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EMPIRICISM

PHIL3072, ANU, 2015Jason Grossman

http://empiricism.xeny.net

lecture 8: 1 September

Logical Atomism

Contents

Recap

Bertrand Russell: reductionism in mathematics and logic

Bertrand Russell: reductionism in physics (logical atomism)

Everyone gets to introduce a question or a small topic to discuss.

Recap: “Hume’s problem of induction”

Note that Hume’s conclusion is that using induction to assign necessaryconnection to causal powers is circular.

“Hume’s problem of induction” is usually used to refer to the conclusionthat using induction to justify induction is circular.

Not the same conclusion at all! But essentially the same argument worksfor both.

“Hume’s problem” of the justification of induction is not actually foundanywhere in Hume. (But it is found in plenty of other places,e.g. Sextus Empiricus — see rationalism lecture notes.)

Recap: What IS causation then?

Since causation is not a necessary connection, but since nevertheless it’sa concept we use, it must be a mere custom or habit.

And the tendency of people to have this habit is unexplained.

“men are not astonish’d at the operations of their own reason, at thesame time, that they admire the instinct of animals, and find a difficultyin explaining it”

“To consider the matter aright, reason is nothing but a wonderful andunintelligible instinct”— David Hume, “A Treatise of Human Nature”, http://www.davidhume.org/texts/thn.html, viewed 2015-08-01, 1.3.16

Recap: Hume’s fork: Treatise version, 1739

“Truth or falshood consists in an agreement or disagreement either tothe real relations of ideas, or to real existence and matter of fact.

Whatever, therefore, is not susceptible of this agreement ordisagreement, is incapable of being true or false, and can never be anobject of our reason.”— David Hume, “A Treatise of Human Nature”, http://www.davidhume.org/texts/thn.html, viewed 2015-08-01, 3.1.1

As used in his analysis of causation:

“real relations of ideas” = “understanding” and “reason” =mathematics or logic

“real existence and matters of fact” = “association . . . ofperceptions” = empirical facts

Recap: Empiricist terminology

Hume’s fork is often taken as a repudiation of metaphysics, but Humespecifically restricts his criticism to “school metaphysics”, i.e. the roughlyAristotelian Scholasticism still being taught in the universities at the time.

Subsequent empiricists mostly follow Hume’s definition of“metaphysics”, especially later empiricists.

Logical positivism, especially, is a detailed attempt to do withoutmetaphysics in this sense . . .

But many others use a much broader definition, so they can agree withHume’s empiricism but still think of themselves as doing metaphysics.

This is why I mostly talk about “ontology” rather than “metaphysics”.

Recap: Hume — conclusion

Hume’s great (and original?) contribution to empiricism:

We can’t know what is outside ourselves

which means we can’t know what produces the regularities thatform our nature (e.g. principles of rationality)

but we can talk about these regularities anyway, exactly aswe can talk about the regularities in Newton’s physics.

So Hume has principles which are effectively a priori but which weinfer only tentatively through our observations.

Recap: Logical positivism

The rise of empiricism among scientists came after early modernscience but before 20th century science:

1687: Newton’s Principia (action at a distance)

1739–1748: Hume

19th century: Mach and other Humeans;Poincare’s empiricist conventionalism

1905: Einstein’s very empiricist Special Relativity, and his earlycontributions to quantum theory

1911–1924: Russell’s logical atomism— First appearance of logical atomism: “Le Réalisme analytique” (1911), translated as “Analytic Realism,” in Collected Papers of Bertrand

Russell, vol. 6, Logical and Philosophical Papers, 1909⣓1913, ed. J. G. Slater. London: Allen & Unwin, 1992, pp. 133⣓46

1915: Einstein’s General Relativity

1921: Wittgenstein’s logical atomism (Tractatus Logico-Philosophicus)

1925–1932: Quantum mechanics

1928–1936: The Vienna Circle and the Berlin Circle . . .

1933: English starts to take over from German as the lingua franca

Positivist doctrines

1. We should not do metaphysics (in Hume’s sense)

2. “sensory observation founds all genuine knowledge”.

3. verificationism: The meaning of a (scientific) statement hassomething to do with the difference it makes to our experiences, at leastin principle.

4. Laws of nature are just our preferred way of describing regularities.

5. Since laws of nature are not fundamental, nor are explanations.

6. The existence or non-existence of unobservable entitiesdoesn’t matter.— Anthony O’Hear, An Introduction to the Philosophy of Science, Oxford: Oxford University Press, 1989, p. 107

Recap: “Principia Mathematica”, 1903 to 1910–1913

The methodology of logical analysis: “The method of ‘postulating’ whatwe want has many advantages; they are the same as the advantages oftheft over honest toil.”— Bertrand Russell, Introduction to Mathematical Philosophy, p. 71

So, instead, define what we want.

Logicism: “The primary aim of Principia Mathematica was to show thatall pure mathematics follows from purely logical premisses and uses onlyconcepts definable in logical terms.”— Bertrand Russell, My Philosophical Development, London: George Allen and Unwin, 1959, p. 74

“The supreme maxim in scientific philosophizing is this:

Wherever possible, logical constructions are to be substitutedfor inferred entities.”

— Bertrand Russell, “The Relation of Sense-data to Physics”, in “Mysticism and Logic”, London: George Allen & Unwin, 1917; reprinted in

Totowa, New Jersey: Barnes & Noble Books, 1951, pp. 108-131. p. 115

Godel destroys the reduction of mathematics to logic

Recall:

Logicism: “The primary aim of Principia Mathematica was to show thatall pure mathematics follows from purely logical premisses and uses onlyconcepts definable in logical terms.”— Bertrand Russell, My Philosophical Development, London: George Allen and Unwin, 1959, p. 74

In 1931, when Godel was 25, he proved (really?) that any consistentaxiomatic mathematical system has indeterminacies.

More precisely — Godel’s First Incompleteness Theorem:

In any consistent formal, algorithmic (recursively enumerable) theorythat includes Peano arithmetic, we can construct an arithmeticalstatement that is true but not provable in the theory.— Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme (On formally undecidable propositions of Principia

Mathematica and related systems), I. Monatshefte fur Mathematik und Physik 1931; 38: 173-98

Godel destroys the reduction of mathematics to logic

Godel’s Theorem completely demolishes logicism

unless we change our logic from the logic of PrincipiaMathematica to something substantially different.

In particular, Godel’s Theorem can’t be proved, and anywaydoesn’t matter, in a paraconsistent logic.

A paraconsistent logic is one which allows for truecontradictions.

Russell on Godel’s Theorem (30 years later)

“In my introduction to the Tractatus, I suggested that, although in anygiven language there are things which that language cannot express, it isyet always possible to construct a language of higher order in whichthese things can be said. There will, in the new language, still be thingswhich it cannot say, but which can be said in the next language, and soon ad infinitum. This suggestion, which was then new, has now becomean accepted commonplace of logic. It disposes of Wittgenstein’smysticism and, I think, also of the newer puzzles presented by Godel.”— Bertrand Russell, My Philosophical Development, London: George Allen and Unwin, 1959, p. 114

Two options:

This construction can be formalised — then it doesn’t work.

It can’t be formalised — then it doesn’t help.

Godel on the analyticity of mathematics

What Godel was opposed to:

“The essence of [the view that mathematics is analytic] is that there is nosuch thing as a mathematical fact, that the truth of propositions whichwe believe express mathematical facts only means that (due to therather complicated rules which define the meaning of propositions, thatis, which determine under what circumstances a proposition is true) anidle running of language occurs in these propositions, in that the saidrules make them true no matter what the facts are. Such propositionscan rightly be called void of content.

. . . the meaning of the terms . . . is asserted to be man-made andconsisting merely in semantical conventions.”— draft V of Godel’s draft manuscript Is Mathematics a Syntax of Language?, in Kurt Godel, Collected Works volume III: Unpublished essays

and lectures. S. Feferman, J. Dawson, S. Kleene, G. Moore, R. Solovay, and J. van Heijenoort (eds.), Oxford: Oxford University Press,

1995; cited at http://plato.stanford.edu/entries/goedel, 12/2/2008

Godel on the analyticity of mathematics

Godel’s response to the above view was that since a mathematicalsystem can’t prove its own consistency (Godel’s SecondIncompleteness Theorem), mathematics can’t be devoid of meaning.

You can’t prove the consistency of mothematics from the inside. . .

and to prove it from the outside, you need(what?)

intuitions (Godel’s preference) or empirical data or somethingwith semantic content.

And you can’t have anything with semantic content if mathematics isdevoid of meaning.

So the necessity for a semantic argument is made explicit andunavoidable.

(Loophole: unless mathematics is inconsistent.)

Russell:phenomenalism &logical atomism

Russell’s reductionism: from maths to physics

“There are many possible ways of turning some things hitherto regardedas ‘real’ into mere laws concerning the other things. Obviously theremust be a limit to this process, or else all the things in the world willmerely be each other’s washing”— Bertrand Russell, “The Analysis of Matter”, 1927, p. 325

Note the pluralism: this is new.

The impact of Einstein on Russell

According to Einstein, “each event had to each other a relation called‘interval,’ which could be analysed in various ways into a time elementand a space element. The choice between these various ways wasarbitrary, and no one of them was theoretically preferable to any other.Given two events A and B, in different regions, it might happen thataccording to one convention they were simultaneous, according toanother A was earlier than B, and according to yet another B was earlierthan A. No physical facts correspond to these different conventions. . . .

What has been thought of as a particle will have to be thought of as aseries of events. . . .

Thus "matter" is not part of the ultimate material of the world, butmerely a convenient way of collecting events into bundles. . . .Quantum theory reinforces this conclusion”— Bertrand Russell, “History of Western Philosophy”, p. 832

This is a rejection of the ontologies of both substance and objects.

See how what was speculative in Hume and Berkeley has now beenendorsed as science by Einstein (who read Hume and Berkeley).

Sometimes I just hate terminology

Russell sometimes referred to his version of empiricism asphenomenalism, and sometimes as logical atomism, especially1911-1924.

The details kept changing. I’m going to focus on Russell’s description ofphenomenalism in “Our Knowledge of the External World” from 1914,and his description of logical atomism in “Logical Atomism” from 1924;but see “The Relation of Sense-data to Physics” (1917) for his views onmaterialism.

Russell distinguished between:

1. sense-data, which are our sensations

= Locke’s phenomena = Hume’s impressions

2. sensibilia, which are potential sense-data

Sense and sensibilia

Russell often (not always) treated sensibilia as material (in Berkeley’ssense):

“What the mind adds to sensibilia, in fact, is merely awareness:everything else is physical or physiological.”

— Bertrand Russell, “The Relation of Sense-data to Physics”, in “Mysticism and Logic”, London: George Allen & Unwin, 1917; reprinted in

Totowa, New Jersey: Barnes & Noble Books, 1951, pp. 108-131. p. 110

Some historians see this as the beginning of Russell’s neutralmonism.

The one thing that is absolutely consistent in Russell’streatment of materialism is his ambivalence!

Later empiricists generally rejected material sensibilia, although not(usually) material objects.

Logicist reductionism

logicism: the reduction of mathematics to logic

. . . + definitions

. . . + maybe other general principles.

Does not necessarily deny the objective reality of mathematical objects(and, in Frege, strongly affirms it).

Logicism is pluralist: it can also be worked out in various differentways.

Phenomenalist reductionism

phenomenalism: the reduction of all knowledge to sensibilia + logic

. . . + definitions

. . . + maybe other general principles such as the principle oflogical analysis itself!

Phenomenalism is pluralist: it can be worked out in various differentways.

Does not necessarily deny the objective reality of physical objects

but does say that objects are parasitic on sensibilia.