Category: History of Philosophy

‘Leibniz’s Law’: A Useless Expression

Pedant and quibbler that I am, it annoys me when I hear professional philosophers use the phrase 'Leibniz's Law.'  My reason is that it is used by said philosophers in three mutually incompatible ways.  That makes it a junk phrase, a wastebasket expression, one to be avoided.  Some use it as Dale Tuggy does, here, to refer to the Indiscernibility of Identicals, a principle than which no more luminous can be conceived.  (Roughly, if a = b, then whatever is true of a is true of b, and vice versa.)  Fred Sommers, referencing Benson Mates, also uses it in this way.  (See The Logic of Natural Language,  p. 127)

Others, such as the distinguished Australian philosopher Peter Forrest, use it to refer to the Identity of Indiscernibles, a principle rather less luminous to the intellect and, in my humble opinion, false.  (Roughly, if whatever is true of a is true of b and vice versa, then a = b.)  And there are those who use it as to refer to the conjunction  of the Indiscernibility of Identicals and the Identity of Indiscernibles.

So 'Leibniz's Law' has no standardly accepted usage and is insofar forth useless.  And unnecessary.  You mean 'Indiscernibility of Identicals'?  Then say that.  If you mean its converse, say that. Ditto for their conjunction.

There is also the problem of using a great philosopher's name to label a principle that the philosopher may not even have held.  Analytic philosophers are notorious for being lousy historians.  Not all of them, of course, but the run-of-the-mill.  If Sommers is right, Leibniz was a traditional logician who did not think of identity as a relation as Frege and Russell do.  (p. 127) Accordingly, 'a = b' as this formula is understood in modern predicate logic does not occur in Leibniz.

 

Hume’s Fork and Leibniz’s Fork

No doubt you have heard of Hume's Fork.  'Fork,' presumably from the Latin furca, suggests a bifurcation, a division; in this case  of meaningful statements into two mutually exclusive and jointly exhaustive classes, the one consisting of relations of ideas, the other of matters of fact. In the Enquiry, Hume writes:

     Propositions of this kind [relations of ideas] can be discovered
     purely by thinking, with no need to attend to anything that
     actually exists anywhere in the universe. . . . Matters of fact . .
     . are not established in the same way; and we cannot have such
     strong grounds for thinking them true. The contrary of every matter
     of fact is still possible, because it doesn't imply a contradiction
     and is conceived by the mind as easily and clearly as if it
     conformed perfectly to reality. That the sun will not rise tomorrow
     is just as intelligible as – and no more contradictory than – the
     proposition that the sun will rise tomorrow.

One question that arises is whether Hume's Fork was anticipated by any earlier philosopher. Leibniz of course makes a distinction between truths of reason and truths of fact that is very similar to Hume's distinction between relations of ideas and matters of fact. See, for example, Monadology #33. In a very astute comment from the old blog, 'Spur' details the similarities and concludes:

     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.

I deny that the basic distinction is the same and I base my denial on a fact that Spur will admit, namely, that for Leibniz, every proposition is analytic in that every (true) proposition is such that the predicate is contained in the subject: Praedicatum inesse subjecto verae propositionis. I argue as follows. Since for Leibniz every truth is analytic, while for Hume some truths are analytic and some are not, the two distinctions cannot be the same. To this, the Spurian (I do not say Spurious) response is:

     The [Leibnizian] distinction is between two kinds of analytic
     truths: those that can be finitely analyzed, and those that can't.
     This is an absolute distinction and there are no truths that belong
     to both classes. Even from God's point of view there is presumably
     an absolute distinction between necessary and contingent truths,
     though perhaps he wouldn't view this as a distinction between
     finitely and non-finitely analyzable truths, because his knowledge
     of truths is intuitive and never involves analysis.

I grant that the two kinds of Leibnizian analytic truths form mutually exclusive and jointly exhaustive classes. But I deny that this suffices to show that "the same basic distinction" is to be found in both Leibniz and   Hume.

One consideration is that they do not form the same mutually exclusive and jointly exhaustive classes. Though every Humean relation of ideas is a Leibnizian truth of reason, the converse does not hold. I think Spur will agree to this. But if he does, then surely this shows that the two distinctions are not the same. I should think that extensional sameness is necessary, though not sufficient, for sameness.

But even if the two distinctions were extensionally the same, they are not 'intensionally' the same distinction.

Consider Judas is Judas and Judas betrays Christ. For both  philosophers, the first proposition is necessary and the second is contingent. But Leibniz and Hume cannot mean the same by 'contingent.' If you negate the first, the result is a contradiction, and both philosophers would agree that it is, and that it doesn't matter whether the proposition is viewed from a divine or a human point of view. The negation of the second, however, is, from God's point of view a contradiction for Leibniz, but not for Hume. For Leibniz, the betrayal of Christ is included within the complete individual concept of Judas that God has before his mind. So if God entertains the proposition Judas does not betray Christ, he sees immediately that it is self-contradictory in the same way that I see immediately that The   meanest man in Fargo, North Dakota is not mean is self-contradictory.

Of course, for Leibniz, it is contingent that Judas exists: there are possible worlds in which Judas does not exist. But given that Judas does exist, he has all his properties essentially. Thus Judas betrays   Christ is contingent only in an epistemic sense: we finite intellects see no contradiction when we entertain the negation of the proposition in question. Given our finitude, our concepts of individuals cannot be complete: they cannot include every property, monadic and relational, of individuals. But if, per impossibile, we could ascend to the divine standpoint, and if every truth is analytic (as Leibniz in effect holds via his predicate-in-subject principle), then we would see that Judas betrays Christ is conditionally necessary: nec
essary given the existence of Judas.

'Contingent' therefore means different things for Leibniz and Hume. Contingency in Hume cuts deeper. Not only is the existence of Judas contingent, it is also contingent that he has the properties he has. This is a contingency rooted in reality and not merely in our ignorance.

Perhaps my point could be put as follows. The Leibnizian distinction is not absolute in the sense that, relative to the absolute point of view, God's point of view, the distinction collapses. For God, both of the Judas propositions cited above are analytic, both are necessarily true (given the existence of Judas), and both are knowable a priori.  But for Hume, the distinction is absolute in that there is no point of view relative to which the distinction collapses.

I'm stretching now, but I think one could say that, even if Hume admitted God into his system, he would say that not even for God is a matter of fact knowable a priori. For the empiricist Hume the world is radically contingent in a way it could not be for Leibniz the rationalist.

The History of Philosophy as Akin to an Intellectual Arms Race

Nicholas Rescher, The Strife of Systems: An Essay on the Grounds and Implications of Philosophical Diversity (University of Pittsburg Press, 1985), pp. 205-206:

The history of philosophy is akin to an intellectual arms race where all sides escalate the technical bases for their positions.  As realists sophisticate their side of the argument, idealists sophisticate their counterarguments; as materialists become more subtle, so do phenomenalists, and so on.  At the level of basics, the same old positions continue to contest the field — albeit that ever more powerful weapons are used to defend increasingly sophisticated positions.

The context is an argument for the thesis that philosophy is susceptible of technical but not doctrinal progress.  The nature of philosophy precludes consensus.  Resolution of "the substantive issues in such as way as to secure general approbation and assent" (206) is out of the question. Such consensus is impossible and therefore not even an ideal.

Strife of Systems is essential reading for anyone interested in metaphilosophy.

Emile-Auguste Chartier

Alain Emile Chartier (1868-1951) was a French professor of philosophy among whose students were Raymond Aron and Simone Weil. Chartier's sunny disposition, however, did not rub off on the brooding Weil. Under the pseudonym 'Alain,' Chartier published thousands of two-page essays in newspapers. What follows is a striking sentence from the essay "Maladies of the Mind" in Alain on Happiness, F. Unger, 1973, p. 25:

An old man is not a young man who suffers from old age; a man who
dies is not a living man who enters into death.

Bertrand Russell on Arabic Philosophy

The following passage is from Bertrand Russell, A History of Western Philosophy (New York: Simon & Shuster, 1945), p. 427. I found it here, but without a link and without a reference. So, exploiting the resources of my well-stocked library, I located the passage, and verified that it had been properly transcribed. Whether Russell is being entirely fair to the Arabs is a further question.

Arabic philosophy is not important as original thought. Men like Avicenna and Averroes are essentially commentators. Speaking generally, the views of the more scientific philosophers come from Aristotle and the Neoplatonists in logic and metaphysics, from Galen in medicine, from Greek and Indian sources in mathematics and astronomy, and among mystics religious philosophy has also an admixture of old Persian beliefs. Writers in Arabic showed some originality in mathematics and in chemistry; in the latter case, as an incidental result of alchemical researches. Mohammedan civilization in its great days was admirable in the arts and in many technical ways, but it showed no capacity for independent speculation in theoretical matters. Its importance, which must not be underrated, is as a transmitter. Between ancient and modern European civilization, the dark ages intervened. The Mohammedans and the Byzantines, while lacking the intellectual energy required for innovation, preserved the apparatus of civilization, books, and learned leisure. Both stimulated the West when it emerged from barbarism; the Mohammedans chiefly in the thirteenth century, the Byzantines chiefly in the fifteenth. In each case the stimulus produced new thought better than that produced by the transmitters — in the one case scholasticism, in the other the Renaissance (which however had other causes also).

Why Brentano is Important

If Edmund Husserl is the father of phenomenology, Franz Brentano is its grandfather: his Psychology From an Empirical Standpoint, along with his lectures at the University of Vienna were powerful influences on the young Husserl who, though a Ph.D. in mathematics (under Weierstrass on the calculus of variations) abandoned mathematics for philosophy. (2) Brentano's dissertation under Trendelenburg, On the Several Senses of Being in Aristotle, was a powerful impetus to Heidegger's ruminations on Being. (3) Brentano, as Gustav Bergmann points out, was "the first linguistic philosopher." (Realism, p. 234) Brentano, then, can be said to stand at the source of both the phenomenological and the analytic streams of thought as they developed in the 20th century.