It is characteristic of an empiricist to eschew metaphysics, on the ground that every factual proposition must refer to sense experience.
Problem: how to account for necessary truths, including notably truths of mathematics and logic since it’s always possible in principle to falsify empirical generalizations.
Ayer needs an account that will get rid of bad metaphysics without throwing out good mathematics.
Thought is an independent source of knowledge.
No! All factual knowledge comes from experience
The Elimination of Metaphysics
The Metaphysical Thesis: philosophy affords us knowledge of a reality transcending the world of science and common sense.
The Absolute enters into but is itself incapable of evolution and progress. (Bradley)
Nothing noths (Heidegger)
Ayer’s Thesis: talk about such a transcendent reality is, literally, meaningless.
“The function of philosophy is wholly critical”
“Philosophy leaves everything as it is.
The business of philosophy is analysis: “the propositions of philosophy are…linguistic in character.”
We’re deluded by language
E.g. the Fido-Fido theory of meaning: every noun names an object
The Wino’s Paradox
Nothing is better than champagne
Thunderbird is better than nothing
Therefore Thunderbird is better than champagne
Challenge: translate this argument into the language of predicate logic!
Russell showed that the correct analysis of the logical form of these claims blocks the inference.
Not your grandmother’s empiricism!
The old Kantian attack on metaphysics was epistemological
Starting from experience all we can validly infer are further facts about experience.
But the metaphysician can just claim access to transcendent reality via “intellectual intuition”
Even if “intellectual intuition” is baloney, this doesn’t show his conclusions are false… just that we can’t know whether they’re true or false.
Logical positivists hold that metaphysical claims are neither true nor false but literally meaningless—i.e. nonsense.
The Business of Philosophy is Analysis
Paraphrasing away: Russell’s “On Denoting” as the paradigm of analysis
Nothing is better than champagne ~ (∃x) (x is better than champagne)
Artificial languages as means to accomplish analysis
Logical constructions and inferred entities
“We are all phenomenalists now.”
Analysis is concerned with cognitive content understood in terms of equivalence and entailment relations.
Goal: the elimination of metaphysics
Is denying metaphysics is just more metaphysics?
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.
So we can’t adopt Kant’s strategy of arguing that metaphysics is psychologically impossible since that would mean showing that there are metaphysical truths that we couldn’t understand—which is itself a metaphysical claim
To avoid just doing more metaphysics we have to show that metaphysical claims are meaningless.
A proposition is verifiable in the strong sense iff its truth could be conclusively established in experience.
A proposition is verifiable in the weak sense iff it is possible to render it probable.
All we require for meaningfulness is weak verifiability
So laws of nature, which are merely very, very, very, very, very highly probable are ok.
Only a “tautology,” a claim which has no factual content and conveys no information about the world, can be anything more than a probable hypothesis.
Example: Either today is Tuesday or today is not Tuesday.
What’s hot and what’s not
Ordinary empirical claims, e.g. “there’s a skunk living in my crawlspace.”
Claims about remote times and places, e.g. “Lucy had 4 children.”
Laws of nature, e.g. “under conditions found on earth, water freezes at 32 F.”
Metaphysics, e.g. “nothing noths.”
Theology, e.g. “God exists.”
Ethics, e.g. “Torturing young children for fun is wrong.”
Aesthetics, e.g. “St. Pauls, London, is one of the 10 most beautiful buildings in Europe.”
Throwing out the baby with the bathwater?
The elimination of metaphysics: mission accomplished.
Theology as nonsense: no problem.
Ethics (and aesthetics) can be reconstructed as expressive or prescriptive.
But with math and logic…we have a serious problem.
The Empiricist’s Math Dilemma
The empiricist must deal with the truths of logic and mathematics in one of the two following ways: he must say either that they are not necessary truths, in which case he must account for the universal conviction that they are; or he must say that they have no factual content, and then he must explain how a proposition which is empty of all factual content can be true and useful and surprising.
J. S. Mill
Not necessary truths!
No factual content!
Mill’s view rejected
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.
“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]
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]
Language, Truth and Logic
Metaphilosophy: the function of philosophy and how it accomplishes its results
Hume’s Fork: “Tautologies” and factual claims
The a priori: math and logic
Factual claims: science and everything else
Nonsense: ethics and theology
(Dis)solutions of traditional philosophical problems
Kant: The Analytic/Synthetic Distinction
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)
They’re a priori (knowable independent of experience) because they’re empty of factual content.
They’re necessary because we don’t allow them to be false, e.g.
if the angles of a figure don’t add up to 180 degrees we don’t count it as a Euclidean triangle.
A meaningful sentence is one or the other
Math and Logic
analytic: true in virtue of language alone. [I]t’s validity depends solely on the definitions of the symbols it contains.
a priori: knowable “prior to” experience
necessary: not logically possible that they be false
synthetic: not analytic. [I]ts validity is determined by the facts of experience.
a posteriori (“empirical”): can only be known “after” (on the basis of) experience
contingent: not necessary
Some Hard Questions
Does anything (respectable) escape Hume’s Fork?
Water is H20
The truths of logic and math are analytic
Objection: If all the assertions which mathematics puts forward can be derived from one another by formal logic, mathematicians cannot amount to anything more than an immense tautology…[C]an we really allow that these theorems which fill so many books serve no other purpose than to say in a roundabout fashion A = A?
Tautologous doesn’t mean obvious
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.
We reject “truths of reason” which purport to establish facts about the world outside of language by a priori reasoning.
And we reject Kant’s synthetic a priori
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.
The business of philosophy is analysis: to elicit those features linguistic usage and reveal entailment relations.
A paradigmatic philosophical question
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???
It’s a question about linguistic conventions!
“North” and “south” trace along longitude lines which converge at the North and South poles.
“East” and “west” trace along latitude lines which are concentric and don’t converge;
“Who cares what games we choose…”
Whether a geometry can be applied to the actual physical world or not, is an empirical question which falls outside the scope of the geometry itself. There is no sense, therefore, in asking which of the various geometries known to us are false and which are true. In so far as they are all free from contradictions, they are all true…[T]he propositions of pure geometry are analytic…the reason why they cannot be confuted in experience is that they do not make any assertion about the empirical world. They simply record our determination to use words in a certain fashion.
All factually significant propositions are a posteriori (empirical)
Sentences which purport to be factually significant but fail the Verification Principle are nonsense.
A priori propositions are devoid of factual content.
They’re meaningful only if they’re “tautologies,” i.e. analytic.
A priori propositions that aren’t tautologies are metaphysical junk—a result of our misunderstanding of language
“Substance” comes from our “primitive superstition” that subject-predicate form reflects the structure of reality.
“Being” comes from the surface grammatical quirk that we express existential sentences with “is” which also does the job of predication. Existence is not a predicate!
What is the status of the Verification Principle itself?
Is it an empirical claim made probable by experience?
Is it a “tautology” true just in virtue of the meanings of words?
Do analytic, a priori, necessary and synthetic, empirical, contingent line up neatly in the way suggested?
analytic and synthetic are semantic notions
a priori and a posteriori concern the way in which propositions are known
necessary and contingent are metaphysical notions concerning the conditions with which propositions are compatible
Suppose the Verification Principle is a methodological prescription: has Ayer fiddled it to let in what he likes but exclude what he doesn’t like, i.e. metaphysics and theology?
Does Ayer have an adequate account of mathematics given Gödel’s proof that in any system rich enough to formalize arithmetic there are propositions which are true within the system that aren’t derivable within the system?
Can the distinction between analytic and synthetic propositions be made in a non-question-begging way?