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A.J. Ayer The Elimination of Metaphysics


									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.
                  What I’m going to do

• The Vienna Circle and its historical antecedents, its influence
  on analytic philosophy

• The Logical Positivist program, including

   – The Verification Principle and anti-metaphysical agenda

   – Philosophy as analysis: the quest for an ideal language

   – Commitment to phenomenalism

• Ayer on the A Priori

   – The analytic/synthetic distinction

   – Math and logic as “tautologous”
    Logical Positivism is a form of Empiricism
                       Thought is an
                    independent source
                       of knowledge.

                                           No! All factual
                                         knowledge comes
                                          from experience

      Rationalist                                            Empiricist

  It is characteristic of an empiricist to eschew metaphysics, on
  the ground that every factual proposition must refer to sense
• 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.
           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” (contra

   – “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

• 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

   – 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.

• So we adopt the Verification Principle as a criterion for
             The Verification Principle

  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.

• Example: “There’s a skunk living in the crawl space under
  my house.”

• I know what experiences would verify the proposition this
  sentence purports to express—for example:

              » Every few days I experience a characteristic

              » My dog was barking like crazy, then ran into
                the house yelping and whining—and stinking.
 Bad Metaphysics flunks the Verification Test

• Challenge: what experiences would verify—or falsify—the
  following metaphysical claims?

   – The Absolute enters into but is itself incapable of evolution
     and progress. (Bradley)

   – Nothing noths (Heidegger)

• Problem: what experiences would verify

   – claims about laws of nature

   – claims about the past, e.g. Lucy had exactly
     four children
Practical Verifiability & Verifiability in Principle

• Propositions about the past can’t now be conclusively verified
  or falsified but we can say what sorts of experiences would
  verify or falsify them.

• Verifiability doesn’t have to be feasible--only possible in

   – There are mountains on the other side of the moon

   – Lucy had exactly four children

• We require only verification in principle: we have to be able
  to say what sort of experience would verify of falsify.

• So propositions about the past are ok.
             Strong and Weak Verification

• 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

  Sense                            Nonsense

• Ordinary empirical claims,     • Metaphysics, e.g. “nothing
  e.g. “there’s a skunk living     noths.”
  in my crawlspace.”

                                 • Theology, e.g. “God exists.”
• Claims about remote times
  and places, e.g. “Lucy had
  4 children.”                   • Ethics, e.g. “Torturing
                                   young children for fun is
• Laws of nature, e.g. “under
  conditions found on earth,
  water freezes at 32 F.”        • Aesthetics, e.g. “St. Pauls,
                                   London, is one of the 10
                                   most beautiful buildings in
   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

• 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.
                     necessary         No factual
                      truths!           content!

        J. S. Mill                                  David Hume
                Mill’s view rejected


                             Lucky for Mill
                             things aren’t
                             nailed down.

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
            Ayer goes with Hume’s Fork
“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
              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)
• Analytic sentences are true in virtue of language alone

• 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
    A meaningful sentence is one or the other

  Math and Logic                  Everything else

• analytic: true in virtue of   • synthetic: not analytic. [I]ts
  language alone. [I]t’s          validity is determined by the
  validity depends solely on      facts of experience.
  the definitions of the
  symbols it contains.
                                • a posteriori (“empirical”):
                                  can only be known “after”
• a priori: knowable “prior       (on the basis of) experience
  to” experience

                                • contingent: not necessary
• necessary: not logically
  possible that they be
    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?

                                     You betcha!
         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.
                         Summing up
• All factually significant propositions are a posteriori

   – 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.

• 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
                    Some questions…

• 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

• 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
                      More questions

• 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?


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