live in suburban homes, drive Toyota Camrys, attend school plays.	Why do you think they live like that? And how do you act differently to your friends?
11	But underneath they know the truth. They are a bag of DNA whose only purpose is to make more of themselves.	That’s obviously not their only purpose, given your previous statement.
12	So be nice if you want. Be involved, have polite conversations, be a model citizen.	It’s quite difficult to be anything else.
13	Just be aware that while technically an Atheist, you are an inferior one.	You obviously feel you are superior (see line 2). I’m not a psychologist, but in my experience, that’s often a way of coping with a feeling of being inferior. I think it’s funny to assume an atheist checklist where you lose points for selecting Suburbs, Camry and Attend School play but you gain points for wanting to be a murderer and rapist and fearing the law.
14	You’re just a little bit less evolved, that’s all.	“Less evolved”. If anything reveals your lack of knowledge of evolution, it’s that comment. Are you a creationist pretending to be an atheist?
15	When you are ready to join me, let me know. I’ll be reproducing with your wife.	You want me to join you after you’ve killed me. I hereby invoke Poe’s Law.

Faith of the faithless: Is atheism just another religion?

From New Scientist - April 2017

By Graham Lawton

I RECENTLY discovered that I am a member of a downtrodden minority, one of the most mistrusted and discriminated-against in the world. As a white, heterosexual, able-bodied, cis-gender male, this is not something I’m used to. But my minority status is undeniable. I am an atheist.

I’m not complaining. I live in one of the world’s most secular countries and work for a science magazine, so it hasn’t got in the way. But for atheists living in societies with a strong religious tradition, discrimination is a real problem. In the US, atheists have one of the lowest approval ratings of any social group. Non-believers are the only significant minority considered unelectable as president – and “unelectable” turns out to be a pretty low bar.

Even when atheists don’t face open hostility or discrimination, we often have to endure put-downs about the sincerity of our (lack of) beliefs. One of the most common is that “atheism is just another religion anyway”. There is no way to prove or disprove the existence of god, the argument goes, so to deny it is a leap of faith. Ergo, atheism is just like a religion.

“This idea turns up all the time, and it is very loaded,” says Lois Lee, who directs the Nonreligion and Secularity Research Network at the University of Kent in Canterbury, UK. “When people say ‘atheism is just another religion’, they normally mean it in a pejorative way.” The subtext is clear: atheists are hypocrites.

But this is more than a personal slight. If atheism really is just another religion, its claim to be a superior way to run the world is fatally weakened. All the criticisms it flings at religion – of being irrational, dogmatic and intolerant – come flying back with interest, and progress towards a more rational and secular society is undermined. So is it true? Is atheism just another religion?

Atheists have been treated with suspicion for centuries. In 1689, philosopher John Locke warned that they are “not at all to be tolerated”. The “just another religion” claim seems to have arisen around a decade ago in response to the rise of New Atheism, a scientifically motivated critique of religion led by Richard Dawkins and underpinned by his 2006 book The God Delusion. Journalists writing about the movement took to using religious metaphors, calling it “the church of the non-believers” and a “crusade against god”. Religious scholars joined the fray to defend their beliefs. Even some scientists took up the cause. In 2007, evolutionary biologist (and atheist) David Sloan Wilson of Binghamton University in New York controversially described the new atheism as a “stealth religion”. His point was that, like many religions, it portrayed itself as the only source of truth and righteousness and its enemies as “bad, bad, bad”.

Losing our religion: Your guide to a godless future

The human mind is primed to believe in god, so why are so many people abandoning religion – and should we be worried about living in an atheist world?

To atheists, such accusations might seem easily refuted. The defining feature of religion is belief in god(s). Atheism defines itself as the absence of belief in god. How can it be a religion? That is like saying that “off” is a TV channel, or not-playing-tennis is a sport.

But atheists arguably have not taken the charge seriously enough. “They’d say, the word just means ‘without god’. That is all. We can go home now,” says Jon Lanman who works on the scientific study of religion at Queen’s University Belfast, UK. Perhaps because of this rather aloof response, atheists have failed to dispel the sense that the critics were on to something.

The truth is that atheism is not simply an absence of belief in god, but also a set of alternative beliefs about the origin and nature of reality. Even though these belief systems diverge in their content and level of fact from religious beliefs, perhaps they originate from the same underlying psychological processes, and fulfil similar psychological needs. Religious ideas, for example, provide stability and reassurance in the face of uncertainty. They help to explain events and provide a moral framework. For these reasons, and others, they are intuitively appealing to human brains. Maybe brains that reject supernatural ideas simply soak up naturalistic ones to take their place. “They may work as replacement beliefs, helping alleviate stress and anxiety as religion does,” says Miguel Farias, leader of the brain, belief and behaviour group at Coventry University, UK.

One candidate for a replacement belief that atheists and others might hold is “progress”. A few years ago, psychologists in the Netherlands tested this idea. It is well known that religious people often turn to their beliefs to deal with emotional distress. Faced with reminders of mortality, for example, they vigorously reaffirm their faith. This may be why churches are full of death imagery – it is good for business. Does the idea of progress work the same magic for atheists?

To find out, the team got volunteers with a secular world view to either write about their own deaths or about dental pain. Then participants read an essay arguing that progress was an illusion. Those who had been prompted to think about death disagreed more strongly with the essay. The anti-progress essay also made volunteers more aware of their own death, as if it were pulling their comfort blanket out from under their feet. A different essay arguing that progress had been substantial did the opposite.

Faced with reminders of morality, both religious people and atheists reaffirm their beliefs

Getty

That’s not all. Another primer known to strengthen religious belief is lack of control over external events. Clinging on to god can help people regain at least a subjective sense of control and predictability. And, yes, atheists do it too. Doing the “progress” experiment with people on board an aeroplane, for example, makes them espouse a stronger belief in progress.

For many atheists, scientific ideas have a similar soothing effect. Stressful situations tend to strengthen their belief in science, especially in theories that emphasise orderliness and predictability over randomness and unpredictability. All of which suggests that religious believers and atheists are more psychologically similar than either would like to think.

That could even extend to supernatural thinking. Proponents of the “psychological impossibility of atheism” argue that supernatural beliefs are so hard-wired into our brains that discarding them altogether is not an option. Evolution, they point out, has endowed us with a suite of cognitive tendencies that make belief in non-material beings come easily. As highly social and tribal animals, for example, we need to keep track of the thoughts and intentions of other people, even when they are not physically present. From there, it is a short step to conceiving of non-physical entities such as spirits, gods and dead ancestors who have minds and intentions of their own, know what we are thinking and have some influence over our lives. And, sure enough, there is evidence that even hardcore atheists tend to entertain quasi-religious or spiritual ideas such as there being a higher power or that everything happens for a purpose.

“It’s like saying that ‘off’ is a TV channel, or not-playing-tennis is a sport”

However, even if letting go completely isn’t an option, that doesn’t mean that atheists are actually religious. “Intuitions about dualism, teleology, and magic are common among non-believers,” says Ara Norenzayan, a psychologist at the University of British Columbia in Canada. “But the case is much weaker for belief in God or gods, where cultural learning is much more powerful.” And experiments show that people can override their tendencies. “There is no evidence for the argument that all people have an implicit belief in the supernatural,” says psychologist Marjaana Lindeman at the University of Helsinki in Finland.

The Sunday Assembly aims to be “something like church but without God”

David Levene / eye vine

So, despite some similarity between religious and non-religious beliefs systems, they are not equivalent. Surely that buries the claim that atheism is just another religion?

Maybe not. There is another way in which atheist beliefs make them religion-like, according to Sloan Wilson. It is the way they play fast-and-loose with scientific facts. “Atheists will say that religion is bad for humanity, that it’s not an evolutionary adaptation – which happens not to be true,” he says. “That is how atheism becomes an ideology. It is organised to motivate behaviour. If it uses counterfactual beliefs in order to do it then there’s really very little difference between atheism and a religion.”

But if using non-factual beliefs to motivate behaviour is enough to make something a religion, then atheism isn’t the only offender. Political campaigns are a religion; Father Christmas is a religion; self-help books are a religion. That would seem to lead to such a broad definition of religion that it is almost useless – and certainly doesn’t make the accusation against atheism especially damning.

Besides, religion is not just about belief. There are many ways in which atheism is not like a religion, according to Dan Dennett, a philosopher at Tufts University in Medford, Massachusetts. When somebody puts it to me that atheism is just another religion, he says: “I ask ‘in what way?’ They usually counter with demonstrably false parallels. We have no rituals, no membership rules, no sacred texts and the small percentage of atheists who belong to specifically atheist organisations are more like people who belong to interest groups like scuba divers or guitar aficionados. And most atheists don’t feel the need to proselytise.”

What’s it all about?

Atheism lacks other features of religion too. “Can atheism provide a strong sense of meaning and purpose?” asks Sloan Wilson. “Can it motivate people to prosocial action, can it get you out of bed in the morning with enthusiasm to do things? I think the answer is theoretically yes… but only for a few individuals.”

So there we have it. Atheism is both like a religion and not like one, depending on which aspects you consider. And therein lies the real problem, and the reason why the question of whether or not atheism is just another religion goes around and around in circles. Atheism is not one thing. Nor is religion. “Asking ‘is atheism a religion?’ is a terrible question,” says Lanman. “You can’t answer it because both are social constructs.” In other words, they are categories that we impose on the world rather than things that exist independently in it.

In that respect they are similar to the category “weeds”. Everybody knows what a weed is, but try to produce scientific criteria to distinguish weeds from non-weeds and you will fail. It is impossible, for example, to develop a weedkiller that kills only weeds. “In the scientific ontology that has been built up through biology and botany, there’s no place for a category ‘weed’,” says Lanman. “The things we label weeds have nothing causally to do with one another.”

Without a causal connection, you can’t do science. You cannot produce a description of a social construct that distinguishes it from other things. You can’t discover what causes it, and you can’t make predictions about it. You certainly cannot answer the question “is social construct A just another instance of social construct B”. You might as well ask “are bushes just another sort of weed?”. Er, sometimes. It depends.

And so it is with atheism and religion. “We’ve been using inadequate concepts,” says Lee. “To answer the question, you’ve got to have a coherent idea of what “religion” is, as well as what “atheism” is.” And that’s not possible. You can identify beliefs and behaviours that are often part of the social construct we call religion and you can do the same for the social construct we call atheism (see “Elements of atheism“). But you can’t really compare the two, says Lanman. Neither really exists.

That, of course, won’t win me an argument in a pub or across the dinner table. But according to Lee, the argument is still worth having. “It may be a daft question, but it gets at a bigger debate about what it means to be religious and what it means to be non-religious. About 50 per cent of Britons are unbelievers of some description, and we really don’t know what we mean by that.” Amen.

Elements of atheism

Religion is not one thing but many. To understand it, you need to break it up into smaller pieces. For example, it often – but not always – features a belief in supernatural agents. And it often – but not always – features a social identity as a member of a group. These are clearly not the same thing, and can be studied in isolation from one another. What are beliefs and where do they come from? What are social identities and how do they form?

By breaking apart religion in this way, scientists find at least five other phenomena. These are: creation beliefs; afterlife beliefs; magical causation beliefs; rituals; and sacred or non-negotiable values. It is tempting to think of these as the “ingredients” of religion, but that is a mistake, says Jon Lanman at Queen’s University Belfast, UK. In fact, religion does not really exist. It is a social construct, the name we give to collections of these beliefs and behaviours (see main feature). The more there are, the more likely we are to call it a religion. But none is essential, and one can be enough.

Lanman has applied the same process to the social construct we call atheism. It breaks down into five elements: moral opposition to religion; absence of belief in nonphysical agents; an atheist social identity; rituals; and sacred values. Again, this is not an ingredient list, but captures the various beliefs and behaviours that we typically call “atheism”.

One conclusion is that religion and atheism do have things in common, sometimes. Both feature sacred values, which are beliefs that people would not trade for material goods. Both have rituals – although atheist ones are rare – and distinct social identities. But the content of these features are very different. An atheist’s sacred value might be that religion should have no place in government, whereas a Muslim’s might be the exact opposite.

Truth in philosophy means...

"Truth in philosophy means that concept and external reality correspond."

- Hegel

My casual reference to the concept of Necessary Truth (using the example of 1+1=2) results in a series of logic failures by a Christian Apologist.  Nine different fallacies repeated multiple times:

Fallacy #	Fallacy	Key Point	See Line #
1	The result of a sum is only true by definition	Each individual symbol has a definition like words in a language, but 1+1 is not defined as being equal to 2. It is equal to 2 in reality.	10
2	We decide what is necessarily true	A necessary truth exists independently of our experience.  We don't decide what's necessarily true - we discover what is necessarily rue.	11
3	The nature of truth varies depending which symbols are used	Different symbols can be used to represent the same truth, just like different languages can describe the same thing.	13
4	1+1 can be used to represent chemical and physical reactions	1+1 essentially represents counting. Starting from zero, we can always add one to an integer. 1+1=2 is an act of the integers.	14
		The symbols  “1+1” do not represent the combining of substances, chemical reactions and physical reactions. There are different symbols and images for those situations, for example the explosive reaction between sodium and water is represented as:  2Na + 2H2O → 2NaOH + H2	19
5	The result of a sum is only true by definition	The result of a sum is true per se and can be formally proven. The formal proof that 1+1=2 is well known.	15
6	Adding numbers is the same as combining substances, e.g. adding sodium to water, adding eggs and milk to flour, etc.	The word “addition” has two different meanings: a) The action of adding something to something else b) The process of calculating the total of two or more amounts The necessary truth of 1+1=2 is addition according to definition #2. Definition #1 is a different process, for example, mixing different substances together. 1+1 refers to items and does not represent the mixing of substances and any resulting chemical or physical reactions.	20
7	Necessary truth only exists as an abstract concept, not in reality	A necessary truth is true in reality and in all possible worlds, and is observed to be true. 1+1=2 is the first (and most fundamental) necessary truth demonstrated to infants.  Roger Penrose provides an elegant explanation of numbers in the physical world in chapter 3 of this book…	12
8	1+1=2 is not a necessary truth because it is not true in all situations.	The fallacy here is disanalogy. 1+1=2 is true in all situations where items are being counted. In other words it’s always true for the phenomenon it describes.  It is fallacious to provide examples of situations that 1+1 does not represent, in order demonstrate that 1+1=2 is not true. It is like arguing that the law of gravity is not always true because sap rises in a tree.	75
9	The symbol “=” represents the consequence of a chemical or physical reaction	The symbol “=” represents equality, and is a fulcrum upon which an equation is balanced, like a set of scales. This means 1+1=2 can be rearranged as long as the balance is maintained, for example: 1=2-1  …and this represents another necessary truth - If someone has two items and one is taken away, they have one item left. But if two substances are mixed together, it doesn’t follow that the reaction is reversible. See also fallacy #4.	89

Here is the transcript...

Line #	Date	Posted by	Post	Commentary
1	10 Feb 2017 at 9:18AM	A heroic outlaw	Off topic. But curious. Does something have to be factual to be true?
2	10 Feb 2017 at 11:01AM	JimC	It depends what you mean by true. LOL. Whole books have been written on this but essentially there are two types of truth in philosophy...
3			- A necessary truth cannot possibly be false e.g. 1+1=2. If you negate a necessary truth, you contradict reality hence the negation is impossible.
4			- A contingent truth is a true statement that could be false. So for example “Greg read a book last weekend" is a contingent truth, because the statement “Greg did not read a book last weekend" could have been true, without creating a contradiction in the fabric of reality. Greg could have chosen not to read a book, or to have read the book next weekend. Note that additional information could turn this into a necessary truth (or necessary falsehood) for example, if Greg has been dead for 10 years.
6			So to answer your question, a necessary truth is factual. A contingent truth is a hypothesis or theory. We may be able to verify if Greg read a book.
6	10 Feb 2017 at 4:58PM	A heroic outlaw	Thank you, now I can go back into my Twitter argument with some people, fully armed.
7	10 Feb 2017 at 5:38PM	JimC	May the force be with you.  And if you have a day to spare...
8			https://plato.stanford.edu/entries/truth/	The Stanford Encyclopedia of Philosophy. A terrific online resource.
9	10 Feb 2017 at 5:54PM	A heroic outlaw	Thanks
10	14 Feb 2017 at 12:15AM	Apologist	The numbers one plus one is defined as equaling the number two.	No.  The words and symbols have their definitions, but they are not the necessary truth.  They represent it.  Key Point Each individual symbol has a definition like words in a language, but 1+1 is not defined as being equal to 2. It is equal to 2 in reality.
11			In the first of your claims regarding a so-called "necessary truth," you state: "A necessary truth cannot possibly be false e.g. 1+1=2. If you negate a necessary truth, you contradict reality hence the negation is impossible." That would imply that (1) a "necessary truth" is actually discernible beyond all doubt and (2) that an abstraction that is artificially defined as truth is actually meaningful and remains completely truthful when applied to concrete situations.	It’s true that experience can be used to validate the truth of 1+1=2 but one cannot get necessity from experience. A necessary truth does not come from experience.  Key Point A necessary truth exists independently of our experience.
12			For example, in the abstract, the numbers one plus one is defined as equaling the number two.	It’s not true to say that 1+1 is defined as equalling 2 (see line 10) but the subject of definitions raises several key points listed below Key Point The truth of 1+1=2 is not abstract. The ability to count from 1 to 2 (and beyond) is a fundamental requirement for living day to day and it couldn’t be more concrete. The same is true of other mathematical principles which may begin life as apparently abstract but are later discovered to define an aspect of reality. Roger Penrose provides an elegant explanation of numbers in the physical world in chapter 3 of this book…
13				Key Point In everyday language, the symbols used in 1+1=2 have default meanings which are well understood. Arguing that 1+1=2 is a fallacy by referring to different uses of the symbols is a fallacious argument. Inventing a new language does not negate truth.   The symbols have definitions of course (see line 10) and different symbols can be used (and are used) to represent the same necessary truth, just like different languages can describe the same concept. For example, we could express 1+1=2 in binary or in Japanese or using Roman numerals… 1 + 1 = 2 1 + 1 = 102 I + I = II いちたすいちはに一足す一波に These statements all say the same thing – they all refer to the same necessary truth. A necessary truth is true in all possible worlds, and hence all languages.  An example where the symbols have different meanings exists in Boolean Algebra where 1+1=1. That’s because… 1 is the symbol for TRUE 0 is the symbol for FALSE + is the symbol for OR This does not negate 1+1=2 because in Boolean Algebra, the symbols “1” and “0” do not represent numerical values and the "+" symbol does not represent addition.
14				Key Point 1+1 essentially represents counting. In terms of a formal proof, Peano shows that starting from zero, we can always add one to a whole number.  Peano defined axioms that accurately capture how the integers act and 1+1=2 is an act of the integers.
15				Key Point Bertrand Russell went even further and used formal logic to prove Peano’s axioms. It’s not until page 362 (!) that Russell gets to the point of saying 1+1=2 The full text of the book can be found here…
16			Certain concrete examples support this interpretation and apply. If there is one coin on a table and another coin is added, there are then two coins on the table--or at least we perceive such to be the case through observation.	There are two coins on the table even if no one observes them (see line #11)
17			A skilled prestidigitationist can make all number of coins appear and disappear through manipulating our perception based on observation, and through smoke and mirrors do likewise with quite large objects--including large animals--as well.	Illusionists can create the illusion of coins (or animals) appearing and disappearing. If an illusionist puts a coin on a table and then adds another coin and we see three coins, we know that does not reflect reality. We know that 1+1=2 is a necessary truth. That’s how we know what we’ve seen is an illusion. It’s not real.
18			Note also that when we add one and one we don't necessarily get two	Yes we do. This is fallacy #1 – see line 10
19			They could combine into a larger "one," or partially combine with perhaps multiple fragments being left over, or one plus one could cause an explosion with nothing left but radically transformed fragments or vapor.	That is a different definition of addition.  Key Point The symbols  “1+1” do not represent the combining of substances, chemical reactions and physical reactions. There are different symbols for those situations, for example:  2Na + 2H2O → 2NaOH + H2 (see also line 67).
20				Key point The word “addition” has two different meanings: 1   1) The action of adding something to something else 2   2) The process of calculating the total of two or more amounts The necessary truth of 1+1=2 is addition according to definition #2. Definition #1 is a different process, for example, mixing different substances together. 1+1 does not represent the mixing of substances and any resulting chemical or physical reactions.
21	14 Feb 2017 at 1:50PM	JimC	A necessary truth cannot be false e.g. 1+1=2. Why? Because if you negate a necessary truth, you contradict reality, hence the negation is impossible. Your example illustrates this nicely: A man puts one coin in his hand, then another coin. He opens his hand, and there are three coins. There are two options here: The man has contradicted reality thereby negating a necessary truth, or it's an illusion. Turns out was an illusion using sleight of hand. In reality, he had a hidden coin, thereby demonstrating another fact: 1+1+1=3.
22			Another example from my own experience. A teacher presented a proof to the class I was in that 1=2 (shown here) This was a shocking moment because the teacher had contradicted reality and negated a necessary truth. Except of course, he hadn't, because the so-called proof contained a flaw (see if you can spot it). Turns out it's a famous puzzle but as children, we didn't know that. The so-called proof did not reflect reality, where 1=1, 2=2, 1+1=2 are all necessary truths.	True story!  It was an epiphany for me.
23	17 Feb 2017 at 1:43AM	Apologist	When you state that "necessary truths are necessary truths" that is a truism.	That is indeed a truism – but I didn’t say it.
24			My point again was that "necessary truths" can not necessarily be established in the real world.	They can.  This is a repeat of fallacy #2 (see line #11). A necessary truth is true in all possible worlds. Furthermore, they are not just established by experience, they are true even in the absence of experience
25			By the way, you ignored my specific examples of one plus one NOT equaling two because claiming one plus one must always equal two was itself false.	No I didn’t. I explained that the third coin was an illusion.  The examples of one plus one not equalling two were based on the wrong definition of “addition”. We know the illusionist is fooling us because nothing can negate the necessary truth of 1+1=2.
26			Combining one and another one of something in the real world does not necessarily produce two of the same kind, but their combination might yield something entirely different. Once you leave the abstract and enter the realm of "reality," you will always face these issues.	This is a repeat of fallacy #6. See line #20.
27	17 Feb 2017 at 9:06AM	JimC	I didn't state that "necessary truths are necessary truths" but if I had said that, you're right, that would have been a truism. The point is that necessary truths can be established, and 1+1=2 is perhaps the most obvious example of a necessary truth, because if you negate that, you negate reality. I explained this with regard to your stage magician example, and we can also use your latest example where two things can be combined to make something different. So let's assume we have two things: a glass of water and a spoonful of salt. If we combine them we no longer have two things, we have one thing (a glass of salty water). But the point is that one glass of water and one spoonful of salt equals two things. The fact that you've combined them afterwards is irrelevant. In order to create the salty water you needed two things: salt and water. If you need two things, that's one thing plus another thing.
28	20 Feb 2017 at 12:57AM	Apologist	Now you are interpreting your abstract truism to state something slightly different: that two things are needed to create one thing in cases where they are combined. What if one thing plus another thing led to a chemical reaction that resulted in any number of things--say, the detritus from an explosive reaction that yields different bits of altered fragments? Can you still state that one plus one still was responsible when such needed to take place in an atmosphere where oxygen was present? I can add as many variables as you like to demonstrate how one plus one yields a different result once it leaves the abstract realm of pure mathematics and is applied to the "real" world.	This is a repeat of fallacies #4 and #6.
29	20 Feb 2017 at 9:59AM	JimC	So to use your latest example: We have one thing and another thing which when mixed together, lead to a violent chemical reaction. So in your example we have two things because we have one thing plus another thing. Let's assume we have a spoonful of sodium and a beaker of water. So the question is, how many things do we need to create that reaction? And the answer is we need two things: Sodium and water. One thing plus another thing equals two things. 1+1=2.
30			If I understand you correctly, you're trying to say that in your example, 1+1=52 because 1 spoon of sodium and 1 beaker of water can result in sodium hydroxide, hydrogen, and 50 pieces of broken glass.
31			I'm wondering if the confusion here is your not understanding what the plus sign "+" means. It's the symbol for addition, and addition means finding a total number of things. It does not represent the resulting quantities in a chemical reaction.
32			Let's build on the concept of 1+1=2 and see how we can count larger quantities. So for example, if you want to bake a sponge cake you need five ingredients: Flour Butter Sugar Eggs Baking Powder How do we know how many ingredients? We use addition: 1+1+1+1+1 = 5 ingredients.  But, you may ask, how many eggs? Well, for the size of cake I have in mind, we need four eggs. That's an egg, and another egg, and another egg and another egg. Which is four eggs. 1+1+1+1 = 4
33			Before we start cooking we put all the things we need on a table. We have a bag of flour, a pack of butter, a bag of sugar, 4 eggs, a sachet of baking powder, a bowl, a whisk and a cake tin. How many things are on the table? The answer is eleven things:
34
35
36		Apologist	Let's not forget how we got off on this tangent. You stated: "A necessary truth cannot possibly be false e.g. 1+1=2. If you negate a necessary truth, you contradict "reality" hence the negation is impossible."	Correct
37			What I'm continuing to demonstrate is that such a "necessary truth" is only an abstraction and that "reality" is another matter entirely!	So far, all such demonstrations have been fallacious.
38			As the observation that "the whole is greater than the sum of its parts" suggests, abstractions do not necessarily retain their meaning and quality in "real world" situations. Likewise with defining a word in common usage per its chemical structure in its abstractly-defined "pure" state--a state that will never be manifest in "real world" situations. That's the point you keep missing--or ignoring!	?
39			Your cake example is all artificially-defined.	Eh? Artificially defined? It’s a real life example!
40			You are likely to mis-measure and/or spill a bit of the ingredients as you prepare the cake--and such ingredients were artificially-defined in the first place. As long as you define what is happening in an abstract sense, you are correct: you have A bag of flour and A bag of sugar, etc. in your example, although all ingredients would be adulterated in a practical sense and there is no standard measure for the volume of "an egg"--nor would the recipe or results ever be exactly duplicated.	None of this has anything to do with 1+1. So what if we “mis-measure”? The point of 1+1 is counting.  Maybe we don’t know the volume of an egg but we know how many eggs there are. We are counting the eggs, not measuring their volume. We can count how many ingredients we need.  And there was nothing abstract about the example.
41			My point, as always: an abstraction does not equal a "real life" scenario in a practical sense!	This is a repeat of fallcy #7 (see line 12)
42	24 Feb 2017 at 11:38AM	JimC	It is indeed possible that some ingredients will be spilled or wrongly measured while making the cake. But that doesn’t alter the fact that we needed the five specified ingredients to make the cake. Perhaps I was a bit hasty jumping to counting five things before resolving how to count two things. So let’s rewind and imagine that we are going to make an omelet using these eggs:
43			I hope you can see that we have an egg, and another egg. How many eggs is that? We use he fact that 1+1=2 so, 1 egg + 1 egg = 2 eggs. We have two eggs.  But those are contingent truths. 1+1=2 is a necessary truth. 1 egg plus 1 egg = 1 omelette is a contingent possibility, but it's not a necessary truth.
44			If you want to challenge the concept of necessary truth, I suggest you use a different approach, i.e. that obviously 1+1=2 because that’s how 2 is defined, therefore it’s a truism.
45			Now, you may argue that in reality, 1+1=1 because one egg and another egg makes one omelet.
46			But the plus symbol doesn't represent the process of cracking eggs into a bowl and whisking them together. It represents addition, which means finding a total number of things. In this case, the total number of eggs.
			You might argue that we could have used three eggs or one egg, you might say that no two eggs are identical and no two omelets are identical, you might argue that 1+1=3 because we could have made three small omelets. And so on.
47	27 Feb 2017 at 1:28AM	Apologist	You are beginning with the "real world" practical sense of one plus one yielding two of the same sort of object.	Doesn’t have to be the same sort of object.  See line 51.
48			I agree with this understanding of one like "thing" plus another like "thing" equaling two of those like "things," assuming those like things are stable enough not to produce volatility when being thusly combined,	Doesn’t have to be a “like thing”. And it doesn’t matter if they are volatile when combined. That is a repeat of fallacy #4 (see line 19)
49			and further recognizing this wouldn't be strictly accurate in a fundamental sense, where virtually everything from the eggs to the hands to the surrounding atmosphere to whatever else is present is to be understood as energy in motion in a vast interactive matrix.	We could indeed argue that an egg, or any object, is almost entirely empty space and consists of a swirling cloud of electrons which only give the illusion of being solid, but that’s not the point. 1+1=2 is a necessary truth when we are counting objects, regardless of what those objects are composed of.
50		JimC	1+1=2 is not limited to counting the same the of object. For example, here are two different things, a pot plant and sunglasses...
51			How do we know there are two things? Because 1+1=2 (one thing and another thing gives us two things). They don't have to be the same type of thing.
52			Here are two things which, to use your words "produce volatility when being thusly combined"…
53
54			How many things do we need to cause volatility when thusly combined? We need two things: A bottle of coke and a packet of mentos. We know it's two things because 1+1=2.
55			Note that the Plus sign and the Equals sign do not represent the combining of chemicals to create an explosion. They represent addition, which means finding a total number of things.	The second definition of addition - see line 20.
56			So again note that a necessary truth cannot be false e.g. 1+1=2. Why? Because if you negate a necessary truth, you contradict reality, hence the negation is impossible. Now of course, reality is complex and arguably unknowable, but the truth of 1+1=2 is part of reality. If I was to put two coins in the palm of your hand, and you looked down and saw three coins, you'd suspect some trickery, because you know that 1+1=2. Not 3.
57	3 Mar 2017 at 1:03AM	Apologist	The "result" is one "thing" and another "thing" being combined--both of which are basically inert in relation to each other--hence two separate "things" are the result of this combination. The transition from abstract "truth" to "reality" applies in this case.	It doesn’t matter whether they are inert or not. 1+1=2 does not represent the mixing together of different substances, inert or otherwise.
58			Your second example is false. The "equal" sign does not apply in this example.	The equals sign applies when we are counting. There are two objects: A packet of mentos and a bottle of coke. One object + another object = 2 objects. The “+” sign does not represent inserting the mentos into the coke bottle. The equals sign represents equality.
59			One thing and another thing are combined, but unlike your previous example, we do not then get "two" things but something "other"--in this case, a likely foam--so this is best translated as one plus one equals "something else."	This is a repeat of fallacy #6 (see line 20) and also note that 1+1=(something else) is a terminology that is never used, because it’s not true.
60	3 Mar 2017 at 10:55AM	JimC	Your statement that 1+1 represents two things being "combined" demonstrates your misunderstanding. 1+1=2 represents addition in order to find a total number of things. So Coke is one thing and Mentos are another thing. How many things do you need to create a Coke geyser? You need two things. How do we know it's two things? Because 1+1=2. But that doesn't describe what you refer to as "volatility when being thusly combined".
62			Perhaps it will help if we use notation to describe the chemical and physical reactions you have in mind. We've seen that 1+1=2 does not represent a physical reaction so below is a symbolic representation that does represent "volatility when being thusly combined"…
62				1+1=(something) does not represent this situation and is never used to represent it.
63			That picture represents a contingent truth rather than a necessary truth.
64			Now let's look at how to represent a chemical reaction. You may remember the explosive reaction between sodium and water from your schooldays and I hope you agree that is a good example of what you call "volatility when being thusly combined". To cause that reaction we need two chemicals: Sodium and water. That's one thing plus another thing, which is two things because 1+1=2.
65			However we've seen that 1+1=2 does not represent any kind of physical or chemical combination or reaction. We can represent the sodium and water chemical reaction in words... sodium and water produces sodium hydroxide and hydrogen
66			...and symbolically...
67			2Na + 2H2O → 2NaOH + H2	Note the use of “→” instead of “=”
68			This results in "volatility when thusly combined" because the reaction releases heat and flammable gas at the same time...	Video showing sodium exploding when added to water.
69			All of this science stuff is fun but it has nothing to do with God or religion so let's use a theological example - the concept of the Trinity. Christianity teaches that God consists of three persons: The Father, The Son and the Holy Spirit. Is that two persons? No because 1+1=2. It's three persons because 1+1+1=3. So if anyone asks you how many persons comprise the Trinity, you can confidently say "three" because you know it's one person and another and another.
70			However... this concept is akin to your "volatility when being thusly combined" concept because Christianity teaches that those three persons are distinct from one another in terms of their origin and relationship, but they are one in all else, co-equal, co-eternal and consubstantial, and each is God, whole and entire. So we see the fact of 1+1+1=3 doesn't help to describe that concept beyond counting the number of persons.	The concept of the Trinity can only be described in words or pictures. 1+1+1=3 does not describe that concept.
71			Just like the physical and chemical reactions described above, we need a different symbolism, and here it is…
72
73	7 Mar 2017 at 12:58AM	Apologist	No, Jim. "1+1" represents addition of one thing and another, of course--but even that is only half of this very basic equation. It's the "=2" where the issue is, since that isn't necessarily the result of adding one thing and another thing.	This is a repeat of fallacy #6 (see line 20)
74			We start with two things--but that doesn't necessarily mean that two things are the result of their being added together. Don't forget the "equals" part of the equation!	This is a repeat of fallacy #6 (see line 20) The “equals part of the equation” is what represents equality. I will have to try and explain how equations are balanced.  I’m reminded of the quote by Sam Harris:  “If someone doesn’t value logic, what logical argument could you provide to show the importance of logic?”
75			A necessary truth must remain true in ALL situations--and we have already seen that it doesn't.	A necessary truth does indeed remain true in all situations – and we have seen that it does.  This is fallacy #8.
76			The reaction equation is a fascinating matter to discuss indeed but irrelevant to the point at hand.	It’s completely relevant. It represents the situation that the Apologist has described. He has simply ignored a point that demolishes his argument.
77			If you refer to "1+1=2" as a NECESSARY truth, it is only a NECESSARY truth in the ABSTRACT--by DEFINITION! Even then I could refer to other ways of using such symbols--for example in binary, 1+1 would equal 10--and in advanced mathematics even in referencing a decimal base there are exceptions as well.	This is a repeat of fallacy #3 (see line 13). Also note that if using binary, this would be written 1 + 1 = 102 In order to indicate the result is binary. The default assumption is decimal.
78
79			The only reason for taking this matter to such a ridiculous extreme was to indicate a more basic truth: what a "necessary truth" is in the abstract--by symbolic definition--is not a necessary truth in "reality."	This is a repeat of fallacy #7 (see line 12)
80			What is "absolute" proof in the abstract--by symbolic definition--does not lead to conclusions that prove anything infallibly in concrete reality.	Nothing could be more concrete than the necessary truth of 1+1=2.
81			So again, the best we can hope for are reasoned conclusions based on reasonable faith that our perceptions and evidence that we reference are accurate. It is impossible to get beyond that faith basis when concluding ANYTHING when referencing "reality."	The necessary truth of 1+1=2 does not require faith. It doesn’t even require people!
82			Regarding the Holy Trinity - Agreed--and in this case you reference three entities which, in combination, are partially distinct and partially part of a common whole. This is an instance that can be symbolized 1+1+1=3, or again could be symbolized as 1+1+1=1. This would not apply to all combinations of 1+1+1.	It can’t be symbolised as 1+1+1=1 because that is not true.  The equals sign represents equality so if 1+1+1=2 then that could be rearranged to show that 1+1=1-1 which is nonsense.  The Concept of the Trinity can be symbolised graphically or in words, but not arithmetically, because it is not an example of values being counted.
83	7 Mar 2017 at 9:56PM	JimC	I think I see where your confusion is – it’s with the word “addition”. The word has two meanings and you are equivocating them (in the same way you equivocate different meanings of the word "faith" and so on). You are right to say, for example, that two chemicals can be added together to make a new compound. That’s the first definition of “addition” •    • The action or process of adding something to something else.  But addition has another meaning:  •    • The process of calculating the total of two or more numbers or amounts.	I should have made this clearer before now. See line 20.
84			1+1=2 represents the second definition. Mathematical notation doesn't make sense with regard to the first definition. That's why for the examples you provide, we need to use pictures...
85
86			...or words...  sodium + water → sodium hydroxide + hydrogen
87			...or different symbols... 2Na + 2H2O → 2NaOH + H2	Key Point When describing physical reactions, the equals sign “=” is not used because this is not the calculation of a total number of things. The arrow represents a process whereby different substances are produced by the reaction.
88			...but what we can't do is use 1+1=2 because that equation does not represent adding substances together, it represents the calculation of a total.
89			You also seem confused about the meaning of the equals sign. The "=" symbol is used in an equation to represent equality. In other words, (1+1) and (2) are equal to each other. The equation remains valid when reversed... 2=1+1 …because the expression “2” and the expression “1+1” have the same value.	Key Point The symbol “=” represents equality, and is a fulcrum upon which an equation is balanced, like a set of scales. This means 1+1=2 can be rearranged as long as the balance is maintained, for example: 1=2-1  …and this represents another necessary truth - If someone has two things and one is taken away, they have one thing left. But if two substances are mixed together, it doesn’t follow that the reaction is reversible. See also fallacy #4.
90			So to reiterate: 1+1=2 does not represent the action or process of adding something to something else, e.g. adding Mentos to Diet Coke, or sodium to water, or flour with milk and eggs, and so on. It represents a total.
91			Coincidentally, I’ve been babysitting my youngest grandchild all day (she’s 10 months old), and she has learned to stack plastic cups (and knock them down). Her cousins who are 9 and 6 joined us after school and I mentioned a funny man in America who thinks 1+1=1. The nine year old suggested I send you a pic of what his baby cousin was up to, so here it is…	This is all true by the way. I’m not making this up.
92
93			His question to you is this: How many cups can you see stacked on the book? (The answer is two by the way). Supplementary question: How many cups in the picture? (I will let you work that one out yourself but as a clue, they are each a different colour: one green, one pink and one yellow).
94			And again from a philosophical angle – note the difference between the necessary truth of 1+1=2 and the contingent truth of flour, eggs and milk making a pancake.
95			You are of course correct to point out that 1+1=10 in binary. I made an assumption that in everyday language, human beings use base 10. So for future reference, note that whenever I refer to numbers, I am using base 10 unless stated otherwise. That's why there are three divine persons in the trinity, not 11 (binary).
95a			THREAD SPLITS HERE  - GO TO LINE 205 FOR OTHER BRANCH
96		A student of philosophy	I think the original point The Apologist was making has been lost; that bringing concepts into a concrete world, or the "real" world, sometimes does not translate completely (see lines 10 to 16)	Sometimes, yes.
97			So, if you were to ask me "hey, what does 1 quart of milk plus 1 quart of water equal?" I would pipe up fairly quickly: 2 quarts. I'm using your definition of addition: (The process of calculating the total of two or more numbers or amounts.) and They represents addition, which means finding a total number of things. As you illustrated with your picture of a plant and sunglasses, they don’t necessarily have to be the same items.	If we are looking at two vessels, one containing water and one containing milk, then yes we have two containers, each containing a quart of liquid. We can count the containers. 1+1=2 Perhaps it’s natural to assume that if we then pour a quart of water into a large bucket followed by a quart of milk we will have 2 quarts of liquid in the bucket, but it’s not necessarily true. A quart is a unit of volume, and volumes vary according to many factors, such as density and temperature. Or maybe there’s a subtle chemical reaction between water and milk that changes the density. I don’t know. The point is that 1+1 does not represent pouring liquid into a bucket.  It represents counting. See line 14.
98			Yet there is this: https://plato.stanford.edu/entries/apriori/ (Please see 1. Examples that illustrate the difference between a priori and a posteriori (empirical) justification)	The Stanford Encyclopedia of Philosophy – my favourite resource for philosophy!  The link contains many helpful examples… https://plato.stanford.edu/entries/apriori/
99			a. 2 + 2 = 4. b. 2 quarts of any liquid added to 2 more quarts of any liquid = 4 quarts of liquid (9b) is false, for if you add two quarts of carbon tetrachloride to two quarts of water you will get less than four quarts of liquid because the molecules pack together in a way that diminishes the total volume. Still, someone not knowing of such examples might be justified in believing (9b).	This is a more extreme example of the milk and water mixture which illustrates the point that 1+1=2 does not represent the mixture of substances.  The Stanford Encyclopedia of Philosophy makes the point that 2+2=4 is true but it doesn’t represent a situation where chemicals are mixed together. See lines 14 and 19.
100			So, the "funny man in America who thinks 1+1=1" came up with examples that are valid in my opinion.	They are not valid examples for the reasons explained in the encyclopaedia… “The first member of the pair is supposed to be an example in which, if we are justified in believing the proposition, we are a priori justified in believing it, and the second member an example in which, if we are justified in believing the proposition, we are a posteriori (that is, empirically) justified in believing it.” 2+2=4 is a necessary truth hence it is justified a priori. But the result of mixing two liquids together cannot be justified a priori – it can only be confirmed empirically. We are also seeing fallacy #9 here (see line 87) because the equation is not balanced. If 1+1=1 then rearranging gives 1=0 which we know is not true.  So 1 + 1 ≠ 1
101			That's coming from a "funny woman in America" who only viewed the totality: 1 quart + 1 quart = 2 quarts.	It depends how the funny woman is using the plus symbol “+”. Is she counting or is she mixing liquids together? If she’s counting, the answer is 2 quarts. If she’s mixing, the total volume might be 2 quarts but not necessarily.
102			My answer to your grandson's supplementary question is 3. And please thank them for the very colorful and practical example.	That is the right answer.
103		JimC	As I said, the word "addition" has two different meanings.	See line 20
104			The arithmetical notation of "plus" and "equals" signs does not describe the combining of substances and chemical or physical redactions. It describes numerical values. So if you add two quarts of carbon tetrachloride to two quarts of water you may well get less than four quarts of liquid because of a chemical reaction. There is a special notation for that kind of process which uses an arrow instead of equals sign, or you can describe the process in words (as you have).	Also see line 67
105			But you can't describe the mixing of two substances using the arithmetical notation 2+2=4 because that describes values. If you want to do the carbon tetrachloride experiment you describe, you will need to acquire 2 quarts of each liquid which is 4 quarts. That's a fact because 2+2=4. If you subsequently mix them together, you can't describe that process with arithmetic notation. The notation 2+2=4 is not applicable to chemical or physical reactions.
106	9 Mar 2017	A student of philosophy	I agree the word "addition" has two different meanings.	Yay!
107			Chemical notation is a horse of a different color. And the equation stays in balance. If you start with 2H you end with 2H even after the chemical reaction.	Yes it is indeed a different type of horse– because it describes a different situation. It applies to the other meaning of “addition” – it doesn’t apply to the meaning used in 1+1=2. And yes chemical reaction equations are balanced – but that doesn’t make chemical reactions a necessary truth. They are a contingent truth.
108			But one of your points was this the different meanings of addition (see lines 83 and 84). Doesn't change my opinion that the examples were valid in translating from the abstract to the concrete.	This is a repeat of fallacy #6. The examples didn’t demonstrate a translation from abstract to concrete. They falsely compared two different phenomena. See line 20
109			So if you see 1+1=2, you need to consider in the concrete world what you are doing…	EXACTLY. If you see 1+1=2 you are counting from 1 to 2 in the concrete world.
110			…a total of things: 1 plastic cup on the book + 1 plastic cup on the book = 2 plastic cups on the book	YES
111			… or combining things: 2H + O --> H20	NO! Notice the absence of the equals sign. The student of philosophy was absolutely right to use the arrow symbol which represents a net forward reaction.  A chemical reaction is never represented as 1+1=2 because it’s not counting values and it’s not necessarily true. The water equation (when balanced) looks like this…  2H2 + O2 → 2H2O …but this is not a necessary truth because hydrogen and water don’t always combine to form water. That equation represents what happens when they do. But that’s very different to 1+1=2 which is a necessary truth.
112			I could be wrong, but I don't think the majority of people seeing 1+1=2 think to themselves: "Wait - that's mathematical notation, so I need to calculate the total, not add one thing to another thing".	I agree. People know intuitively what 1+1=2 means when they see it.  They know it’s true, and they intuitively know that 1+1=1 is not true.  No one ever uses the symbols “1+1” to describe the combining of substances.  Also, the link on line 98 explains this in terms of a priori and a posteriori
113	9 Mar 2017 at 11:56AM	JimC	If you refer to the link you provided, you will see what I mean:  9a. 2 + 2 = 4. 9b 2 quarts of any liquid added to 2 more quarts of any liquid = 4 quarts of liquid.  9a is a true proposition 9b is a false proposition.  https://plato.stanford.edu/entries/apriori/  Similarly for the other examples in that article.
114			In the concrete world, 1+1=2 represents a total number of things, it does not represent the combining or mixing of things. 1+1=2 does not represent pouring a quart of one liquid into a container with a quart of another liquid.  I think the majority of people understand what 1+1=2 means. Perhaps not everyone realises what happens if you combine chemicals, but nevertheless, 1+1=2 is not a notation that is used when combining chemicals.
115	10 Mar 2017 at 1:54PM	A student of philosophy	In referring back to the link I provided, I think it is important to include the information that follows after 9b was determined to be a false proposition. I've cited the site, as you have, so I won't again, but the article also says:  (9b) is false, for if you add two quarts of carbon tetrachloride to two quarts of water you will get less than four quarts of liquid because the molecules pack together in a way that diminishes the total volume. Still, someone not knowing of such examples might be justified in believing (9b). And in the second paragraph: Just as we can be empirically justified in believing a false proposition (e.g., 9b), we can also be a priori justified in believing a false proposition.	That is the point. 9(b) is false even if some people believe that it’s true.  We can refer back to the water and milk example on line 97. It’s natural to assume that a quart of water and a quart of milk makes two quarts of liquid, but it might not be true. It’s not a necessary truth. 1+1=2 is a necessary truth but doesn’t represent the mixing of substances. It’s how we count values.  1+1=2 is a necessary truth because it is independent of our experience.
116			I agree that 1+1=2 is not a notation that is used when combining chemicals. I think it's pertinent that the article did not say the proposition was false because you cannot pour one liquid into another; rather, that the total volume was diminished because of the way the molecules pack in the combination of the two.	The proposition was false because when you pour one liquid into another, we cause a chemical or physical reaction. We have to measure the outcome. We are not counting values. Hence that situation is not represented by 1+1.
117			I also think it's important the words "empirically justified" were used in the second paragraph. So I think you are saying is that you can place a coin on the table, and then another coin on the table, to equal two coins. You then can place a quart of milk on the table, and a quart of water on the table, and you have two quarts. (using the 2nd definition you provided, mathematical notation).	Correct. But the 2nd definition doesn’t refer to mathematical notation. It’s a definition of addition in the sense of counting values. Mathematical notation is just language to express that truth.
118			Then, if you want to determine the total volume of the two quarts, you combine them (determining value by the first definition of addition you provided, and excluding items that are either physically or chemically reactive). Is this right?	That sounds over complicated. If you want to estimate the value of the total volume when two substances are mixed together, and you are not an expert in chemistry, you can add the two volumes together, but you won’t know for sure what the actual resulting volume is unless you measure the volume of the mixture after the mixture has been created. One doesn’t need to be an expert I anything to know that 1+1=2.
119	10 Mar 2017 at 3:45PM	JimC	The result of any situation where substances are added together does not qualify as a necessary truth. It is a contingent truth at best, for the reason explained (a priori) in the article you linked to.  "A priori justification is a type of epistemic justification that is, in some sense, independent of experience."  With regard to the example you give, if you place a quart of milk on the table, and a quart of water on the table, you have two quarts of liquid on the table because 1+1=2. We can count the items but even if we couldn't, it's a necessary truth that if you have a bottle of something and a bottle of something else then you have two bottles.  If you combine the water and milk into a single container, it is tempting to believe we have two quarts of liquid and you could reasonably predict that it will consist of two quarts. But whatever you believe or predict, whatever your justification, it's not necessarily true. The only way to be sure of the volume of the milk/water mixture is to measure it. 1+1=2 is a necessary truth but a quart of milk added to a quart of water might not have a volume of two quarts. It's an a posteriori situation. As the article says, we can be empirically justified in believing a false proposition. But, the only way to verify that proposition is to measure it empirically.  Note the symbols you used previously for your hydrogen and oxygen reaction. You didn't use an equals sign, you used an arrow -> and you were absolutely right to do so. That arrow represents produces rather than equals because an equation representing the mixing of substances does not represent equality in the way 1+1=2 does.
120	13 Mar 2017 at 1:17AM	Apologist	If you place a quart of milk on the table, and a quart of water on the table, you have two quarts of liquid on the table because the abstract happens to translate well into the concrete in this example.	1+1=2 translates perfectly when we are counting values, which is what it represents and which is what is happening in this example.
121			But remember what you just said above: "The result of any situation where substances are added together does not qualify as a necessary truth."	That’s correct. Adding substances together is not the same as counting values. Once you’ve counted your ingredients, you could mix them up in all sorts of ways. The necessary truth of 1+1=2 applies when you count them.  See line 20.
122			It's the "=" that is at issue here, and that "=" symbol appears in the equation you proffered as a "necessary" truth.	The ‘=” sign is not the issue. This is a repeat of fallacy #9 (see line 89). The symbol “=” represent equality and the equation is balanced like a set of scales, around the “=”.  That’s why the following are all necessary truths: 1+1=2 2=1+1 1=2-1 They are all balanced rearrangements of the same equation. That’s what the “=” allows us to do.
123			You say 1+1=2 but it is '10' in the case of  , or 'II' in the case of Roman numerals, and that's just while we're in the process of interpreting your given abstract offering of "1+1=2" and claiming that it is a "necessary" truth!	This is a repeat of fallacy #3. “2”, “10”, “two” and “II” are just some ways of representing “2”. There are many others. But they all represent the same thing. If we write 1+1=2 in Japanese or Arabic characters, it’s still a necessary truth because it’s true in all possible worlds which means it’s true in all possible languages.  See line 13
124			We can count bottles if bottles are the subject because they are (presumably) inert relative to each other and remain distinct entities when combined, with the result being two distinct entities. we've already noted that combining two volatile substances "equals" something else entirely!	This is a repeat of fallacy #4 (see line 19)
125			You asked us to take at face value--without elaboration or explanation or qualification or even defining the symbols themselves--that "1+1=2" is a NECESSARY truth!	That’s true. I took it for granted that the symbols I used for 1+1=2 would be well understood (and it seemed to be by the person I addressed it to).   It didn’t occur to me that someone would consider “1+1” as an appropriate way to describe combining substances.
126			Need I state it one more time? The point--the fundamental point--the ONLY relevant point in discussion here at this point--is that "absolute" and "necessary" truths only exist in the abstract! Sometimes those abstractions translate well and are relevant to real life circumstances-- sometimes they do not and are not.	This is a repeat of fallacy #7 (see line 12)
127			So--once again--referring to "necessary truths" that exist only in the realm of the abstract will never allow us to bridge the gap in our own interpretations of "reality" without our relying on a necessary faith component in the process. That is also true of "scientific" experiments on supposedly falsifiable matters and whatever "verification" processes are offered as evidence for conclusions drawn from such. Any claim that "faith" can be ruled out by following such processes only reflects the illusions of those proffering such assertions!	This is a repeat of fallacy #7 (see line 12) The comments regarding faith don’t seem relevant at all!
128	13 Mar 2017 at 9:27AM	JimC	The equals sign represents equality. The equation 1+1=2 represents the necessary truth. Note that "10" in binary and "II" in Roman numerals are all equivalent to "2" in base 10. They are all different symbols for the same necessary truth. It doesn't matter what language we use: "uno mas uno es igual a dos" is just as true as "one plus one equals two". 1+1=2 is a necessary truth even if there were no symbols, even if human beings never existed. It is "true in all possible worlds."
129			I think you've become further confused about the symbols thing because you've responded to what I've said without reading what a student of philosophy provided. To clarify, when A student of philosophy referred to a chemical reaction, she (rightly) used the arrow symbol rather than equals. That is the convention in chemistry. Here's a clue. I previously showed what happens when sodium is put in water and here is the chemical equation:
130			2Na + 2H2O → 2NaOH + H2
131			The arrow means "produces" or "yields". An equals sign is inappropriate when describing chemical or physical reactions. Can you guess why?
132			If you're still unsure about the concept, I would refer you to the link A student of philosophy provided which explains a priori propositions versus a posteriori propositions.
133	17 Mar 2017 at 12:51AM	Apologist	I note that you are now adding multiple qualifiers to your original statement--"1+1=2" as a "necessary" truth--and continue to ignore the matter of combining one thing and another thing does not necessarily result in two "things" at all when those two things are not distinct and/or are volatile in combination, nor when this formula does not even necessarily apply in higher mathematics.	This is a repeat of fallacy #4  - see line 19
134			All of this is not to say that abstractions aren't useful or that "1+1=2" is a generally sound and meaningful understanding of mathematics applied to "real" life in many--if not most-- practical circumstances.	This is a repeat of fallacy #7 – see line 12. Interestingly, the Apologist seems to have his own rules on when it’s appropriate to apply 1+1=2. I wonder how he determines when it’s appropriate and when it’s not?
135			This all brings us back to the original point: when attempting to apply abstract "absolutes" to "real life" circumstances/scenarios, things get murky. "Necessary" truths lose their necessity unless qualified to such an extent that they become meaningless.	This is a repeat of fallacy #7 – see line 12. Things only get murky when they are not applied properly. The necessary truth of 1+1=2 is perfectly clear to anyone who has learned how to count – that’s one of the most basic skills that we are taught even before we attend school.  Far from being meaningless, it is fundamentally meaningful.
136			The biggest revelation of failure when one relies on abstract constructs and principles, of course, eventually leads to the collapse of "scientific" abstractions--including the "laws" of physics and chemistry--to account for the creation of our universe per its principles, and for that matter for life, consciousness, and independent thought and creativity itself.	This is irrelevant. The laws of physics and chemistry are not necessary truths.
137	17 Mar 2017 at 10:27AM	JimC	As I said, 1+1=2 is a necessary truth even if there were no symbols, even if human beings never existed. It is "true in all possible worlds." Your so called "real life examples" are not examples of 1+1=2 which is why they are irrelevant. If the necessary truth of 1+1=2 didn't apply in real life (which is what you seem to be suggesting) then reality would be very different.  A question for you: If 1+1=2 was not a necessary truth, would our universe even be able to exist?  I've been looking for some online resources which will help explain the concept, and I think this is good: but please note it goes much further than 1+1=2 (it progresses to 2+2=4 and 4+4=8 for example). It also alludes to subtraction. So for example, the necessary truth of 1+1=2 can be rearranged to illustrate another necessary truth: 2-1=1 so for example, if you have two things, and I take one away, you will be left with one thing.  Note that your reference to the laws of physics and chemistry is a completely different topic. The laws of nature are not necessary truths. The laws of nature are defined by human beings and they have been revised and created many times and continue to be. From a philosophical angle, they are contingent truths, not necessary truths because the laws of nature may not be true in all possible worlds. However, some philosophers disagree. For example, there's an argument from Intelligent Design that says certain forces (such as the strong force and the electromagnetic force) are a necessary truth because they are "fine tuned" to a precise value and therefore God designed the universe. Creationists therefore deny the existence of other universes (or regions in our universe) where those values can be different.	Oh the number one is not my favourite number Cos one means only me and there’s no you. But just add one more you’ll see That makes two that’s you and me! Adding makes things fun when one and one are two. Adding, adding, adding Such a nifty thing to do  It’s such fun to add when one and one make two. Oh the number two is not my favourite number Though two is fine, I’d love to add some more. So let’s add another two  That’s the perfect thing to do Adding makes things fun when two and two are four. Adding, adding, adding It’s a thing that I adore It’s such fun to add when two and two make four. The number four is not my favourite number C’mon let’s add some more I just can’t wait. Cos right now we have four I say why not add four more? Adding makes things fun when four and four are eight. Adding, adding, adding Boy oh boy is adding great It’s such fun to add when four and four make eight. Now four and four are eight And that’s really kinda great. Eight and one is nine And that’s one more friend of mine. Now if we add one more You know what happens then?  Nine and one makes ten of us and so let’s sing again Adding, adding adding Boy oh boy is adding fun But now our little adding song is done Yes now our little adding song is done We’ve added up together song is done. See how great adding is Bert?
138	20 Mar 2017 at 1:24AM	Apologist	"1+1=2" is an arrangement of visible linear shapes requiring interpretation. Interpreting "1+1=2" as "one plus one equals two" gives those shapes limited meaning in the abstract.	This is a repeat of fallacy #7 – see line 12.  Not limited meaning. Fundamental meaning.
139			Applying that abstraction to real life circumstances requires further clarification as to when how and why that applies. Real life circumstances consist of endless variables and myriads of approaches to interpreting such. Applying an abstraction to all of those circumstances, variables and approaches requires further and further elaboration and noting of exceptions to the abstract principle. "Necessary truth"--which brooks no exceptions--gets lost in the process.	Hopefully I have provided that clarification, but I must admit it’s rare to meet an adult who needs the concept of 1+1=2 to be clarified.
			The universe is able to exist whether or not "1+1=2" applies in all circumstances. The universe needn't explain or account for its existence through your assertion on the matter, Jim--rather the other way around!	If the result of 1+1 was variable, there would be no universe. Even if there was, the Apologist wouldn’t know how old he was, what day it was, what time it was, or how many children he had. We wouldn’t be having this conversation because there’d be no computers.  1+1=2 is true in all possible worlds.
140			No Sesame Street or pre-school concept applies to my reasoned response, Jim-- but I completely understand how your mind set is locked that way!	Sesame Street and pre-school concepts are what the Apologist has failed to grasp.  They are vital concepts – that’s why they are taught in pre-school.
141			Necessary truths brook no exception, Jim--if what we learn from contingent truths demonstrate otherwise, then necessary truths aren't necessary truths!	It’s true that a necessary truth brooks no exception. Contingent truths are not necessary truths (there are several types of truth). But contingent are not exceptions to necessary truths. They represent a different situation.
142			Who in the world is presenting an argument from the perspective of intelligent design here? Are you again proffering unsupported insinuations and suggestions and pretending that they have a rational basis?	The Apologist introduced the laws of physics on line 136.  Given the context of necessary truth and contingent truth, it seemed reasonable to me to examine those laws in that context and to consider if anyone considers the laws of physics to be necessary truth. The only example of that I can think of is intelligent design and the concept of fine tuning.
143	20 Mar 2017 at 1:30PM	JimC	Your introduction of the nature of language and symbols takes us in a different direction, but let's run with it. The necessary truth of 1+1=2 doesn't lie any "visible linear shapes" as you put it, be they numeric, English, Japanese, Spanish, Braille or whatever. It was always a necessary truth even before human beings existed, and it always will be. "True in all possible worlds".  Bonus question for you: What's the best way to illustrate 1+1=2 if not using symbols and text? Clue: How would teach 1+1=2 to a two year old child?  What human beings have been able to do, beginning (I think) with Isaac Newton, is to provide formal proofs that 1+1=2.  But again note: the necessary truth of 1+1=2 does not come from human beings. Let me give you a religious analogy.  From a theistic point of view:  a) The reality of God doesn't come from words or symbols on a page. b) The reality of God is independent of how any such statement is written or expressed  c) Any attempt to express the reality of God using any kind of written text or symbols is bound to fall short of describing the true nature of God  Do you disagree with any of those points?  You shouldn't dismiss what you call "pre-school concepts" because that's where we have to learn necessary truths such as 1+1=2. The importance of what we learn before we are 5 years old cannot be overstated. So much else is built on that and follows on from that. Imagine how your life would be if you could not count (and neither could your calculator or computer). Your life would be impossible.
144			And again regarding your point on laws of nature - note the difference between a necessary truth such as 1+1=2 and the laws of nature. The laws of nature are not necessary truths. They are defined by human beings and they have been revised and created many times and continue to be. They are contingent truths.  I think by far the best resource provided on this topic here came from A Student of Philosophy and so I provide it again...
145			On the other hand, some philosophers disagree that the laws of nature are contingent truth, and argue that they are necessary truths. For example, philosophers who advocate Intelligent Design argue that certain forces are a necessary truth because they are "fine tuned" to a precise value - the universe wouldn't exist if they were not true and therefore God designed the universe.
146	23 Mar 2017 at 12:42AM	Apologist	You didn't begin by stating that "one plus one equals two" is a necessary truth--you began by stating "1+1=2" is a necessary truth. That's the first error, because it relies on our assumption that we interpret "1+1=2" as "one plus one equals two." A trivial matter in and of itself, but part of my overall point that anything proffered as a "fundamental truth" needs to be deconstructed and examined from the start to see how--or if--it translates from the abstract to "reality" without further qualifications and definitions becoming necessary.	The first part of this paragraph is a repeat of fallacy #3 – see line 13. The second part is a repeat of fallacy #7 (see line 12)
			1+1=2 is not true in all possible worlds, Jim, because I've demonstrated otherwise. Adding one thing to another thing does not necessarily give you two "things." Adding one thing to another thing might yield an entirely different result. I've made this point over and over, and you are ignoring it.	This is a repeat of fallacy #8 – see line 75.
			With regard to teaching 1+1=2 to a two year old child, one could just use language without using symbols or writing systems at all--one need not even be literate to understand the concept--or for that matter one could silently place one inert thing next to another inert thing, and repeat as often and with as many "things" as necessary to impart the idea.	Language is not a great idea (just look at the confusion in the preceding posts) but silently placing things next to other things is much better. For example, wooden blocks are a great way to teach the necessary truth of 1+1=2 to infants. I think I remember being taught that way. They can see a thing and a thing. It can also demonstrate subtraction. However, I have used that approach here by means of graphical images, and it hasn’t worked.
			That might lead to a more fundamental grasp on "reality" than relying on symbols and abstractions because doing so--your case being a good example--might lead one to invest more "absolute certainty" in the symbols themselves and what they stand for in a practical sense than is really justifiable.	I have never claimed “absolute certainty in the symbols themselves” – this is a repeat of fallacy #3
147			It is a useful  fundamental concept with myriads of applications--but it isn't an "absolute truth" in all circumstances.	This is a repeat of fallacy #8 (see line 75)
148			Your conclusion on intelligent design and fine tuning is a non sequitur, as you very well know--not that it is the wrong conclusion, but that it requires further explanation.	If something requires further explanation, that doesn’t make it a non sequitur.  I’d be happy to provide further explanation if it’s needed.
149			Because you know this, you falsely state the issue as well because that isn't the only reasoning involved and that is not the way those who advocate intelligent design arrive at their conclusion. therefore, false representation followed by false reasoning is a straw man	Falsely state? I stated a fact - philosophers who advocate Intelligent Design argue that certain forces are a necessary truth because they are "fine tuned" to a precise value - the universe wouldn't exist if they were not true and therefore God designed the universe. Those philosophers are taking the “all possible worlds” one step further and saying there is only one possible world.  (And it’s obviously not a straw man).
150	23 Mar 2017 at 2:51PM	JimC	It’s true that I began by stating that 1+1=2 is a necessary truth. I made the assumption that you would know what those symbols meant but you are absolutely correct to say that any proposition must be clearly defined. I was hoping that had now been done, but I see you continue to choose the wrong meaning of the word “addition”. The word has two meanings as I said before, and your examples of chemical and physical reactions are not examples of 1+1 so they are irrelevant.
151			You gave the wrong answer to the bonus question. The best way to illustrate 1+1=2 to a two year old child is definitely not to use language. That’s probably the worst method (and if you look at this discussion you can see why!) The best way to demonstrate any necessary truth is by means of reality. For example, we can use small wooden blocks. Without using words or symbols one can experience that block and block is block block. And if you have block block, taking away a block leaves block. We can of course represent that symbolically as;
			1+1=2  2-1=1
152			... or we can describe it in words etc. but the important thing is that the symbols and words are not the necessary truth, they are simply a way of representing it. The necessary truth exists in the absence of words, symbols and indeed, human beings, because it is true in all possible worlds, and it would indeed be possible to have a world that does not include human beings.
153			Regarding your point that the “laws of physics and chemistry cannot account for the creation of our universe, life, consciousness”, etc. - you have to bear in mind that those laws are not necessary truths. They are contingent truths. Or are they? Some philosophers argue that they are necessary truths. For example, philosophers who advocate Intelligent Design argue that certain forces are a necessary truth because they are "fine tuned" to a precise value - the universe wouldn't exist if they were not true and therefore God designed the universe. I think your point is that there’s no such thing as a necessary truth, in which case I assume you disagree with the argument that the laws of nature are necessary truths (as I do).
154	27 Mar 2017 at 1:50AM	Apologist	My examples of chemical and physical reactions are not irrelevant at all, Jim. "One plus one" is also in need of elaboration and clarification. If "one" chemical component is added to "one" other chemical component, the result is not necessarily a "two" as I have amply demonstrated.	This is a repeat of fallacy #4 – see line 19
155			You now object and claim that there is a separate "meaning" of the word where your necessary truth still applies, even though it obviously doesn't apply in the "other" meaning for which I provided an example.	I made it clear there were different meanings some time ago – see line 83.  Of course the necessary truth of 1+1 doesn’t apply to the other meaning.  That’s the point.
156			All this leads to a more fundamental point: when we attempt to apply absolutist abstractions to "reality" they don't necessarily apply in the way in which they were presented, and actually the more variables that exist in "reality" the more and more qualifications, explanations and exceptions to the rule must be added to the original abstraction in order for it to retain any meaning or relevance.	This is a repeat of fallacy #7
157			All this leads to the most fundamental point: statements which are self-defined by our terminology as "necessary" truths tend to lose their "necessariniss" the more complex the situation one applies such in matters of "reality." "Necessary" in its abstract definition in human language--not necessarily  "necessary" as understood in those terms when applied to "reality."	This is a repeat of fallacy #8
158			My way of teaching 1+1=2 to children is superior because the child does not have to learn theoretical definitions that come with a claim that they "necessarily" apply to "reality"--s/he can merely witness "reality" and draw conclusions of how to conceptualize and describe such on their own, in a much more relevant and  open minded manner.	My suggestion of using wooden blocks or pictures does not require theoretical definitions. The necessary truth of 1+1=2 can be observed. Although I do wonder if we are both advocating the same method here i.e. to avoid any kind of language. Perhaps we are at cross-purposes?  I will provide some exercises which may help to clarify.
159	27 Mar 2017 at 1:15PM	JimC	I thought I had explained that "one plus one" does not represent adding chemical components together. That is a different meaning of the word "add". If you are struggling to understand the necessary truth of 1+1=2 then think of counting and imagine what would happen to reality counting from 1 to 2 wasn't a necessary truth. Learning to count is different to learning about chemical or physical reactions and you have to master the former before you can master the latter. The examples you are providing are contingent truths not necessary truths. For more detail, refer to the explanation of chemical and physical reactions earlier in the thread. Also I implore you to read the material A Student of Philosophy provided.
160			Your suggestion to use language to teach children how to count is definitely not superior - it couldn't be worse! That's because of the ambiguity of language which you yourself have highlighted the problems of. Your approach is further compounded by your logorrhoea which would baffle any child and most adults! So the best way to illustrate 1+1=2 (or any necessary truth) to a two year old child is by means of demonstrating reality itself without resorting to language at all. For example, we can use small wooden blocks. Without using words or symbols one can experience that block and block is block block. One can feel them if one is blind, one can see them if one is deaf. And furthermore, it is easy to demonstrate that if you have block block, taking away a block leaves block. So another necessary truth emerges which is 2-1=1 which I hope you can see is simply a rearrangement of 1+1=2. We can of course represent all of that symbolically and verbally as well, but that can come later.
161			Have a go at these exercises (just Set A for now) and see how you get on. I can provide the solutions.
162			Regarding your point that the “laws of physics and chemistry cannot account for the creation of our universe, life, consciousness”, etc. - I'm not sure why you raised that point in this thread, but anyway, you have to bear in mind that those laws are not necessary truths. They are contingent truths. They may not be true in all possible worlds. But is it that simple? Some philosophers argue that they are necessary truths. For example, philosophers who advocate Intelligent Design argue that certain forces are a necessary truth because they are "fine tuned" to a precise value - the universe wouldn't exist if they were not true and therefore God designed the universe. I think your point is that there’s no such thing as a necessary truth (correct me if I'm wrong). If that is your argument, it would be interesting to see how you would challenge the creationist argument.
163	31 Mar 2017 at 1:23AM	Apologist	Stop right there, Jim. You made the posit that "1+1=2 is a NECESSARY truth." Period! No explanations--no further "clarifications"--just a "necessary" truth, in and of itself! In the abstract that would be generally correct, although I could also demonstrate that there are exceptions to 1+1=2 even in the abstract structure of mathematics itself.	This is a repeat of fallacy #3 and fallacy #8.
164			Yet a single exception demolishes your "necessary" truth, and that has been more than provided. So back to the basic point: absolutes and "necessary" matters (where they actually exist) as defined in the abstract do not necessarily translate well when applied to "reality." Got it?	A single exception would negate the concept of necessary truth, but the apologist has not provided a single exception. All his examples are fallacious, specifically fallacies #4 #6 and #8
165			What part of silently demonstrating the result of combining one object with another would you define as "logorrhoea" Jim?	Silently demonstrating would be a good thing, and that was my point all along.  Hence my use of graphics during the course of this conversation.  But using language… nope.
166			I didn't say that there are no necessary truths, Jim--just that they may generally be beyond our grasp.	I wonder if he can give an example of a necessary truth?
167			"Necessary" truths for someone like you--who thinks in terms of rigid categorizations-- may have trouble grasping that concept, as already demonstrated in your assertion of "1+1=2" being a "necessary" truth in and of itself. Basically, you believe that the human constructs that have been devised within the limits of human language and understanding and bound by the limitations of the human condition have meaning and applicability beyond those constraints.	This is a repeat of fallacy #3
168			As for "creationists" arguing--in your view--on behalf of "fine tuning," I see those arguments as hoisting those who believe in Scientism on their own petard. They are using the arguments of scientific naturalists and their subscription to the philosophical assumptions of logical positivism to demonstrate how the universe could not have come about per their assumptions. Also, whether you admit it or not (which you won't), your assertion that god's existence is "unlikely" ultimately rests on those same deconstructed and discredited assumptions--and that is what makes your desperate ploys to avoid admitting such to be such a fascinating thing to  witness!	None of this addresses the point regarding necessary truth of the laws of physics according to Creationism and Fine Tuning.
169	31 Mar 2017 at 1:03PM	JimC	It's true that I assumed that the necessary truth of 1+1=2 didn’t need an explanation, but I hope you agree I have subsequently provided you with an explanation and many, many examples. Also note  the examples and source material provided by A Student of Philosohy and the differences between a priori, a posteriori, necessary truth, contingent truth, the analytic and the synthetic and so on.
170			I wonder if you're now confusing demonstrating with proof. Note that demonstrating 1+1=2 using two objects is very different to proving 1+1=2. Let me know if you want to see the formal proof but in the meantime note another basic philosophical principle: We cannot get necessity from experience. 1+1=2 is a necessary truth because it is independent of any experience. It is a necessary truth even if there is no life existing to experience it. Hence it is true in all possible worlds.
171			Later in your post you seem to suggest that you agree there is such a thing as necessary truth. If you don't accept 1+1=2 is a necessary truth, then can you give an example of what you do consider to be a necessary truth? As a prompt, here are two more necessary truths. Tell me what you think...  a) 17 is a prime number. b) If Greg is a bachelor, he is unmarried.
172	3 Apr 2017 at 12:39AM	Apologist	When you refer to the examples and source material provided by A Student of Philosophy and the differences between a priori, a posteriori, necessary truth, contingent truth, the analytic and the synthetic and so on, you are parroting a matter that has been deconstructed and responded to multiple times. If you have nothing to offer in response to such, I accept your tacit concession to my perspective on such matters.	LOL
173			Here's more food for thought on the matter:  https://www.quora.com/When-does-one-plus-one-not-equal-two-1	This is pretty good and illustrates what I’ve said with regard to the use of symbols on lines 31, 49, 128 etc. Symbols are of no use if they are not defined. So for the necessary truth of 1+1=2 we have to define what "1" means, what "+" means what "2" means and what "=" means. And that's exactly what Russell’s formal proof does (see line 15).
174			It’s true that 17 is a prime number in the abstract, by definition.	This is a variation of fallacy #1. The number 17 is not a prime number by definition; it is a prime number because it fits the definition of a prime number.
175			Note that it is consistent with the definition of a prime number.	Yes! That’s more like it.
176			"1+1=2" is not a definition, but a formula.	1+1=2 is not a formula, it is an equation. This is because of the equals sign and because there are no variables. A formula has more than one variable – it is more like a recipe. For example, Coca Cola have a secret formula.  If we stick to mathematical examples… x = 2y - 1 is a formula (two variables, x and ) a2 + b2 = c2 is a formula (three variables, a, b and c) x2 – 16 = 0 is an equation  And again note the point on line #89 – the equals sign is like a pivot about which the equation balances. 1+1=2 therefore 1=2-1. And so on.
177			1+1=2 is a claim that one added to one equals two	It’s not a claim. It’s a necessary truth.
			As for the statement “If Greg is a bachelor, he is unmarried” - Same point as above.	?
178	3 Apr 2017 at 9:59AM	JimC	The link you've provided illustrates my point: language and symbols are of no use if they are not defined. So for the necessary truth of 1+1=2 we have to define what "1" means, what "+" means what "2" means and what "=" means. And that's exactly what the formal proof does (in fact most of the formal proof consists of those definitions). As I said before, if you want to see the formal proof, let me know. But the important point here is that the necessary truth of 1+1=2 is a necessary truth regardless of the language or symbols. Those are just a means of expressing a necessary truth.  I didn't quite follow your final point - are you saying "17 is prime" is a necessary truth?
179	6 Apr 2017 at 1:16AM	Apologist	No, Jim—the point that language and symbols are of no use if they are not defined was MY point!	LOL
180			You made a very simple claim:"1+1=2 is a NECESSARY truth!"	That’s true.
181			No it's not, on its own, except in the abstract.	It is a necessary truth on its own, in the abstract, in reality and in all possible worlds.
182			I don't have to take this conversation in the direction of having to explain to you the exceptions even in the purely abstract realm of mathematics--or rather, how the structural weaknesses of the human tool of mathematics allows for error, such as when attempting to divide by zero.	So far, the exceptions haven’t been exceptions. They’ve been examples of a different situation rather than 1+1. This is fallacy #8 again.  The reference to divide by zero harks back to another misunderstanding of mathematics the Apologist revealed a few years ago, where he claimed divide by zero was “a built in glitch” in mathematics!  This time he thinks divide by zero is a structural weakness. LOL
183			Most significantly, we know of exceptions in the "real" world. Adding one "thing" to another "thing" quite often can result in something other than two discreet "things."	This is a repeat of fallacy #4. See line 19.
184			You are lost in abstract theories and fail to note when they don't translate well to concrete "reality."	1+1=2 translates perfectly well into concrete reality. Life would be impossible if it didn’t.
185			The definition of a prime number is quite straightforward: it is a number not divisible by any other whole number other than one or itself.	Close.  To be strictly accurate, a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
186			It is a definition that only exists in the abstract, however, relevant only to the artificial construct of mathematics itself.	That’s not true. Prime numbers are extremely relevant in real life.
187			It is not a formula which makes a claim--such as "one thing plus another thing equals two things."	A prime number isn’t a formula, it’s a number. But there are formulas which generate prime numbers, such as… where n+1 is prime if and only if n!mod(n+1)=n.  Note that “one thing plus another thing equals two things is not a formula – it’s an equation.”
188	6 Apr 2017 at 9:01AM	An Australian	The number "1" would fit that definition but it is not regarded as a prime number	True. The definition provided by the Apologist wasn’t the full definition.
189	10 Apr 2017 at 11:50PM	Apologist	Yes, it's all about the way abstract concepts happen to be defined for abstract purposes--again a matter that may or may not translate well into "real life" situations and purposes.	That’s his way of saying he got the definition wrong. LOL
190	6 Apr 2017 at 11:19AM	JimC	I was hoping you were now up to speed with the definitions of "1" "+" "2" and "=" but your comment that "adding one thing to another thing quite often can result in something other than two discreet things" suggests that you don't. Your comment about dividing by zero illustrates a deeper issue with your understanding of mathematics, which is disappointing because I've addressed that before, albeit a couple of years ago. Here's a reminder
191			Your comments regarding prime number suggests you don't appreciate how mathematics models reality. Imagine you had 17 things and you wanted to distribute them equally to people, yet keep the things whole. What are your options? If you don't know what I mean imagine you had 8 things and you wanted to distribute them equally. Your options would be to give them all to one person, or one thing to 8 people, or 2 things to 4 people, or 4 things to 2 people. So... if you had 17 things your options are...? For bonus points, can you think of other practical applications of prime numbers?	Should I mention the application of prime numbers in cryptography? Nah.
192			As a footnote, I again plead with you to refer to the source material provided originally regarding the nature of truth.
193	10 Apr 2017 at 11:51PM	Apologist	Your reference to definitions is just you parroting a matter that has already been deconstructed and responded to. If you have nothing further to offer, I accept your tacit concession to my perspective on the matter.	LOL
194			As for the practical applications of prime numbers, same point as above. I never claimed that mathematics has no useful applications, much less that it isn't reliable in a vast number of such--under specific circumstances.	The point being avoided here is the Apologist’s false assertion that necessary truth only exists as an abstract concept, not in reality.  This is fallacy #7.
195			The issue, again, has to do with FUNDAMENTAL TRUTH(S)--which brook NO EXCEPTIONS!	It’s not an issue. A necessary truth is true in all possible worlds.
196			The next point following that observation is that "fundamental" truths--as defined in the abstract--can quickly get "messy" when applied to real-life situations, requiring further and further nuanced explanations to apply to the situation at hand for whatever purpose is relevant to its application.	It became messy when the Apologist introduced “real life situations” that were not examples of 1+1. And it became messier as he tried to justify his false analogy. This is a repeat of fallacy #4.
197			That's it, and as far as I can see it's the only relevance to the subject at hand for religious discussion purposes. If you believe that what you are stating above regarding mathematics is relevant in any other way to purposes under discussion here, then clarify that matter and we'll take it from there.	The Apologist seems to have forgotten that he started this entire conversation when he jumped in after I answered a question for someone else (see lines 1 to 9). I have tried to introduce a religious angle (see lines 69-72, 137, 143, 145, 153, 162, etc.) but the Apologist wasn’t interested.
198			I won’t refer to the source material provided originally regarding the nature of truth without your clarification of the points you are claiming are relevant to the subject at hand, Jim. State such clearly, along with what your reasoning on the matter, and we can take the discussion from there.	LOL
199	11 Apr 2017 at 10:57AM	JimC	If you read the thread from the top you can see things only get messy when you misapply the concepts so that they don't reflect real life situations or when you use the wrong definitions.
200			But on a wider point - are you saying there's no such thing as a necessary truth? Again - look at the philosophy sources provided by A Student of Philosophy and myself towards the start of the thread.
201	14 Apr 2017 at 1:02AM	Apologist	Rather the opposite, Jim--I'm the one providing "real life" examples and noting how your abstract concepts don't necessarily apply--remember?	This is a repeat of fallacy #8 (see line 75)
202			Of course "necessary truths" exist--they're just difficult to translate from abstractions to real life situations. Even the way we conceptualize them may be faulty, given that they are supposed to have applicability beyond our human limitations of language and reasoning.	Excellent. I will ask him for an example of a necessary truth. That will help.
203	14 Apr 2017 at 2:02PM	JimC	So can you give an example of a necessary truth?	Can’t wait to find out!
204			<NO RESPONSE>	DOH!
205			THIS BRANCH COMES FROM LINE 95a
206	10 Mar 2017 at 12:05AM	Apologist	Hold it right there, Jim,--you can't see the forest for the trees! Remember how this all started?	Yep! See line 1.
207			I refer you back yet again to your original quote:  "A necessary truth cannot possibly be false e.g. 1+1=2. If you negate a necessary truth, you contradict reality hence the negation is impossible."	Correct.
208			Now I gave you the benefit of the doubt in rendering "1+1=2" as "one plus one equals two," except where I pointed out the binary equation, where 1+1=10. Note that I also mentioned instances in higher math where this equation is also not a "necessary truth" even in a decimal system--happy to elaborate--but that would be irrelevant to the point.	Actually, when using binary, it would be written 1 + 1 = 102 The default number system which people use in day to day conversation, is decimal, so the subscript ”2” would be used to denote binary is being used. Perhaps the apologist thinks 10 in binary is “ten” but 10 in binary is actually 2. Or to use the correct notation, 2 = 102   In any case this is a repeat of fallacy #3 (see line 13)
209			The point is that you made an assertion which you claimed was a NECESSARY TRUTH. A NECESSARY truth would not brook a single exception.	Correct
210			In admitting two definitions to "addition" you have already demolished the basis of your assertion!	The fact that the Apologist bases his examples on the wrong definition demolishes his argument. See fallacy #4 on line 19
211			So once again, the basic point: "NECESSARY" truths expressed in precisely defined abstract terms don't necessarily translate from the abstract to "reality." Got it?	This is a repeat of fallacy #7 – see line 12
212	10 Mar 2017 at 7:47AM	JimC	Your reference to binary is confusing. 10 is the binary representation of two so 1+1=2 in decimal is equivalent to 1+1=10 in binary. They are both saying one plus one equals two. You're not suggesting that 10 in binary represents ten are you? Regardless of what symbols or language we use, 1+1=2 remains a necessary truth. (It's true in "every possible world" as the philosophers say). We could for example, use the Roman system where: I + I = II (that's not eleven by the way).
213	13 Mar 2017 at 1:13AM	Apologist	But that's not the way you put it. You wrote "1+1=2," and tried to pass it off as a "necessary truth" and you are still doing so!	I didn’t try to pass it off as a necessary truth. It is a necessary truth (see line 8)
214			I provided the interpretation "one plus one equals two," remember? A small difference, but one which yet again demonstrates how translation from abstract to concrete can go awry--even on the symbolic level.	That’s not an interpretation. That’s the same thing. There’s no difference.   This is a repeat of fallacy #3 (see line 13)
215	13 Mar 2017 at 9:08AM	JimC	If you prefer to state 1+1=2 in English: "one plus one equals two" - that's fine with me.
216	7 Mar 2017 at 1:10AM	Apologist	Already addressed in my response in the branch of this thread above.	?