Learning negation

I have a further question about this discussion and generally about any argument that we learn logical laws by experience, observation or induction or anything like that. Suppose it is argued that I learn that no x is white and not white by observing particular x's and noting of each one that it is either white, or not white. I then generalise this to 'no x is white and not white', and further generalise (by substituting other predicates like 'round', 'soft', 'large' etc) to 'no x is F and not F'.

I ask, how did I learn the meaning of the negation 'not'? Is this a sign whose meaning I understood correctly before all these observations? Or as part of the process of observation that led to the general conclusion? Surely not the first. Could anyone who thought it was possible that 'Socrates is white and Socrates is not white' was true, really understand the meaning of the word 'not'? It means negation, and negation means denial, and how could you assert and deny the same thing at the same time? So not the first.

But if the second, that means we learn the concept of negation by observation. Perhaps by your teachers pointing to different things and saying 'not white' when they were not white, and 'white' if the things were white. But that doesn't tell me whether the predicate 'not white' also applies to the white things. To do that, my teachers would have to say 'not not white' when pointing to the white things. And that still doesn't of itself tell me how to use the negation operator for I still haven't been taught that 'not not not white' applies to the not white things, and so on ad infinitum. To understand negation properly, I would have to understand its basic properties before all this took place. But if I understood that, the first point would apply, i.e. I would have to understand that 'x is white and x is not white' can never be true, on account of the meaning of the negation sign.

On the point attributed to Tim Crane, namely that one can perceive something 'as A and not-A' but rejects it through giving greater weight to the principle of contradiction, I'm not sure we can perceive something as A and not-A. Rather, it may seem that it is A and not A, but our understanding of the meaning of the word 'not' assures us that it is not the case that it is A and not A.

Objectivist epistemology

Researching the early history of Wikipedia, and in particular the effect of Ayn Rand's 'Objectivism' on the early development of Wikipedia, I came across this Usenet post from April 1994 by Jimmy Wales, one of the founders of Wikipedia.

Essentially, in Peikoff's presentation, the process goes like this: I perceive (directly, via observation) that "this man is not both white and nonwhite" (at the same time and in the same respect, of course). I see that this pail of water is not both wet and non-wet. At a later point in time, I abstract from the particulars that I've observed and note that "No being is both A and non-A." This holds no matter what being and what attribute is being considered. 

Peikoff is a leading exponent of 'Objectivism'.  Thoughts?  My initial question is how one can perceive, and 'directly, via observation' that this man is not both white and not white.  How exactly do we perceive this?

Contradictions do not exist

By chance, I found where ‘contradictions do not exist’ came from. See chapter seven (“The Exploiters and the Exploited”) of Ayn Rand’s Atlas Shrugged.

I'll give you a hint. Contradictions do not exist. Whenever you think that you are facing a contradiction, check your premises. You will find that one of them is wrong.

Taken literally, i.e. in the standard logical use, this is horribly wrong, even if the intended meaning is not. A ‘premiss’, in traditional logic, is one of a set of propositions that are used to support the conclusion of an argument. Being ‘wrong’ is not a term of traditional logic, but ‘false’ is clearly what is meant. It is certainly true that if two or more propositions involve or imply a contradiction, then at least one of them is false. But that does not imply, as Rand imagines, that contradictions do not exist. For a contradiction is simply defined as two premisses (or propositions) that contradict each other. If the premisses exist, so does the contradiction, just as a left and a right shoe make a pair.

What Rand probably meant was that contradictory premisses cannot be true. That is perfectly correct, and is the Principle of Contradiction itself. So she probably meant something quite simple and obvious, indeed a law of logic. Why she chose to put it that way is more difficult. Perhaps by ‘facing a contradiction’, she meant facing the state of affairs that is the truthmaker for a contradiction. And of course there could be no such truthmaker, even if there were truthmakers for other propositions (which I deny, of course).

How Objectivism informed Wikipedia

I have been reading Jeff Howes' Crowdsourcing and Andrew Lih's The Wikipedia Revolution. More on Lih's book at some point, but I was gripped immediately by this curious passage (p.36):

The three of them [i.e. Jimmy Wales, Larry Sanger, Tim Shell] were attracted to Objectivism for a reason.  The Objectivist stance is that there is a reality of objects and facts independent of the individual mind.  By extension, a body of knowledge could be assembled that was considered representative of this single reality. Put simply, objectivity relates to what is true, rather than ruling whether something is true or false. And their encyclopedia could detail what is true in the world without judgments. Sanger would put it this way: "Neutrality, we agreed, required that articles should not represent any one point of view on controversial subjects, but instead fairly represent all sides".

Considered as a whole, this makes very little sense.  Many philosophical systems, and many non-philosophical ones, such as basic common sense, consider that there is a reality of objects and facts independent of the individual mind.  It's not that Objectivism has a monopoly on this idea. It follows (given a few other assumptions, such as reliable sense perception) that a body of knowledge could be established or documented which was representative of external reality.  More common sense.

And then he writes "Put simply, objectivity relates to what is true, rather than ruling whether something is true or false."  This is at best incoherent, and at worst a non sequitur.  What is meant by 'relates to what is true'?  Does it mean that the assembled body of knowledge is true?  Well of course it must be, otherwise it wouldn't be true (first year philosophy students learn that 'knows that p' implies 'p').  And why 'without judgments'?  Isn't judgment required to assemble a 'body of knowlege'?  Finally, there is the statement quoted from Sanger, which I discussed earlier here, about not representing any one point of view.  Larry Sanger is a competent philosopher, and I'm sure that whatever he said to Lih when he was interviewed got pretty garbled and mixed up by the time it reached the printing presses.

Truthbearers and truthmakers

According to my commenter Anthony, "reality exists". I assume this is a reference to Ayn Rand's principle that 'existence exists'.  His idea seems to be that when we assert anything, what we assert must exist. Therefore we cannot assert anything false, for there is no state of affairs corresponding to a false statement.  If I utter 'Anthony is sitting', and Anthony is standing, there can be no state of affairs corresponding to my utterance. Therefore I cannot state anything.  The utterance exists, but what it tries to state does not.

There are many problems with this idea.  For every true statement, there is a corresponding negation.  Assume that Anthony is standing, and so the sentence 'Anthony is standing' states something true.  What about 'Anthony is not standing'?  It cannot be true, for it cannot be true that Anthony is both standing and not standing. But it cannot be false, for if this 'objectivist' account is true, there are no false statements.  Yet it seems to be a statement for all that.  If I can meaningfully assert that Anthony is standing, why can I not equally deny that?

What about beliefs?  Can I believe that Anthony is not standing, when he is standing?  Apparently not, for the object of my belief is a state of affairs (Anthony-not-standing) that has no existence, and according to Rand, only existence exists.  So I believe nothing.  Only when Anthony sits down can I have such a belief.

What about questions?  I ask 'is Anthony standing?'.  The person who says 'yes' has agreed to something.  The one who says 'no' has disagreed with the same thing, and so disagreed with something that exists.  So you can say 'no' to a true statement, yet you cannot make the corresponding negation.  You can say 'no' to 'is Anthony standing?', but you cannot say that Anthony is not standing.  That is quite puzzling.

The Stoic philosophers resolved the problem by distinguishing between utterance (phone) which may be mere noise, e.g. 'arxas grexurgh', articulate speech (lexis) which may be meaningless, e.g. 'green is happy', and discourse (logos) which is meaningful speech.  They also gave the name lekton to that which is signified by meaningful speech.  Lekton is derived from the Greek verb legein, which signifies 'to mean' as well as 'to say' (somewhat like that Latin dico).

Sextus Empiricus* gives the most complete account of their theory:

The Stoics say that three things are linked together, that which is signified, that which signifies, and the existing thing. That which signifies is the utterance, e.g. 'Dion'. What is signified is the thing indicated by the utterance and which we apprehend as subsisting with our thought, but the barbarians [i.e. non-Greek speaking] do not understand, although they hear the utterance. The existing thing is that which exists outside, e.g. Dion himself. Of these, two are corporeal, i.e. utterance and the existing thing, while one is incorporeal, i.e. what is signified, i.e. the lekton, which is true or false.

Thus we can distinguish between the state of affairs asserted by 'Anthony is standing', which some modern philosophers call the truthmaker, and the lekton, which some modern philosophers call the truthbearer.  The truthmaker exists in reality, given that Anthony is standing.  No truthmaker exists for 'Anthony is not standing'.  The truthbearer, by contrast, is an immaterial, nonphysical entity, the meaning of 'Anthony is standing'.  This has the value true.  A truthbearer also exists for 'Anthony is not standing', but that has the value false.

There is nothing in Rand's theory that precludes the existence of such non-physical truthbearers or lekta. So long as such non-physical things exist, they are a form of reality (albeit a non-physical form).  I don't know, of course, whether Rand's theory does preclude non-physical things.  But if it does, it faces the difficulty of explaining statements which are false.

*Adv. Math. viii 11, 12.

Does Existence exist?

Maverick mentions a wonderful piece by David Bentley Hart on Ayn Rand.  Peppered with stuff like this: "The essential oafishness of Rand’s view of reality ... what made her novels not just risibly clumsy, but truly shrill and hideous, was the exorbitantly trashy philosophy behind them ... Had she not mistaken herself for a deep thinker, she might have done well enough, producing books that filled out that vital niche between Forever Amber and Valley of the Dolls."  And this part is priceless:

And, really, what can one say about Objectivism? It isn’t so much a philosophy as what someone who has never actually encountered philosophy imagines a philosophy might look like: good hard axiomatic absolutes, a bluff attitude of intellectual superiority, lots of simple atomic premises supposedly immune to doubt, immense and inflexible conclusions, and plenty of assertions about what is “rational” or “objective” or “real.” Oh, and of course an imposing brand name ending with an “-ism.” Rand was so eerily ignorant of all the interesting problems of ontology, epistemology, or logic that she believed she could construct an irrefutable system around a collection of simple maxims like “existence is identity” and “consciousness is identification,” all gathered from the damp fenlands between vacuous tautology and catastrophic category error. She was simply unaware that there were any genuine philosophical problems that could not be summarily solved by flatly proclaiming that this is objectivity, this is rational, this is scientific, in the peremptory tones of an Obersturmführer drilling his commandoes.

It garnered 166 comments, which I did not have the stomach to read.  Maverick has an interesting analysis of her 'existence' claim in a post here.

Ayn Rand: lost in translation

The strange arguments continue in my comments box below and I continue to be mystified. One of the 'objectivists' there claimed that

1. If the premises [of an argument] are known to be false, are arbitrary, or from revelation, then even if the logic is valid, the proof [i.e. the conclusion] is indeed not a claim about reality.

To which I immediately objected

2. God can reveal to me the truth of a mathematical theorem, which is a claim about reality, therefore (1) is false.

This is a standard form of argument used in philosophy. Someone claims 'if p then q'. If you are able to give an example of 'p and not-q' that is obviously true, then you have refuted them. Since (1) is equivalent to the claim that no conclusion revealed by God is about reality, it is clearly refuted by (2).

This argument (which as I say is a standard type of argument you learn early on when you study philosophy) drew a number of objections. The first was

3. If you can suddenly prove a mathematical theorem, which can be validated to all fair rationals in the world, you are within your rights to say you got it from God if you wish.

This is not an objection to my argument. I am arguing that (1) above is false, because according to (1), it is impossible for the premisses of an argument to be true, and for the conclusion to be about reality, i.e. for the conclusion to be true. But the example (2) clearly demonstrates that it is possible for true premisses to be derived from revelation. It might be questioned whether I knew the conclusion to be true, because I was relying on revelation and not mathematical understanding. But a true proposition is unquestionably true, whether I know it or not. The next objection was

4. Your (hypothetical) revelation from God is no demonstration of its truth. If the content of the revelation, once examined in real world terms, is found to be true, then logic prevails from the latter reasoning, not from the former.

The argument here is that because the conclusion is not demonstrably true (because its truth is revealed), therefore it is not true. This is false again, and seems to rest on a confusion between truth and demonstrable truth. If a proposition is true, it is true, even if it is not demonstrably true. The next objection was

5. Even if metaphysically factual, the mathematical revelation is not epistemically true.

I don't understand what are meant by 'metaphysically factual' or 'epistemically true'. The latter probably means 'is not known to be true'. To be sure: if God reveals a true proposition to me, without my understanding why it is true, I probably cannot be said to know it. But that does not show it is not true.

When I suggested that 'objectivists' tend to make claims about truth and logic and metaphysics as though they were experts on the subject, which turn out to be nonsensical or silly, or ill-thought out, it was objected that this is because non-objectivists use concepts 'loosely'. This contradicts my impression that objectivists (or at least the ones here) use concepts loosely. It seems to me that they confuse the notions of truth and validity, of truth and knowledge of truth, of proofs and statements. These are all concepts used by logicians and which have a clear meaning that is carefully taught in elementary logic classes. I put it to the objectivists that it is not logicians who 'use concepts loosely'.

The supporters of Ayn Rand

I was going to follow up the previous post on Rand with a few comments but Triablogue beat me to it. There are also some excellent comments on the post made by Dominic Tennant in the course of a running argument with someone called John Donohue. Tennant leaves me with very little to say on Rand's 'existence exists' axiom. But fortunately it leads me to another thought that had been in the back of my mind, about supporters of Rand. I judge the worth of a writer by reading them. But also instructive to read what their supporters say. Supporters of Rand, in my experience, tend to be shrill, and philosophically and logically illiterate. Perhaps that tells us something about Rand?

Tennant points out the 'Existence exists' is incoherent - existence is commonly regarded as a second-order property. Not by everyone, I should point out, but certainly Frege's view that existence is a second-order predicate is accepted by nearly all those in mainstream analytic philosophy. Nor is Donohue's restatement, "whatever exists exists" in any way useful, because it is either merely tautological and doesn't tell us anything, or it is equally incoherent (for it dubiously assumes that existence is a first-order predicate).

Donohue objects "All truth discovered by Objectivism is through induction, and all induction is consistent with the constraint that all existents named/claimed in the induction must actually exist in objective reality". Tennant immediately objects that if the entire worldview is inductively inferred, there is no certainty in it, for induction is an informal fallacy. Donohue objects that induction is not a fallacy, and that its goal is to deploy reason with greater and greater precision until a given proposition/claim achieves a position of "true" and "certain" within the context of human knowledge. Tennant objects that he cannot be serious. Induction is an informal fallacy—it is a kind of logically invalid inference which may nonetheless yield true results. "In logic, a type of nonvalid inference or argument in which the premises provide some reason for believing that the conclusion is true. Typical forms of inductive argument include reasoning from a part to a whole, from the particular to the general, and from a sample to an entire population. Induction is traditionally contrasted with deduction. Many of the problems of inductive logic, including what is known as the problem of induction, have been treated in studies of the methodology of the natural sciences. (Britannica Concise Encyclopedia, 'induction'.)"

As Tennant correctly points out, what Donohue is describing here —"greater and greater precision"—is characterized by deduction. Induction works in the opposite direction: from greater precision and certainty towards less and less of the same. How can Donohue not be familiar with the problem of induction? How can he not be aware that absolute certainty is not guaranteed by merely inductive inference? Perhaps this is because Donohue has only read Rand, which does seem consistent with his ignorance of basic logical concepts. "Next time, take a Logic 101 course and read some introductory philosophy before you head out into the real world and try to pontificate on a blog published by people who have a clue and can call your bluff."

All very true, and remember that Donohue is one of the more articulate supporters of Rand. This began with problems at the Wikipedia article on Rand. Rand supporters turn up in large numbers to make sure that any 'objective' assessment of Rand's work is impossible, and they wear out the more logically-minded editors with this endless logically illiterate ranting. There is nothing in Wikipedia's policies that prevents this happening. Everything on Wikipedia is done by 'consensus', even if that is a consensus of idiots. This would not have mattered in the days when Wikipedia was a tiny website run by a dedicated band of enthusiasts. Now it really is used by everyone on the planet. If only it really were the sum of all human knowledge. Governments are now forcibly taking over banks. Why can't they forcibly take over Wikipedia?

Ayn Rand and Wikipedia

Was Ayn Rand a philosopher? That is the question now being taken to the important mediation committee of Wikipedia. There is currently a disagreement about whether the article about her should qualify her as a 'popular' or 'commercially successful' philosopher, or an 'amateur philosopher' (as Anthony Quinton did in his article on popular philosophy in the Oxford Companion to philosophy), or whether she is a philosopher without qualification.

This involves many difficulties, the main one being that Wikipedia has no concept of 'expert opinion'. We simply cannot ask Anthony Quinton or Ted Honderich or any of the philosophical establishment to weigh in on this important question. The question must be settled by whoever of the anonymous and mostly unqualified editors who turn up at the article talk page to thrash out a consensus. Which is not as bad as it sounds. Wikipedia has strict rules about 'reliable sources' and an entire manual devoted to citation. The rules are orientated towards mainstream academic consensus, and against 'original research' and using duff sources. This means you should use primary sources, however good, to support a claim. You should avoid using a blog or other self-published sources. Reliable and authoritative secondary sources are the preferred method of citation. Thus articles like Wittgenstein can be pretty good. The prose is often awkward and amateurish, and you have to put up the usual slavish political correctness of Wikipedia. But the results are not nearly as bad as you might have expected.

The difficulty is to assess writers like Rand, who have been so marginalised by the academic establishment that it is hard to find any reliable sources dealing with her, or her work. Who was Rand? That is the first question that non-American readers are likely to ask. I had not read any of her work until last week, and had only heard of her through Quinton's passing reference in the Oxford Companion. Well, read the article linked to above, which gives you a flavour of her work. There is a helpful lexicon on a pro-Rand website here, which contains samples of her writing. Otherwise there a few reliable sources which give a critical assessment of her work. Try these posts by the philosopher William Vallicella, who has a good explanation here of how Rand fails to understand Kant, and here where he points out some elementary - really elementary - logical errors in her work.

My view, based on a cursory reading of her actual writing, was that she lacked even a basic understanding of the essentials of the subject. I was particularly intrigued by her views on existence. But that is a personal view which, despite my qualifications, counts for nothing in Wikipedia. More about this later.

Meanwhile, let the excellent Brandon have the last word. He shows well how it is possible to combine sympathy with frankness (something the Wikipedia article should aim at, in my view). "Is she a bit of a hack when it comes to philosophy? Definitely. But I think what we see in Rand is someone of considerable native talent and ability whose reason never underwent the sort of discipline that would have made that talent genuinely shine."