Saturday, January 31, 2009

Snow in London

Alan Rhoda has been defending the idea that there must be some necessary connection between the present and the future in order for propositions about the future to be true or false. I restate his argument as follows. A true proposition depends on what exists - a 'state of affairs' - for its being true. The state of affairs that makes the proposition true at some particular time must exist also at the same time. Accordingly, it cannot be true now that there will be snow in London tomorrow, unless this truth 'supervenes upon present reality', i.e. there is some existing state of affairs which makes this proposition about the future true. Which is absurd. Why should snowing in London tomorrow be logically connected with any state of affairs existing today?

The mistake lies in his assumption that what makes a proposition true at some time must exist at that same time. Certainly there is a connection between truth and existence. This was recognised by the scholastic philosophers of language. Unumquodque sicut habet esse, ita et veritatem "As each thing is in respect of being, so it is in respect of truth", taken from Aristotle Metaphysics book 2 (993b 31). A proposition signifying that some state of affairs exists, is true or false depending on whether that state of affairs exists or not.

A corollary of this is what I shall call the Adequacy Principle: that the state of affairs signified to exist by the proposition can be no more (and no less) than what makes the proposition true. Otherwise, suppose a proposition signifies the existence of more than what is required to make it true, e.g. suppose that it signifies the existence of X and Y, but Y alone is sufficient to make it true. Then so long as Y exists, the proposition will be true, even if X does not exist, and even though the proposition signifies that X does exist. This is impossible, therefore a proposition can signify the existence of absolutely no more than what is sufficient to make it true. (A similar argument proves that a proposition can signify the existence of no less than what is necessary to make it true, but that is not relevant here).

From the Adequacy Principle it follows that a proposition in the future tense, signifying that some state of affairs Y will exist, depends for its truth on the future existence of Y, and nothing else, particularly nothing else in the present. The proposition 'It will snow in London' can be analysed as

* Snowing in London will be the case

which signifies that the future state of affairs 'snowing in London' will exist. It signifies no more than that, in particular, it does not signify that some state of affairs X exists now. Why should it? It may be that some present state of affairs (large cold front sweeping in from Siberia) will be the cause of the snow. But the proposition in the future tense has nothing to say about cold fronts.

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Thursday, January 22, 2009

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'.


Scotus on future contingency

I mentioned in this post last year that I was working on Scotus' discussion of the problem of future contingents, in his Questions on the Perihermenias, and I said I would discuss it in the future. Alan Rhoda's post on 'alethic openness' has finally got me round to doing so. Alan writes:

For a proposition to be true, what it represents as being the case must
correspond to reality, to what is the case. Likewise, for a proposition to be
true now, what it represents as being the case must correspond to present
reality, to what is the case now. [my emphasis]
Scotus discusses a claim very similar to this in Book I of the Questions, qq 7-9. He disputes the claim apparently made by Rhoda above, namely that the truth of a proposition about the future must correspond in some way to 'present reality'. He writes:

It must be understood that a proposition about the future can be understood to
signify something in the future in two ways. So that the proposition about the
future signifies it to be true now that something in the future will have to be
true [verum esse habebit] (for example, that ‘you will be white at a’ signifies
it now to be in reality so that at time a you will be white). Or it can be
understood that it signifies now that you will be white then: not that it
signifies that it is now such that then you ought to be white, but that it
signifies now that then you will be white. For to signify it to be [the case]
now that you will be white at a, signifies more than to signify that you will be
white at a.
It rather hangs upon what Rhoda means by 'true now'. Scotus argues for something like a redundancy theory of future truth. A proposition that says that S will be P so is (now) true iff it will be P, and false if it will not be P. If you mean by 'is now true' something like 'something exists now in reality that makes the proposition true' then Scotus would disagree (and so probably would I). If you mean that 'now' simply indicates the present tense of the 'is' in 'is true', then this is harmless and trivially true.

I think Scotus puts this very neatly, and we do have to take seriously his claim that "to signify it to be [the case] now that you will be white at a, signifies more than to signify that you will be white at a."

See also my discussion of rain tomorrow.

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Monday, January 19, 2009

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?

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Tuesday, January 13, 2009

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."

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