The Open Question question

The Maverick has argued (in effect) that the meaning of the word 'exist' is an open question. However, if the meaning of 'exist' is what the thin theorist stipulates it is, it would not be an open question. Therefore the meaning of 'exist' is not what the thin theorist stipulates it is.

Against. It is not an open question whether 'Pegasus does not exist' means the same thing as 'There is no such thing as Pegasus'. But the meaning of 'There is no such thing as Pegasus' is not an open question. Therefore the meaning of 'Pegasus does not exist' is not an open question. Our understanding of sentences such as 'there is such a thing as x' and 'there are such things as Fs' is entirely settled, and indeed is entirely the understanding advocated by the thin theorist.

The thin theorist can also explain why some philosophers think there is an open question. For the 'thick' theorist of existence is tempted to think that the following is a valid inference,

(A) Pegasus does not exist therefore there is something that does not exist

or at least that it is an open question as to whether it is a valid inference. However it is not an open question as to whether it is a valid inference. For the inference is equivalent to

(B) There is no such thing as Pegasus therefore there is something such that there is no such thing as it

which is obviously invalid (for the antecedent is true but the consequent is false). The 'thick' theorist is tempted by the grammar of 'Pegasus does not exist' into thinking that '- does not exist' is a predicate. However, the grammar of 'There is no such thing as Pegasus' does not tempt us into thinking that 'There is no such thing as –' is a predicate. Thus there is absolutely no question about the semantics of 'exist', although its grammar tempts some people into thinking that there is.

An interesting net

The discussion continues here as Maverick and others ask whether Meinong could have made an elementary mistake about logic. If ‘some things do not exist’ is a logical contradiction, how come he did not spot it?

I commented that all anti-metaphysical and positivistic theories need to explain how metaphysicians got it so wrong. It’s not like dispelling superstition, belief in which we can explain by mere ignorance or lack of education. Meinong was clever and obviously well-educated. Many clever and well-educated academics are still disciples of his theories. So the anti-metaphysical theory about the meaning of the verb ‘exist’, and generally any anti-metaphysical theory, needs to explain how clever people got an apparently simple matter so wrong.

Accordingly, Ockham puts it down to ignorance of true logic. This causes people to fall into many errors “by ignoring valid argument as though it were sophistry, and mistaking sophistry for valid argument”. Mill, following Ockham, says that metaphysics is a 'fertile field of delusion propagated by language', i.e. language has the habit of playing tricks on us, even clever people.

 Wittgenstein discusses the problem in many places. 'A clever man got caught in this net of language! So it must be an interesting net. ' ' Human beings are entangled all unknowing in the net of language.' ' In philosophy it's always a matter of the application of a series of utterly simple basic principles that any child knows, and the – enormous – difficulty is only one of applying these in the confusion our language generates.'

On donkeys and deformed thinking

I found the Wittgenstein quotation I was thinking of, which is in the Logic Museum here.

"Mathematical logic" has completely deformed the thinking of mathematicians and of philosophers, by setting up a superficial interpretation of the forms of our everyday language as an analysis of the structures of facts. Of course in this it has only continued to build on the Aristotelian logic.

It's what he says about Aristotelian logic which is the interesting one. There's a school of thought in the medievalist world according to which Aristotelian (scholastic) logic is somehow more faithful to ordinary language than modern mathematical logic. Wittgenstein would clearly have disagreed. I have also been looking at the donkey sophism in Worcester 13 again. The problem is that 'every man's donkey is running' has the form 'every A is B', where A = man's-donkey and B = running. According to Aristotelian logic 'every A is B' and 'every A is non-B' are contraries, they can't both be true at once. But clearly the ordinary language sentences 'every man's donkey is running' and 'every man's donkey is not running' can both be true at the same time, namely in the case where every man has two donkeys, one of which is running and the other of which isn't. It's not a problem for ordinary language at all. But it is a problem for the Aristotelian formalism of the sentence. In that formalism every sentence has two terms, joined by a copula and a quantifier attached to the subject term. It is a procrustean bed which fits our actual thinking very badly, in some cases.

I also noticed this other comment by Wittgenstein in the same place:

The curse of the invasion of mathematics by mathematical logic is that now any proposition can be represented in a mathematical symbolism, and this makes us feel obliged to understand it. Although of course this method of writing is nothing but the translation of vague ordinary prose.

What on earth does he mean by that?

'Anybody who knows ...'

One of the comments at the discussion raging at Vallicella's site illustrates perfectly the 'translation problem' that I mentioned in an earlier post. The problem is that any attempt at 'proving' or 'disproving' an ordinary language statement by using the well-defined proof procedure of the modern predicate calculus is highly vulnerable to the process of interpreting the ordinary language statement in the calculus. If the interpretation is not correct, then the proof, though perfectly valid, may be proving the wrong thing.

Suppose we want to prove the validity of an ordinary language consequence having the following form.

(*) If it was the case that A was identical with B then it is the case that A is identical with B

We can try to do this by translating the placeholders A and B (which substitute for grammatically singular OL terms) into the 'a' and 'b' of the predicate calculus (which substitute for logically singular terms), and translating the tensed statements of OL into the 'nec' or 'necessary' of predicate calculus, as follows:

(1) a=b (Assumption for conditional proof)
(2) a=b -> (Fa -> Fb)
(3) Nec(a=a)
(4) a=b -> (Nec(a=a) -> Nec(a=b)) (Substitution Instance of (2))
(5) Nec(a=a) -> Nec(a=b) (Modus Ponens, 1&4)
(6) Nec(a=b) (Modus Ponens, 3&5)
(7) a=b -> Nec(a=b) (Conditional Proof, 1-6)

The problem is that the 'proof', if understood as a proof of the ordinary language consequence, can't possibly be valid. Substitute 'the president of the US' for 'A' and 'John F. Kennedy' for 'B' to give

(*) If it was the case that the president of the US was identical with John F. Kennedy then it is the case the president of the US is identical with John F. Kennedy

But ex vero nunquam sequitur falsum: the false cannot follow from the true. Whenever the antecedent is true and the consequent false, consequentia non valet, the consequence is not valid. But the antecedent is true - the president of the US was (in September 1963) identical with John F. Kennedy, and the consequent false - the president of the US is (in September 2010) not identical with John F. Kennedy. So the consequence is not valid. If the formalised part of the proof is valid (which I am not denying), it follows that the translation of our ordinary language consequence into the formal consequence (i.e. (7) above) is wrong. But that is just the place we forgot to look.

At this point, the formalist will object that the translation "would be accepted by just about anybody who knows how to translate from ordinary language to formal logic". And that is another problem: a cultural problem, not a logical or philosophical one. We were taught as students the 'correct' way to translate awkward and messy ordinary language statements into the clean language of MPC. I too was taught this (using what was only 10 years old then, but has since become a classic text) quite some time ago. Having learnt this, we 'know' how to translate from ordinary language to formal logic. And, proud of this knowledge, we are now 'anybody who knows', and we can put down anyone who does not know.

What a formidable barrier to progress.

The Truth Operator

A modified version of my comment on Maverick Philosopher, about the distinction between truth as a predicate, which as Bill argues seems to commit us to realism about truthmakers, and truth as an operator, which does not appear to lead to such a commitment.

I subscribe to an 'operator' theory of truth. Each sentence has a syncategoric semantic component which corresponds to assertion. This component is always locked inside the main verb of the sentence. The operator 'that', which forms a that-clause from the sentence, strips out this assertoric component to convert the sentence into a categorematic expression signifying a possible object of thought, belief, assert, judgment etc. The operator 'it is true' replaces the assertoric component again to give us back the sentence (although the main verb is now the 'is' of 'it is true' rather than the verb of the operated-on sentence).

Thus the expression 'it is true that' is a sentence-operator that contains two operators, namely 'is true' and 'that'. The operator 'that' operates on sentences to produce a that-clause:a noun-phrase that names a content, a possible object of belief and judgment. It does this by removing the assertoric element from the sentence. The operator 'it is true' operates upon that-clauses, to form whole sentences. Such sentences have the same truth-conditions as the original sentence. Thus:

(1) Snow falls

is a sentence that asserts something, via the assertoric component embedded in the main verb 'falls'.

(2) that snow falls

is a that-clause naming a possible object of judgment or belief, such as in the sentence 'John believes that snow falls', which we parse as 'John / believes / that snow falls' to clarify its relational form 'X believes Y'. Note that in the belief sentence the verb 'falls' is no longer the main verb. The truth or falsity of 'John believes / that snow falls' no longer depends on whether snow does fall or not. Rather it depends on whether John believes this or not. Finally

(3) It is true that snow falls

Gets us back to a sentence with the same truth-conditions as (1), but with a different semantics. The main verb is now the 'is' of 'it is true', and the verb 'falls' is a subordinate verb. The assertoric component of (3) lies in the 'is' of 'it is true', the assertoric component of (1) lies in 'falls'. We can parse (3) as 'It is true / that / snow falls' to make it clear that there are two operators rather than one (Frege's mistake was to think there is only one). Or we can parse it as 'It is true that / snow falls' to make it clear that the combination of 'it is true' and 'that' gives us a further operator.

This may remove the temptation to suppose that there are such things as 'truthmakers'. (Well it won't, I imagine the supporters of truthmaking will continue in the deep error of their ways, but that is the way). The operator approach is of course consistent with a thoroughgoing nominalist program. I wonder whether, if ordinary language had the right synactic structure so that operators and existence-verbs and the like were clearly identified, the users of that language would be so committed to realist semantics. Could we even 'do' metaphysics in such a language?

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]

Being and Nothingness

Too good to keep off the internet. A companion piece to Dens of Robbers.

"The reflective nihilation, however, is pushed further than that of the pure for-itself as a simple self-consciousness. In self-consciousness, in fact, the two terms of the dyad 'reflected-reflecting' were so incapable of presenting themselves separately that the duality remained perpetually evanescent and each term while positing itself for the other became the other. But with reflection the case is different since the 'reflection-reflecting' which is reflected-on exists for a 'reflection-reflecting' which is reflective. Reflected-on and reflective, therefore, each tend toward independence, and the nothing which separates them tends to divide them more profoundly than the nothingness which the For-itself has to be separates the reflection from the reflecting. Yet neither the reflective not the reflected-on can secrete this separating nothingness, for in that case reflection would be an autonomous for-itself coming to direct itself on the reflected-on, which would be to suppose an external negation as the preliminary condition of an internal negation. There can be no reflection if it is not entirely a being, a being which has to be its own nothingness. (Sartre, Being and Nothingess, Pt III c1. , 4)

Hobbes and Ockham on ordinary language

There are two approaches to ordinary language philosophy, one represented by Hobbes, the other by Ockham. According to the first, there is no problem at all with ordinary language. The apparent difficulties are the result of meaningless technical language (in Hobbes' day, the Latin of the schoolmen), designed for the defence of what is really absurd and untrue. According to the second, the problem is ordinary language itself, which is systematically misleading. Thus, Ockham argues our propensity to believe every name is the name of something is the source of all philosophical error (Summa Logicae 1.51)

Wittgenstein represents both views. In his polemics against mathematical logic and set theory, to be found in his mathematical writings of the early 1930's and in the Remarks on the Foundation of Mathematics, he takes the Hobbesian line. '"Mathematical logic" has completely deformed the thinking of mathematicians and of philosophers, by setting up a superficial interpretation of the forms of our everyday language as an analysis of the structures of facts. Of course in this it has only continued to build on the Aristotelian logic'.

At other times, he takes an Ockhamist approach. 'A clever man got caught in this net of language! So it must be an interesting net. ' ' Human beings are entangled all unknowing in the net of language.' ' In philosophy it's always a matter of the application of a series of utterly simple basic principles that any child knows, and the – enormous – difficulty is only one of applying these in the confusion our language generates.'

See here for all the Wittgenstein quotes.

Dens of robbers

Here is a passage from Locke, in a similar spirit to Hobbes, and with the same ingredients. The gibberish of metaphysicians, contrasted with the solid good sense of the statesman, the businessman and the 'contemned mechanic'.

"For, notwithstanding these learned disputants, these all-knowing doctors, it was to the unscholastic statesman that the governments of the world owed their peace, defence, and liberties; and from the illiterate and contemned mechanic (a name of disgrace) that they received the improvements of useful arts. Nevertheless, this artificial ignorance, and learned gibberish, prevailed mightily in these last ages, by the interest and artifice of those who found no easier way to that pitch of authority and dominion they have attained, than by amusing the men of business, and ignorant, with hard words, or employing the ingenious and idle in intricate disputes about unintelligible terms, and holding them perpetually entangled in that endless labyrinth. Besides, there is no such way to gain admittance, or give defence to strange and absurd doctrines, as to guard them round about with legions of obscure, doubtful, and undefined words. Which yet make these retreats more like the dens of robbers, or holes of foxes, than the fortresses of fair warriors: which, if it be hard to get them out of, it is not for the strength that is in them, but the briars and thorns, and the obscurity of the thickets they are beset with. For untruth being unacceptable to the mind of man, there is no other defence left for absurdity but obscurity."

Hobbes: Ordinary Language Philosopher

"There is yet another fault in the discourses of some men; which may also be numbered amongst the sorts of madness; namely, that abuse of words, whereof I have spoken before in the fifth chapter, by the name of absurdity. And that is, when men speak such words, as put together, have in them no signification at all; but are fallen upon by some, through misunderstanding of the words they have received, and repeat by rote; by others from intention to deceive by obscurity. And this is incident to none but those, that converse in questions of matters incomprehensible, as the schoolmen, or in questions of abstruse philosophy. The common sort of men seldom speak insignificantly, and are therefore by those other egregious persons are counted idiots. But to be assured, their words are without anything correspondent to them in the mind, there would need some examples; which if any man require, let him take a schoolman in his hands and see if he can translate any one chapter concerning any difficult point, as the Trinity; the Deity; the nature of Christ; transubstantiation; free-will, &c., into any of the modern tongues, so as to make the same intelligible; or into any tolerable Latin, such as they were acquainted withal, that lived when the Latin tongue was vulgar. What is the meaning of these words, "The first cause does not necessarily inflow anything into the second, by force of the essential subordination of the second causes, by which it may help to work?" They are the translation of the title of the sixth chapter of Suarez' first book, "Of the concourse, motion, and help of God." When men write whole volumes of such stuff, are they not mad, or intend to make others so? " (From the Leviathan)