Logical Positivism. Ayer on The A Priori. Language, Truth and Logic. Ayer ’ s report on what the Vienna Circle was doing, for English-speaking folk. LOGICAL POSITIVISM. What I ’ m going to do. The Vienna Circle and its historical antecedents, its influence on analytic philosophy
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Ayer on The A Priori
Ayer’s report on what the Vienna Circle was doing, for English-speaking folk.
Thought is an independent source of knowledge.
It is characteristic of an empiricist to eschew metaphysics, on the ground that every factual proposition must refer to sense experience.
No! All factual knowledge comes from experience
Wittgenstein says, "in order to draw a limit to thinking, we should have to think both sides of this limit," a truth to which Bradley gives a special twist in maintaining that the man who is ready to prove that metaphysics is impossible is a brother metaphysician with a rival theory of his own.
To state the circumstances under which a proposition is true is the same as stating its meaning. (Schlick)
A sentence is factually significant to any given person, if and only if, he knows how to verify the proposition which it purports to express.
Not necessary truths!
No factual content!
J. S. Mill
The course of maintaining that the truths of logic and mathematics are not necessary or certain was adopted by Mill. He maintained that these propositions were inductive generalizations based on an extremely large number of instances.
2 + 2 = 4
Lucky for Mill things aren’t nailed down.
“All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of fact. Of the first kind are the sciences of Geometry, Algebra and Arithmetic... [which are] discoverable by the mere operation of thought ... Matters of fact, which are the second object of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing.” [Hume, Enquiry Concerning Human Understanding]
necessary – a priori - analytic
contingent – a posteriori - synthetic
If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion. [Hume, Enquiry Concerning Human Understanding]
In all judgments in which the relation of a subject to the predicate is thought … this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A… In the first case, I call the judgment analytic, in the second synthetic…I merely draw out the predicate in accordance with the principle of contradiction, and can thereby at the same time become conscious of the necessity of the judgment (Kant)
Math and Logic
Does anything (respectable) escape Hume’s Fork?
Water is H20
The power of logic and mathematics to surprise us depends…on the limitations of our reason. A being whose intellect was infinitely powerful would take no interest in logic and mathematics.
There is a sense in which analytic propositions do give us new knowledge. They call attention to linguistic usages, of which we might otherwise not be conscious and they reveal unsuspected implications in our assertions and beliefs.
A bear walks a mile south, a mile east and a mile north—and ends up where he started. How is that possible?
We know the answer of course…
But how come it only works near the North Pole???