logicism: the seminal work by Frege and Russell identifying mathematics with logic logical atomism: first attempts by Wittgenstein and Russell to export lessons from the new logic into a general philosophical context

logical positivism: the "Vienna Circle" attempt to assasinate metaphysics. Formality and syntax become more conspicuous in analytic method. linguistic analysis: formality into the wilderness as the influence of the later Wittgenstein pushes common discourse front stage

formal analysis: our proposed new analytic method, appropriately formal, shorn of empiricist excess, presented in comparison with its ill-fated predecessors.

Logicism: see also: logicism

mathematics is analytic concepts definable and principles derivable from logical concepts and principles

Mathematics Only, logicism is an initial triumph of analysis applied to mathematics using Frege's new logic Begriffschrift, the greatest advance in logic since Aristotle, finally delivers a formal logic adequate for the derivation of mathematics

definability: concepts are shown to be definable in term of a small number of logical and set theoretic concepts derivability: theorems are shown to be derivable by a fixed set of rules from a small number of logical and set theoretic axioms

analysis: is reductionist in logical and ontological terms loose ends: arise from reservations about the logical status of ontological principles and from the essential incompleteness of formal systems, shown later by Gödel

Logical Atomism:

sentences are analysed as truth functional combinations of atomic propositions atomic propositions are pictures of atomic facts of which the world is made

What must the world be like? given what we have learnt of the logical structure of language from the new logics? Semantics: can we learn anything of the nature of the world by semantic analysis of language?

Linguistic Analysis: of sentences as truth functions of atomic propositions Metaphysical Analysis: of the world as a collection of atomic facts, of which atomic propositions are pictures

Metaphysics Pruned, by vigorous application of occams razor Empiricism possibly through the identification of atomic facts and sense data

Logical Positivism: see: Carnap's Syntactical Method

the verification principle eliminates metaphysics formal analysis advocated philosophical statements into the formal mode

new position on semantics, in which the meaning of a sentence is identified with its mode of verification syntactic analysis, is advocated, yielding a classification of meaningful sentences as analytic synthetic or contradictory

scientific statements: must be synthetic and empirically verifiable philosophical statements: must be analytic, are therefore about language and best presented in "the formal mode", i.e. explicitly about language

metaphysics, is a term of abuse applied to anything which is neither verifiable nor analytic, and henceforth is synonymous with meaningless

Linguistic Analysis:

formality into the wilderness as the influence of the later Wittgenstein pushes "ordinary language" front stage

formality out formal logical systems are no longer regarded as good models of natural languages or as ideal languages

analysis for clarification: ordinary language is analysed to clarify its meaning, eliminating confusions that sometimes arise philosophy not special? philosophers not supposed to deliver a priori or analytic truths, these and other classifications come to be regarded with suspicion

diversity of language is emphasised, including purposes other than description, distancing natural from formal languages no systematic theories it is no longer necessary for philosophers to put forward theories, they can now rest content with pulling them down

Formal Analysis:

our proposed new analytic method, appropriately formal, shorn of empiricist excess, presented in comparison with its ill-fated predecessors.

formal analysis yields analytic truths, we deliberately focus down on this special kind of knowledge through analysis empiricism limited to the a priori/analytic and a posteriori/synthetic identifications, no phenomenalistic analysis

deductive reasoning, wherever it appears, can be validated by formalisation precision of language can be reached through formal abstract modelling metaphysics is OK: choices of how to model concrete objects using abstract

focus on abstract modelling: abstract modelling makes clear the domain in which an argument holds good arbitrary abstract ontology: within bounds of consistency, abstract ontology is choice of subject matter

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© created 1997/12/27 modified 1997/12/28