Every man is an animal

But is 'Every man is an animal' true when there are no men? Some new pages in the Logic Museum on the medieval dispute about this question. The main page outlines the controversy (which lasted from the early thirteenth to the late sixteenth century). The first subpage contains new translations (and Latin sources fresh to the web) of early writings on the subject. Much more to follow.

The Ontological argument

A new page here in the Logic Museum on the ontological argument. Kicks off with Aristotle's proof of the existence of God from the Metaphysics, and Descartes argument from Meditations V. Coming later will be Augustine's argument (from On Free Will), Anselm's version of the ontological argument proper, Aquinas comments on Anselm's argument, and Scotus' very complex version of the cosmological argument.

Originals and Covers, Covers and Originals

When the Levee Breaks. The cover by Zeppelin, and the original by Memphis Minnie.

Fields of Gold. Eva Cassidy's version, and the original by Sting.

Crossroads. The original by Robert Johnson, and a cover by Clapton.

Is 'every man is an animal true' when there are no men?

A splendid new page in the Logic Museum here.

The Square of Opposition

Just to draw attention to the page in the Logic Museum on the famous square. Plenty of material there, and plenty coming up, particularly of relevane to my dispute with Terence Parsons about the semantics of the O proposition.

Buridan on Individuation

Here is a splendid passage from the 14C logician John Buridan. The Latin you can find on Peter King's website, here, of which my hasty English translation is below. The passage is interesting because, while logicians like Ockham anticipate Russell's idea of scope distinction (i.e. between ~ the F is G and the F is ~ G), Buridan here also anticipates the idea that proper names are telescoped definite description. (Buridan uses the wonderful Latin word circumlocutio). Note also the examples of 'teacher of Alexander' (magister Alexandri) and 'student of Plato' (discipulus Platonis) as the relevant circumlocutio of 'Aristotle'. These are familiar from Kripke, but he just got them from Frege, who had a good German classical education, and probably got them from some unknown scholastic source.

Another familiar idea is that genuinely singular terms are really demonstrative. Buridan says that a proper name is a circumlocution, but that a truly singular term is used in the presence ('prospect') of something, whose function is not to indicate similarity, but to indicate that it can belong to no other thing.

See also the following pages in the Logic Museum.

Aquinas on the name 'God'.
Ockham's Theory of definite descriptions.

'But if you say, how can I conceive Aristotle in a singular way, when he was never in my prospect? In reply, I say that it is not possible for you, properly speaking, because you do not conceive him differently from other men except according to a sort of circumlocution, such as 'the greatest philosopher', 'the teacher of Alexander', 'the disciple of Plato', who composed the books of philosophy which we read &c. Now although this description does not in truth belong to anyone but him, yet it is not properly a singular term (terminus singularis) - Although it does not belong to anyone except him alone, it is not inconceivable (repugnat – fudge) that in this way of signifying or imposition that it may belong to many and stand (supponat) for many, and if there were another God similar, the name 'God' would belong to him and would stand for him without a new imposition of the word – and so if there were another who were the greatest philosopher and the master of Alexander and the disciple of Plato &c, the said description would belong to him and would stand for him.

'For thus it is not a term that is absolutely and properly singular. Because if this thing in my prospect I call 'Socrates' by a proper name, it is not because he is such and such but because the name 'Socrates' would never belong to those other things insofar as they are similar – unless from another imposition [that name] were imposed to signify that other thing, and thus equivocally'.

The Frozen Past

Most scholastic philosophers, with the exception of St Peter Damian, say that God cannot change the past.

St Thomas includes it on his list in Summa Contra Gentiles (II. 25) of what God cannot do (Deus non potest facere quod praeteritum non fuerit). In
On Eternity he says that the proposition that the past did not exist contains in itself a contradiction. For which reason Augustine says in the book against Faustus [xxvi c.5] 'Anyone who says "If God is omnipotent, let him bring it about that those things which happened, did not happen", does not see that he says 'If God is omnipotent, let him bring it about that those things which are true, are false in that very thing by which they are true' [PL 42, 481.].

The problem with this is that it is a logical argument, and for that reason it applies to the future as well as the past. Paraphrasing Augustine, 'The Future' means 'those things which will happen', and God cannot bring it about that the Future will not happen they way it will, otherwise we have the contradiction that those very things which will happen, are not those very things.
Yet we are more tempted to say that God could change the future. The future is not frozen in the way the past seems to be. But if this being frozen is not a logical being, what is it?

That was the same cat as this

Brandon argues here, that if 'this cat' has no tail, but 'that cat' did not have a tail, then the title sentence is false.

Let's assume that 'this' is a true demonstrative, made in the physical presence of the object we are pointing to. But for the same reason, 'that' cannot be, for Tibbles-of-yesterday is not present – literally not present – for us to point to. So the 'that' must be some sort of referring description, perhaps 'the cat we saw sitting on the front doormat of the Jones's house yesterday'.

But why would we ask whether that was the same cat as this? Perhaps we are wondering whether the Jones have two cats or not. Brandon argues that the cat we saw yesterday had a tail, but this cat (here) does not. Thus 'That was not the same cat as this is'. Ocham agrees. Of course, the cat here is not the same, in the sense of *qualitatively* the same, as the one we saw yesterday.

But Ocham happens to have seen the accident when a car ran over this cat's tail, and it fell off. Thus, argues Ocham, the Jones really have just one cat. The cat we saw yesterday, and the cat we see here now, are one and the same cat. They are 'numerically the same'. Ocham agrees that this cat is not qualitatively the same as that cat, but they are numerically the same (and so of course are not really 'they' at all).

And I wonder, would we say 'the car ran over this cat's tail' (pointing to this cat here), or 'the car ran over that cat's tail' (meaning the cat we saw yesterday).

The Logic Museum

The Logic Museum is a collection of source material, much of it Latin and medieval, on logic and metaphysical writing, and particular on the "big questions" like, does existence exist, for how long, and, is it open on Sundays sort of thing. Links below.


Logic Museum Home

The latest set of pages (July 2006) is on connotation.

Some other of the big subjects:

Time and Eternity
Infinity
Traditional Logic

Plus lots of other stuff, which you can access easily from the main page.

In June 2006 I will be working on a translation of the commentaries of Abelard, Boethius and Aquinas of the De Interpretatione.

On Miracles

Alan Rhoda has found a link to a fascinating debate here, on whether there is "Historical Evidence for the Resurrection of Jesus?" between William Lane Craig and Bart D. Ehrman.

All these have more of the theatrical and gladiatorial than the logical and rational. One feels that a hatchet or a knife or even a gun should be issued at a suitable point in the proceedings so they can get down to the real business. And what is always so fascinating, is the irrationality of the argument increases with the obvious intelligence of the participants. But interesting all the same.

Both sides misrepresented Hume. Hume's point, in the essay On Miracles, is that in considering the evidence for an extremely implausible event (which is what the word 'miracle' really implies, namely something amazing or to be wondered at, something which is scarcely believable), we must always consider which is more implausible, the miraculous event itself, or the possibility that the evidence for it is flawed in some way, however small.

Also no one mentioned the possibility that the evidence is flawed is greatly increased, is when the person producing the evidence have some interest in what it is evidence for. I don't know much about what motivated the authors of the gospels to write them. If the motive for writing the gospels were in any way correlated (think of official histories) with the need to prove them correct, we might deservedly be suspicious.

Some of the sillier quotes.

"Hume had an excuse for his abject failure: the probability calculus hadn’t yet been developed in his day.".

"everybody’s read The DaVinci Code" (false - I haven't).

"In order to show that that hypothesis is improbable, you’d have to show that God’s existence is improbable. But Dr. Ehrman says that the historian cannot say anything about God. Therefore, he cannot say that God’s existence is improbable."

Overheard in a bar

'I worked with him a few years ago and he was always trying to convert me to Islam. It would drive me mad. Finally, I said "So you believe that when I die, I will go to hell and suffer eternal punishment, and so will my wife, and so will my two beautiful daughters". He thought about this for a bit then said "Yeah. But let's not let that get between us as mates"'.


A similar thought, isn't it, to this "The Roman Catholicks are certainly the most zealous of any sect in the Christian world; and yet you will find few among the more sensible people of that communion who do not blame the Gunpowder-treason, and the massacre of St. Bartholomew, as cruel and barbarous, though projected or executed against those very people, whom without any scruple they condemn to eternal and infinite punishments. All we can say in excuse for this inconsistency is, that they really do not believe what they affirm concerning a future state; nor is there any better proof of it than the very inconsistency." (Hume, Treatise of Human Nature, I. iii. 9).

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)

Ockham on Past and Future

The latest exhibit in the Logic Museum is a parallel Latin English translation of Ockham's theory of past and future tenses, in chapter 7 of book II of his Summa Logicae. Find it here. It is connected with the discussion going on below concerning the problem of supplying truth conditions for past and future tense propositions.

Rain tomorrow

"There is some actual state of affairs which constitutes its now being the case that it’s possible that it rain tomorrow"

But is this actual state of affairs is the same state of affairs as the state of affairs which will obtain when it rains tomorrow? This seems to be the argument.

1. A statement must be true or false, and so there must be conditions under which it is true.

2. To state the conditions when a given proposition is true, is to say what IS the case, if it IS true. Merely to state the truth conditions is to specify something that exists now.

3. Thus statements about the future can be reduced to statements in the present tense. For if the truth condition obtains, the statement that it obtains, is true now. If it does not obtain, the statement that it does not obtain, is true now.

But why should the truth conditions be in the present tense? I agree that a proposition like 'Tom thinks it will rain tomorrow' says something about the present. It says that Tom has a certain thought, right now, in the present. Similarly 'the weather forecaster says it will rain tomorrow' says something about what the person on the TV says, now. Likewise 'It is causally determined that it will rain tomorrow'. Similarly also for 'it is possible that it will rain tomorrow', which says something about the speaker's present state of knowledge.

But 'it will rain tomorrow' doesn't say anything about the present. 'It will rain tomorrow' is true if and only if it WILL rain tomorrow.

Locke on Truths of Reason

And here is Locke on the distinction between truths of reason and truths of fact, from Bk 4 ch xi, 13 ' Of our Knowledge of the Existence of Other Things'

13. Only particular propositions concerning concrete existences are knowable. By which it appears that there are two sorts of propositions:—(1) There is one sort of propositions concerning the existence of anything answerable to such an idea: as having the idea of an elephant, phoenix, motion, or an angel, in my mind, the first and natural inquiry is, Whether such a thing does anywhere exist? And this knowledge is only of particulars. No existence of anything without us, but only of God, can certainly be known further than our senses inform us. (2) There is another sort of propositions, wherein is expressed the agreement or disagreement of our abstract ideas, and their dependence on one another. Such propositions may be universal and certain. So, having the idea of God and myself, of fear and obedience, I cannot but be sure that God is to be feared and obeyed by me: and this proposition will be certain, concerning man in general, if I have made an abstract idea of such a species, whereof I am one particular. But yet this proposition, how certain soever, that “men ought to fear and obey God” proves not to me the existence of men in the world; but will be true of all such creatures, whenever they do exist: which certainty of such general propositions depends on the agreement or disagreement to be discovered in those abstract ideas.

The distinctions that Locke makes (see previous post) are therefore as follows:

1. propositions which are truths of reason, but merely trifling or verbal;

2. propositions which are truths of reason, but where the predicate is not actually contained in the subject, but is a necessary consequence of it;

3. propositions which are simply matters of fact, not deducible by reason alone.

Locke on Analytic vs Synthetic

Here is a passage from the Essay (Bk IV, c. viii, 8) that is suggestive of the Analytic / Synthetic distinction.

8. … We can know then the truth of two sorts of propositions with perfect certainty. The one is, of those trifling propositions which have a certainty in them, but it is only a verbal certainty, but not instructive. And, secondly, we can know the truth, and so may be certain in propositions, which affirm something of another, which is a necessary consequence of its precise complex idea, but not contained in it: as that the external angle of all triangles is bigger than either of the opposite internal angles. Which relation of the outward angle to either of the opposite internal angles, making no part of the complex idea signified by the name triangle, this is a real truth, and conveys with it instructive real knowledge.

Hume's Fork

Spur writes here

Leibniz and Hume have the same basic distinction in mind, between those truths which are necessary and can be known a priori, and those which are contingent and can only be known a posteriori. The two philosophers use slightly different terminology, and Leibniz would balk at Hume's use of 'relations between ideas' in connection with truths of reason only, but the basic distinction seems to me to be the same.

But the question is more difficult, and is related to a change in logic that happened at the very beginning of the early modern era. The scholastic logicians said that in a proposition (which for them meant a sentence) the predicate is affirmed or denied of the subject. 'Subject' and 'predicate' here are objectively existing things.

Influenced by Descartes, Antoine Arnauld argued that it is not one THING that is predicated of another thing, but one IDEA that is predicated of another idea. Locke (who studied Arnauld's logic carefully) introduced this to the English world (Book IV of the essay is the locus classicus). For example, he sets its down as a principle, that all our knowledge consists in perceiving certain agreements and disagreements between our ideas.

There you have Hume's fork. Before, there was the difference between accidental and essential propositions. An essential proposition is where the predicate belongs in the subject by right, as it were. An accidental proposition is whether the predicate belongs in the subject, but possibly may not. It is not relevant whether this can be known or not. There are (as Aquinas notes) essential propositions which cannot be known because mere humans cannot understand the true meaning of the word which signifies the subject. But the notion of a proposition true in itself but unknowable because the 'subject' is unknowable, is impossible where the proposition consists of ideas stuck together.

In summary: Hume's fork is a consequence of the early modern view of the proposition. The scholastic view was that the proposition connects things. The early modern view is that it connects ideas. The distinction between truths of reason and truths of fact only makes sense on the latter view.

There a number of passages which support this argument & I will make a posting in due course.