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.

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.

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

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.

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.

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.

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.

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."

Commentaries on the Perihermenias

A new set of pages in the Logic Museum (index here) consisting of Boethius' translation (from Greek to Latin) of Aristotle's 'On Interpretation', and three commentaries on them: Boethius' own, Abelard's and Aquinas'. The commentaries are both excellent introductions in their own right to Aristotle's work, and a useful insight into the medieval conception of logic.

Endorsement

Wow, great page [Logic Museum]. I'm a philosophy student and have had a long and abiding interest in the medieval period and especially in the history of logic. As you say this history is severely misrepresented to the average student which I gradually became aware of as an undergraduate by reading outside class from various medieval histories and journals on the era. Thanks so much for your site.

David

[Any time - Ocham]

Azzouni and equivocation

There is a very fine argument in Ockham's Summa Logicae book II, chapter 4. He is objecting to the claim that the verb 'to be' is ambiguous in certain arguments. But this is completely irrational, he says " for it amounts to destroying every argument form. For whenever it pleases me, I will say that 'to be' is equivocal in the premisses, and I will ascribe at will a fallacy of equivocation to every syllogism".

Absolutely right. The verb 'is' is implicit in every proposition. If this verb is ambiguous, we can disprove any argument whatever at will, by appealing to this ambiguity or equivocation. But that is irrational, and amounts to destroying all logic. For logic is about the form of arguments, and not about what we can 'ascribe at will'. If we can challenge the validity of any argument 'at will', you destroy all logic.

This claim that Ockham objects to is precisely the claim that Jody Azzouni appears to be making when he argues against the 'triviality thesis', which is the thesis that the existential quantifier just means 'there is', and 'there is' just carries ontological commitment. Azzouni argues that the triviality thesis is wrong since there are assertions of the form 'there are Fs' that do not always carry ontological commitment.

If Azzouni is correct, it really does amount to destroying all logic. I have already argued this in my objection to William Craig's claim that there is no contradiction in 'some x's are numbers and no numbers are created' and 'all x's are created by God', by reason of equivocation on the existential quantifier. If an argument as basic as this is invalid, all argument is invalid.

Here are two more arguments for this.

1. Meinongians say there are fictional entities. Nominalists say 'there aren't'. Regardless of what is the correct position, this disagreement could not take place at all unless both sides were agreed on the meaning of 'there are' and 'there aren't'. When the nominalist says that there aren't any fictional entities, he is denying exactly what the Meinongian asserts when she says that there are such things. The expression 'there are' is completely unambiguous in this argument, and has to be, in order that there can be an argument at all.

2. Azzouni might argue that (for example) 'there are hobbits in Tolkien' is true, but 'there are hobbits in Jane Austen' is false. But this is not an argument that 'there is' is equivocal. On the contrary, it means exactly the same in both cases. What is asserted is different, for in one case we say there are hobbits in Tolkien, in the other, that there are hobbits in Jane Austen. It is the qualifying 'in Austen' or 'in Tolkien' that changes the assertion. But in both cases 'there are' means the same. If it doesn't mean the same it amounts, as Ockham says, to the destruction of all logic.

Cicero in the Logic Museum

Another parallel translation in the Logic Museum: Cicero's commentary on Aristotle's Topics

The Toils of Metaphysics

Here are three quotations on the nature of philosophy (or 'metaphysics') that have something in common. They are all from the eighteenth century (Isaac Watts, known to members of the Anglican communion from the many hymns he wrote, David Hume and Thomas Reid). They all defend philosophy in some way while conceding its defects.
Watts criticises the 'subtlety' of scholastic metaphysics, and like Hobbes, disparages the tendency of philosophers to invent meaningless names.

Both Hume and Reid underscore their point with a staggering variety of metaphors. Both compare idle speculation to a net. Hume speaks of the 'intangling brambles' of religious fears and prejudices. Reid warns against being 'intangled in metaphysical toils'. Hume invokes Locke's comparison to the robber's den. Reid speaks of the 'bogs and quagmires' into which philosophy may entice us, and at the end compares Philosophy to a fair but wayward lady, whom he must trust until he finds 'infallible proofs of her infidelity'.

"In order to make due Enquiries into all these and many other Particulars which go toward the compleat and comprehensive Idea of any Being, the Science of Ontology is exceeding necessary. This was what was wont to be called the first part of Metaphysicks in the Peripatetick Schools. It treats of Being, its most general Nature, and of all its Affections and Relations. I confess the old popish Schoolmen have mingled a Number of useless Subtleties with this Science; they have exhausted their own Spirits, and the Spirits of their Readers in many laborious and intricate Trifles, and some of their writings have been fruitful of Names without Ideas, which hath done much Injury to the sacred study of Divinity. Upon this Account many of the Moderns have most unjustly abanded the whole Science at one, and thrown abundance of Contempt and Raillery upon the very name of Metaphysicks; but this Contempt and Censure is very unreasonable, for this Science separated from some Aristotelian fooleries and scholastic Subtleties is so necessary to a distinct Conception, solid Judgment, and just Reasoning on many subjects, that sometimes it is introduced as a Part of Logic, and not without Reason. And those who utterly despise and ridicule it, either betray their own Ignorance, or will be supposed to make the Wit and Banter a Refuge and Excuse for their own Laziness." [Isaac Watts - Logick, or the Right use of Reason, I. 6. ix]

"But this obscurity in the profound and abstract philosophy, is objected to, not only as painful and fatiguing, but as the inevitable source of uncertainty and error. Here indeed lies the justest and most plausible objection against a considerable part of metaphysics, that they are not properly a science; but arise either from the fruitless efforts of human vanity, which would penetrate into subjects utterly inaccessible to the understanding, or from the craft of popular superstitions, which, being unable to defend themselves on fair ground, raise these intangling brambles to cover and protect their weakness. Chased from the open country, these robbers fly into the forest, and lie in wait to break in upon every unguarded avenue of the mind, and overwhelm it with religious fears and prejudices. The stoutest antagonist, if he remit his watch a moment, is oppressed. And many, through cowardice and folly, open the gates to the enemies, and willingly receive them with reverence and submission, as their legal sovereigns.

"But is this a sufficient reason, why philosophers should desist from such researches, and leave superstition still in possession of her retreat? Is it not proper to draw an opposite conclusion, and perceive the necessity of carrying the war into the most secret recesses of the enemy? In vain do we hope, that men, from frequent disappointment, will at last abandon such airy sciences, and discover the proper province of human reason. For, besides, that many persons find too sensible an interest in perpetually recalling such topics; besides this, I say, the motive of blind despair can never reasonably have place in the sciences; since, however unsuccessful former attempts may have proved, there is still room to hope, that the industry, good fortune, or improved sagacity of succeeding generations may reach discoveries unknown to former ages. Each adventurous genius will still leap at the arduous prize, and find himself stimulated, rather than discouraged, by the failures of his predecessors; while he hopes that the glory of achieving so hard an adventure is reserved for him alone. The only method of freeing learning, at once, from these abstruse questions, is to enquire seriously into the nature of human understanding, and show, from an exact analysis of its powers and capacity, that it is by no means fitted for such remote and abstruse subjects. We must submit to this fatigue in order to live at ease ever after: and must cultivate true metaphysics with some care, in order to destroy the false and adulterate. Indolence, which, to some persons, affords a safeguard against this deceitful philosophy, is, with others, overbalanced by curiosity; and despair, which, at some moments, prevails, may give place afterwards to sanguine hopes and expectations. Accurate and just reasoning is the only catholic remedy, fitted for all persons and all dispositions; and is alone able to subvert that abstruse philosophy and metaphysical jargon, which being mixed up with popular superstition, renders it in a manner impenetrable to careless reasoners, and gives it the air of science and wisdom." [David Hume, An Inquiry concerning Human Understanding, section I].

"In the meantime, the unprosperous state of this part of philosophy [epistemology] hath produced an effect, somewhat discouraging indeed to any attempt of this nature, but an effect which might be expected, and which time only and better success can remedy. Sensible men, who never will be sceptics in matters of common life, are apt to treat with sovereign contempt everything that hath been said, or is to be said, upon this subject. It is metaphysic, they say: who minds it? Let scholastic sophisters entangle themselves in their own cobwebs; I am resolved to take my own existence, and the existence of other things, upon trust; and to believe that snow is cold, and honey sweet, whatever they may say to the contrary. He must either be a fool, or want to make a fool of me, that would reason me out of my reason and senses.

"I confess I know not what a sceptic can answer to this, nor by what good argument he can plead even for a hearing; for either his reason is sophistry, and so deserves contempt; or there is no truth in human faculties - and then why should we reason? If, therefore, a man find himself intangled in these metaphysical toils, and can find no other way to escape, let him bravely cut the knot which he cannot loose, curse metaphysic, and dissuade every man from meddling with it; for, if I have been led into the bogs and quagmires by following an ''ignis fatuus'', what can I do better than to warn others to beware of it? If philosophy contradicts herself, befools her votaries, and deprives them of every object worthy to be pursued or enjoyed, let her be sent back to the internal regions from which she must have had her original.

"But is it absolutely certain that this fair lady is of the party? Is it not possible she may have been misrepresented? Have not men of genius in former ages often made their own dreams to pass for her oracles? Ought she then to be condemned without any further hearing? This would be unreasonable. I have found her in all other matters an agreeable companion, a faithful counsellor, a friend to common sense, and to the happiness of mankind. This justly entitles her to my correspondence and confidence, till I find infallible proofs of her infidelity. " [Thomas Reid, An Inquiry into the Human Mind, works, introduction, ''ibidem'' p. 105]

Ontological dependence

My argument again. The following formally expressed statements are inconsistent.

1. (E x) number(x)
2. (x) number(x) implies not created(x)
3. (x) God created x

If (1) some x is a number, then (2) that x was not created. But (3) for all x, God created x, so God created that x. Contradiction.

Given this, it doesn't help to say that existentially quantified statements such as (1) don't really express or imply existence, or that (1) has no 'ontogical commitment'. This is irrelevant. Even if (1) is true of some x's to which we have no ontological commitment, it still logically follows that (3) is true of all x's, and so (presumably) is true of x's to which we are not ontologically committed. This is no way out.

Azzouni argues that our criterion for existence should be 'ontological independence'. If an object's properties depend wholly upon us (as in the case of fictional objects) then that entity does not exist. If our method for establishing the truth about an object is trivial (as in the case of mathematics) then it is ontologically dependent upon us. Accordingly, mathematical objects do not exist.

This does not help with the theological problem above. Even if (1) is true of ontologically dependent objects, there is still a contradiction, because there is nothing to prevent the universal quantifier ranging over such objects. If God created all things, then he made ontologically dependent things. But according to (2) some ontologically dependent things (numbers) are not created. Contradiction.

And Azzouni's suggestion creates another problem. I can meaningfully ask whether there are such things as 'ontologically dependent' objects. If yes, then why does Azzouni say that such objects do not exist? If not, in what sense is Azzouni offering any kind of solution at all? More on this later.

Azzouni on Ontological Commitment

Deflating Existential Consequence: A Case for Nominalism. Jody Azzouni, New York: Oxford University Press, 2004

I haven't got hold of a copy of this book yet, but the next best thing is a review. Three below.

Mark Colyvan
Thomas Hofweber
Joseph Melia

Did God create all things?

Vlastimil Vohanka has drawn my attention to an article by the American theologian William Lane Craig, which deserves a separate post. Craig, despite the fact he tends to include rather creepy-looking pictures of himself in his published work, is an admirable writer, who generally manages the trick that is essential to good philosophy, of being both clear and difficult at the same time. Here, he raises the question of whether numbers could have been created by God. He says that Christian theology requires us to say that everything that exists apart from God was created by God (John 1:3). But numbers, if they exist, are necessary beings. They thus would seem to exist independently of God. And (simplifying his point somewhat) the number 3 must have existed prior to God’s creating the number 3, which is impossible! "I remember the sense of panic that I felt in my breast when I first heard this objection raised at a philosophy conference in Milwaukee. It seemed to be an absolutely decisive refutation of theism. I didn’t see any way out."

First of all, I'm not sure this raises any genuinely theological issues. Craig should have read Augustine, who says (On the Literal Exposition of Genesis IV, c. 7) 'Six is a perfect number, not because God completed all things in six days, but rather, conversely, the reason God completed things in six days, was because that number is perfect, which would be perfect even if those things did not exist'. Moreover the second part of the verse from John which Craig quotes ("Through him all things were made; without him nothing was made that has been made") leaves open the possibility that there are some things which weren't made or created at all.

In any case, the solution that Craig comes up with does not do the trick. His solution is to propose some half-way house between being a thing of any sort whatever, and being a thing to which we are 'ontologically committed' (a favourite expression of his). Thus he agrees that we can 'quantify over' numbers, i.e. admit that there are such things as numbers, but not admit that numbers 'really exist', or that we are 'ontologically committed' to them.

There is a lot I could say about this, including how this is a good example of how pretensions to formal logic completely obscure something that should be quite simple. Here, I will briefly note that this manoeuvre does not resolve the difficulty at all. The first part of John's verse says nothing about real existence, or about 'ontological commitment'. It simply says 'God created all things'. Whether we are ontologically committed to numbers or not, whether they 'really exist' or not, Craig agrees that numbers are things, i.e. that some things (perhaps things that are fictional, or which don't really exist in any strong sense) are numbers. In which case, it logically follows that God created numbers.

Ironically, he says that "The existential quantifier simply serves to facilitate logical inferences." Quite. But then logical inference is what guarantees the move from 'God created all things, and some things are numbers' to 'God created numbers', and that is precisely the inference that creates his problem.

Note that Craig mentions a book by Jody Azzouni, Deflating Existential Consequence: A Case for Nominalism which I mean to read one day, and which will deserve a post or two when I have.

Part I of the Summa Theologiae

Questions 106-110, Questions 111-114, and Questions 115-119 of Part I of the Summa now available in the Logic Museum. This brings us to the end of the First Part of the work. Only Part II, I and II, and Part III to go. This is the only parallel Latin-English version on the Internet. Also the only complete one. There are a number of missing bits of the internet versions currently available.

The Frozen Present

I am translating Scotus' questions on Aristotle's On Interpretation (the Peryhermenias) and have reached the part where he discusses the problem of future contingents. Scotus' take on this is interesting and I will discuss it in a future post. Meanwhile I am reading around the subject. I dusted off Gilbert Ryle's Dilemmas, which was one of the first philosophy books I read, a discussion by Prior in a paper called 'It was to be', and older discussions by Boethius, Abelard. Today it is Aquinas. He writes (in his commentary on the Peryhermenias, I l 15. n2).

Omne quod est necesse est esse quando est, et omne quod non est necesse est non
esse quando non est. Et haec necessitas fundatur super hoc principium:
impossibile est simul esse et non esse: si enim aliquid est, impossibile est
illud simul non esse; ergo necesse est tunc illud esse. [my emphasis]

I.e. everything that is the case, is necessarily the case, when it is the case. This is because (he argues) it is impossible that the same thing should be the case, and not be the case at the same time. At first sight his argument seems absurd. It is sunny now. Might it not be sunny now? Of course. And this doesn't involve supposing a contradiction, because although 'it is sunny' is true now, to suppose that it were not sunny now involves supposing that 'it is sunny' is not true now. So no contradiction is involved. Aquinas seems to be confusing the possibility of its being p, but being possibly not-p, i.e.

possibly( p and possibly not-p)

which does not involve a contradiction, with the possibility of being p and not-p, i.e.

possibly( p and not-p)

which does involve a contradiction.

Or does he mean something else? Is he denying the sort of 'instantaneous counterfactual' that we take for granted in modern philosophy? In everyday life, we take it for granted that the realisation of any possibility takes time. Might it not be sunny? Only if the clouds pass in front of the sun. But when the clouds pass in front of the sun, it will not be now, and the qualification 'when it is sunny' no longer applies. Time must pass in order to realise the possibility. Perhaps this is the meaning of Aquinas qualification 'when it is p' (quando est). This would be consistent with Augustine's view that God cannot change the past, because would be to turn what was the case, into what wasn't the case. For the same reason, he cannot change the present. For if it took take time to do that, it would no longer be the present. If it did not, this would be turning what is the case, into what isn't. See The Frozen Past.