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Single Idea 21648

[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism ]

Full Idea

A major flaw of the neo-Fregean program is that it is more impressed by the technical result that Peano Arithmetic can be interpreted by second-order logic plus Hume's Principle, than empirical considerations about how numbers come about.

Gist of Idea

Neo-Fregeans are dazzled by a technical result, and ignore practicalities

Source

Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.3)

Book Ref

Hofweber,Thomas: 'Ontology and the Ambitions of Metaphysics' [OUP 2018], p.159

A Reaction

This doesn't sound like a problem that would bother Fregeans or neo-Fregeans much. Deriving the Peano Axioms from various beginnings has become a parlour game for modern philosophers of mathematics.

The 30 ideas from 'Ontology and the Ambitions of Metaphysics'

21634 Metaphysics is (supposedly) first the ontology, then in general what things are like [Hofweber]
21635 Without propositions there can be no beliefs or desires [Hofweber]
21636 'Singular terms' are not found in modern linguistics, and are not the same as noun phrases [Hofweber]
21637 If two processes are said to be identical, that doesn't make their terms refer to entities [Hofweber]
21638 Syntactic form concerns the focus of the sentence, as well as the truth-conditions [Hofweber]
21639 'Background deletion' is appropriately omitting background from an answer [Hofweber]
21640 'It's true that Fido is a dog' conjures up a contrast class, of 'it's false' or 'it's unlikely' [Hofweber]
21641 Inferential role semantics is an alternative to semantics that connects to the world [Hofweber]
21643 The inferential quantifier focuses on truth; the domain quantifier focuses on reality [Hofweber]
21644 Numbers are used as singular terms, as adjectives, and as symbols [Hofweber]
21645 'Semantic type coercion' is selecting the reading of a word to make the best sense [Hofweber]
21646 The Amazonian Piraha language is said to have no number words [Hofweber]
21647 Logicism makes sense of our ability to know arithmetic just by thought [Hofweber]
21648 Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber]
21649 How can words be used for counting if they are objects? [Hofweber]
21652 Our perceptual beliefs are about ordinary objects, not about simples arranged chair-wise [Hofweber]
21653 Maybe not even names are referential, but are just by used by speakers to refer [Hofweber]
21654 The "Fido"-Fido theory of meaning says every expression in a language has a referent [Hofweber]
21655 Compositonality is a way to build up the truth-conditions of a sentence [Hofweber]
21656 Proposition have no content, because they are content [Hofweber]
21657 Since properties can have properties, some theorists rank them in 'types' [Hofweber]
21658 Properties can be expressed in a language despite the absence of a single word for them [Hofweber]
21659 'Being taller than this' is a predicate which can express many different properties [Hofweber]
21660 Reality can be seen as the totality of facts, or as the totality of things [Hofweber]
21661 There are probably ineffable facts, systematically hidden from us [Hofweber]
21662 Do there exist thoughts which we are incapable of thinking? [Hofweber]
21663 Counterfactuals are essential for planning, and learning from mistakes [Hofweber]
21664 Supervenience offers little explanation for things which necessarily go together [Hofweber]
21666 'Fundamentality' is either a superficial idea, or much too obscure [Hofweber]
21665 The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber]