logicism love

# logicism

## Definitions

• n. The doctrine that mathematics is a branch of logic in that some or all mathematics is reducible to logic.

• n. (philosophy) the philosophical theory that all of mathematics can be derived from formal logic

## Etymologies

Sorry, no etymologies found.

## Examples

• The rejoinder to this is that the similarity that Frascolla, Black and Savitt recognize does not make Wittgenstein's theory a “kind of logicism” in Frege's or Russell's sense, because Wittgenstein does not define numbers “logically” in either Frege's way or Russell's way, and the similarity (or analogy) between tautologies and true mathematical equations is neither an identity nor a relation of reducibility.

Wittgenstein's Philosophy of Mathematics

• “the philosophy of arithmetic of the Tractatus ¦ as a kind of logicism” (Frascolla, 1994, 37).

Wittgenstein's Philosophy of Mathematics

• This attitude allowed him to accommodate various ideas coming from rival foundational directions, that is, logicism, formalism and intuitionism.

Lvov-Warsaw School

• A principled demarcation of logical constants might offer an answer to this question, thereby clarifying what is at stake in philosophical controversies for which it matters what counts as logic (for example, logicism and structuralism in the philosophy of mathematics).

Logical Constants

• Tarski also showed new perspectives for logicism by defining logical concepts as invariants under one-to-one transformations.

Lvov-Warsaw School

• No. To see why it is not, notice that the ascription of limitations and confusions to his logical theory depends almost entirely on taking a special point of view on the nature of logic, namely the viewpoint of Fregean and Russellian logicism, which posits the reducibility of mathematics (or at least arithmetic) to some version of second-order logic.

Kant's Theory of Judgment

• Fregean logicism is just one way in which this template can be developed; some other ways will be mentioned below.

Platonism in the Philosophy of Mathematics

• The slide towards this sort of formalist attitude to axioms can also be traced through Frege's logicism.

Non-Deductive Methods in Mathematics

• Pragmatism's injunction to abandon metaphysics might then be thought of as setting the stage for the radically different idioms of Heidegger's ontology and Carnap's logicism, or what is sometimes called the Continental/analytic divide.

enowning

• PFO alone does not have sufficient expressive power to accommodate the needs of neo-logicism.

Plural Quantification