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I  Kant’s „awakening from his dogmatic slumber“ through Hume (Kant in 1783) took place not around 1770 but much earlier, between 1755 (German translation of Hume’s First Enquiry) and 1762 (publication of Kant’s Only Possible Argument).

II  Already in his pre-critical period Kant accepted Hume’s destruction of all metaphysics. This destruction if founded on logic, not on epistemology: propositions of metaphysics are not beyond the reach of our epistemic powers, but rather they simply make no sense, they have no content whatsoever. They do not determine anything that could be true or false.

III  The key element in this destruction is Hume’s class separation of analytic propositions (relations of ideas) from synthetic propositions (matters of fact). This makes traditional metaphysics an unclear mixture of both: it would have to be analytic as well as synthetic – if it was to demonstrate (analytically) God’s existence (a synthetic claim). If metaphysics were to be purely demonstrative according to the Principle of Contradiction – it would have to be analytical and to coincide with logic. The status of the (synthetic) Principle of Sufficient Reason was notoriously unclear.

IV  In his 1762-3 book on The Only Possible Argument [Der einzig mögliche Beweisgrund zu einer Demonstration des Daseins Gottes] Kant offered first of all a thorough and systematical critique of all possible demonstrations for God’s existence, especially of the ontological proof. Kant explains that „existence is no predicate“ – and this alone destroys the ontological proof.

He also gave his own argument for the Existence of God – and this argument is no demonstration but an early version of a transcendental argument: Kant emphasizes that it involves no contradiction to claim that God does not exist, but if thought is to be possible at all – there must be something existing that supplies the data for thought. If thinking exists it is thus impossible that nothing at all should exist.

V  Kant 1762/3 (AA 2, 79): It is entirely impossible that nothing at all should exist.

That which takes away all possibility, this is entirely impossible. These two expression are synonymous.

Now, that which contradicts itself takes away the formal requirement of all possibility, namely the conforming to the Principle of Contradiction – and therefore everything which contradicts itself, is entirely impossible.

This, however, is not the case we have to consider concerning the total lack of all existence. To be sure, this would not involve any inner contradiction, as we have shown. However, that which takes away everything material and all data for everything possible, this will deny all possibility. Now, this will happen if all existence is being taken away – this will also take away all possibility. Therefore it is entirely impossible that nothing at all should exist.

VI  In later years Kant no longer classified this argument no longer as a formal proof – and he restricted the scope of transcendental arguments to questions involving experience.

VII  Thus the entire time-span from 1763 until 1781 must be regarded as devoted to the further working-out of Kant’s non-metaphysical, but transcendental philosophy. Thus Kant tried to establish propositions that are both synthetic (non-empty) and a priori (not derived from experience). This can only work because these propositions reflect on the nature of experience. In this way Hume can indeed be regarded as the single most important influence on Kant’s formative years – and it took Kant almost twenty years to work out his answer to Hume.

 

Abstract

The lecture will discuss the following issues:

I  In traditional logic we have no type distinctions, we are dealing with concepts only. These can occur both in subject or predicate position:  Some S is P and Some P is S are both meaningful.

II  Traditional logic thus is about conceptual relations only (just like Hume’s relations of ideas), and therefore it has no connection to facts or existence claims.

III  Traditional logic also knows of no objects or individuals. The „singular judgments“ like „Socrates is mortal“ are no exception: They are interpreted as a relation between the „individual concept“ Socrates and the concept mortal. The proposition therefore expresses a necessary a priori truth. Singular judgments are treated „just like general judgments“ (as Kant remarks).

IV  Thus traditional logic is unable to explain the essential difference between substance and accident which we meet in sentences of ordinary language (like „Socrates is mortal“ – in language „Mortal is Socrates“ makes no sense, because „Socrates“ cannot be used as a predicate). This is the main reason why there is no traditional philosophy of language based on logic.

V  Existence cannot be expressed in traditional logic – the only way to introduce existence is by presupposition: We can say that in judgments of a certain kind (say „All S are P“) we always presuppose that the concepts S or P involved are non-empty.

VI  Kant distinguished general, or formal, logic which knows of no existence, from transcendental logic – the logic concerned with speaking about objects of experience. This transcendental logic, however, is not logic in the usual sense but it is rather Kant’s type of philosophy in his Critique of Pure Reason.

VII  Frege wanted to treat ordinary as well as scientific contents in a logical manner. He wanted to connect logic and science. Thus he started his logic with ordinary propositions of the form „A is the case“. His first move in logic was to introduce a type-distinction between concepts and objects. His most simple proposition has the form f(a) – this expresses that the object a has the property f. Both elements cannot be exchanged because their nature is essentially different.

VIII  Frege himself remarked that he originally started to construct his logic with the linguistic elements Subject and Predicate, but that he could achieve much more flexibility if he used the function-argument distinction (known from mathematics) instead. Thus he wanted to free logic from being modeled too closely on linguistic forms. He wanted to „break the tyranny of language over thought“. Ironically, this moving away from language actually effected that Frege’s logic could do much better justice to ordinary language than did traditional logic.  Frege thus became the founder of all philosophy of language based on logical analysis. Russell and Wittgenstein only followed him in this respect. (His later distinction between sense and reference was only his second most important contribution to philosophy of langauge.)

IX  Only if we distinguish objects from concepts can existence be expressed: Existential propositions state that „there are objects x which have the property f“. Frege does not have to presuppose existence, he can express explicitly that there are, or are not, objects of certain properties.

X  The Boolean tradition in logic introduced mathematical notation but it had no type-distinction between objects and concepts. Boole, Schroeder and Peirce all talked of „classes“ – but this talk can all be translated into concept-talk. Thus the Boolean tradition belongs to the field of traditional logic, systematically speaking. (It was only with the invention of set theory that the distinction between a class and its member was introduced into this tradition.)

XI  It is often claimed that Peirce invented quantifiers (expressing existence) independently from Frege. This, however, is false and even impossible, because the logic Peirce used does not distinguish between objects and concepts. The two „quantifiers“ (general and existential) Peirce uses are not mutually interdefinable: the expression „all“ is primitive and can be negated to yield „not-all“ while the expression „none“ is also primitive (and cannot be expressed in terms of „all“) and can be negated to yield „not none“ (i.e. „some“).

XII  While in traditional logic only necessity and no facts can be expressed – in Frege’s logic we have the reverse situation: it is difficult to express necessity. When Frege expresses generality, he cannot (in his quantifier notation) distinguish between accidental and necessary generality. In traditional logic the old example: „All men are mortal“ expressed the conceptual truth that „all mortal men are mortal“ – this follows from the definition of „man“. After Frege this proposition „All men are mortal“ will be regarded as an „empirical generalisation“ – a statement that can only hypothetically be regarded as correct – as long as some human beings are still alive.

Frege considered even his logical axioms to have some factual content – from his perspective logic no longer could be formal, simply because all proposition need to have at least some content.

XIII  Although he admired Frege greatly, Wittgenstein believed that Frege (and Russell) had misunderstood the nature of logic. According to Wittgenstein, logic must be absolutely independent of any questions about the world and anything existing. Thus he tried to restore the traditional idea that in logic everything must be strictly a priori and necessarily. While he followed Frege in starting from factual propositions, he found that there cannot be „logical propositions“ at all. „Logical propositions“ are tautologies or contradictions – but these are relations between propositions where the content of the contributing propositions cancels out. Therefore they have no content whatsoever and logic itself is purely formal and analytic again.