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.

According to the Bible

Here is a case where the position I have argued for seems to be uncontroversially true. Consider

(A) The earth was created around 6,000 years ago.
(B) According to the Bible, the earth was created around 6,000 years ago.

Fundamentalists will say that (A) is true, non-fundamentalists that it is false. But both agree, indeed everyone who is familiar with the Bible agrees, that (B) is true. According to the Bible, the earth was created at a certain point in human history.

In this case, no one is tempted to say that the Bible is about some parallel Biblical world, such that all the statements in the Bible are by their nature true of that parallel world. On the contrary, both fundamentalists and non-fundamentalists agree that the statements in the Bible are about our world, and that (B) is not a statement about some Bible-world, but about what the Bible says.

Given the existentially conservative explanation works in this case, what reason is there to suppose it should not work in the case of fiction?