Wednesday, November 11, 2009

The meaning of Meinong

Bill Vallicella has an interesting defence of Meinong here. The statement

(1) There are items that have no being

is clearly self-contradictory. This is the reading attributed to Meinong by analytic philosophers (boo!) reading Meinong. But perhaps Meining meant this

(2) Some items have no being.

which (Bill argues) is not self-contradictory.

This argument entirely depends on the meaning of the word ‘being’. Bill’s claim that (1) is self-contradictory suggests he is reading it as expressing what ‘there are’ expresses. I.e. he would regard ‘there are blue buttercups’ as semantically equivalent to ‘blue buttercups have being’. Call this the ‘being/there are’ equivalence thesis. By contrast, his claim that (2) is not self-contradictory suggests he is reading ‘some’ statements as not expressing being. I.e. he would regard ‘some buttercups are blue’ as different both from ‘blue buttercups have being’ and ‘there are blue buttercups’. Call this the ‘some/there are’ non-equivalence thesis.

But what if I say

(3) There are no items that do not have being ?

Am I contradicting one who claims that some items have no being? Apparently not, for if according to Bill we are to read statements beginning ‘there are’ as expressive of ‘being’, then (3) does not deny (2) at all, indeed is perfectly consistent with it. I show this as follows. The statement

(4) ‘There are no X’s that are Y’ is equivalent to ‘any X that is Y does not have being’

follows from Bill's ‘being/there are’ equivalence implied above. I then substitute (4) into (3) to give

(5) Any item that does not have being, does not have being

Thus the statement that there are no items that fail to have being is apparently consistent with the statement that some items fail to have being. But that hardly seems correct. The natural reading of (3) is as the denial of (2), and hence its contradictoru. If one is true, the other is false.

Bill’s error (as I see it) is in denying the equivalence of ‘some’ and ‘there are’ statement. Is there really any logical difference between ‘there are blue buttercups’ and ‘some buttercups are blue’? Or between ‘there is a bridge crossing the river between Barnes and Hammersmith’ and ‘a bridge crosses the river between Barnes and Hammersmith’? I doubt it. But if we uphold ‘some/there are’ equivalence, and we uphold the ‘being/there are’ equivalence, we are led into contradiction again: if (1) is self-contradictory, (2) is.

Alternatively we could deny the ‘being/there are’ equivalence. But then we have the difficulty of what ‘being’ statements mean. We have no difficulty understanding ‘there are’ statements. You know what I mean when I say ‘there is a bridge crossing the river between Barnes and Hammersmith’. If you are stuck in Barnes and want to get to Chiswick via Hammersmith, it is very helpful to learn that statement is true, and you can act upon it accordingly. But ‘a bridge crossing the river between Barnes and Hammersmith has being’ is obscure, and not one a motorist can readily deal with. He either interprets it as meaning *there is* a bridge crossing the river. But that is no different from ‘some bridge crosses the river’ or ‘at least one bridge crosses the river’, and it follows a simili that (2) is self-contradictory. Or he regards it as altogether mysterious, and it follows that Meinong’s claim is mysterious and obscure. That is the dilemma.

Thursday, June 04, 2009

The Theory of Descriptions according to Wikipedia

So Peter Smith couldn't help correcting Wikipedia's entry about the Theory of Descriptions here. I am not sure if his point is entirely fair. (Certainly there are far worse things on Wikipedia philosophy and logic he could have tried to fix, e.g. this abomination).

It depends on what problem the Theory of Descriptions is intended to fix. The medieval Latin philosophers faced a similar problem and they arrived at a substantially similar solution to Russell, but they didn't have a distinction between 'a' and 'the' (which is the focal point of Peter's correction). So logicians such as Ockham were no wiser than Wikipedians?

The problem that Ockham (and the early Scotus, Robert Kilwardby and many others) were trying to fix was that 'Chimera is white' and 'Chimera is not white' are both false. But Aristotle says that de quolibet dicitur affirmatio vel negatio vera - either the affirmation of any sentence is true, or its negation is. Ockham argues that the second sentence is not really a negation of the first, for it can be unpacked as 'Chimera is something and it is not white'. The real negation, by contrast, is 'Chimera is not something or it is not white'. (Ockham like the other medievals was not worried here about uniqueness claims).
If the problem to be solved is not a 'non denoting description' but rather the one outlined above, namely that '[the] present King of France is bald' '[the] present King of France is not bald' are both false, then the original Wikipedia entry is not off the rails entirely.

Or perhaps he is objecting to something else, namely that unpacking 'chimera is white' into 'chimera is something-white' leads to an infinite regress. The medievals discussed this problem too. They saw that if 'Caesar est homo' = 'Caesar est ens homo', i.e. 'est' always unpacks into 'est ens', then this leads to an infinite regress, 'Caesar est ens homo' = 'Caesar est ens ens homo' and so on. Nicholas of Paris, Robert Bacon (not to be confused with Roger) discussed this in the early 13th century. But that is something else.

Sunday, March 01, 2009

Priscian's Institutiones Grammaticae

Priscian's Institutiones Grammaticae now available (Latin version only) in the Logic Museum annex. I had ignored Priscian before, thinking of him as a grammarian. Which he is, mostly, but there are interesting philosophical and logical insights in this enormous work. Such as that the present time is that of which part is past, part is future (Book 8, p. 414). Scotus uses this to explain how a sentence in the present tense (e.g. "Robert is just passing through the door") may be true even when the event it refers to may just be over.

Praesens tempus est cuius pars praeteriit, parsque futura est

Sunday, February 22, 2009

Osmund Lewry

A link here to an article in the new Logic Museum about Osmund Lewry, a Dominican who made some outstanding contributions to the history of logic in England, particularly in Oxford, in the thirteenth century. The article is part of the new Medievalists category which is designed to remedy the poor coverage of scholarly bibliography on the web.

I am trying to find a copy of Lewry's often-cited PhD thesis - "Robert Kilwardby's writings on the logica vetus studied with regard to their teaching and method". There are copies in the Bodleian and in the British Museum but previous experience suggests that this will be a painful and time-consuming process. The academic world still has to come to grips with the Internet and the concept of 'Open Access'.

I shall keep my regular readers amused with the story of my progress.

Saturday, February 07, 2009

Andrew of Cornwall

A link to my article about Andrew of Cornwall here in an attempt to discover why Google seems consistently to favour Wikipedia. I created a smaller version of the same article in Wikipedia (which I will not link to for obvious reasons), but Google sadly ignores it.

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.

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.

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?

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."