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Single Idea 17444

[filed under theme 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation ]

Full Idea

Husserl famously argued that one should not explain number in terms of equinumerosity (or one-one correspondence), but should explain equinumerosity in terms of sameness of number, which should be characterised in terms of counting.

Gist of Idea

Husserl said counting is more basic than Frege's one-one correspondence

Source

report of Edmund Husserl (Philosophy of Arithmetic [1894]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3

Book Ref

-: 'Notre Dame Journal of Formal Logic' [-], p.193

A Reaction

[Heck admits he hasn't read the Husserl] I'm very sympathetic to Husserl, though nearly all modern thinking favours Frege. Counting connects numbers to their roots in the world. Mathematicians seem oblivious of such things.

Related Ideas

Idea 17446 Counting rests on one-one correspondence, of numerals to objects [Frege]

Idea 17451 We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]

The 44 ideas from Edmund Husserl

21226 Husserl sees the ego as a monad, unifying presence, sense and intentional acts [Husserl, by Velarde-Mayol]
21228 Husserl's monads (egos) communicate, through acts of empathy. [Husserl, by Velarde-Mayol]
21225 The psychological ego is worldly, and the pure ego follows transcendental reduction [Husserl, by Velarde-Mayol]
21224 Pure mathematics is the relations between all possible objects, and is thus formal ontology [Husserl, by Velarde-Mayol]
21222 Logicians presuppose a world, and ignore logic/world connections, so their logic is impure [Husserl, by Velarde-Mayol]
21223 Phenomenology grounds logic in subjective experience [Husserl, by Velarde-Mayol]
22216 Phenomenology studies different types of correlation between consciousness and its objects [Husserl, by Bernet]
22218 There can only be a science of fluctuating consciousness if it focuses on stable essences [Husserl, by Bernet]
22217 Phenomenology aims to validate objects, on the basis of intentional intuitive experience [Husserl, by Bernet]
22219 Husserl saw transcendental phenomenology as idealist, in its construction of objects [Husserl, by Bernet]
22220 The phenomena of memory are given in the present, but as being past [Husserl, by Bernet]
19263 Imagine an object's properties varying; the ones that won't vary are the essential ones [Husserl, by Vaidya]
22221 We know another's mind via bodily expression, while also knowing it is inaccessible [Husserl, by Bernet]
22201 The use of mathematical-style definitions in philosophy is fruitless and harmful [Husserl]
22202 The World is all experiencable objects [Husserl]
21218 The sense of anything contingent has a purely apprehensible essence or Eidos [Husserl]
22203 Only facts follow from facts [Husserl]
21221 Direct 'seeing' by consciousness is the ultimate rational legitimation [Husserl]
22204 Start philosophising with no preconceptions, from the intuitively non-theoretical self-given [Husserl]
22205 Feelings of self-evidence (and necessity) are just the inventions of theory [Husserl]
22206 Natural science has become great by just ignoring ancient scepticism [Husserl]
22207 Epoché or 'bracketing' is refraining from judgement, even when some truths are certain [Husserl]
22208 'Bracketing' means no judgements at all about spatio-temporal existence [Husserl]
22210 After everything is bracketed, consciousness still has a unique being of its own [Husserl]
22209 Our goal is to reveal a new hidden region of Being [Husserl]
22211 As a thing and its perception are separated, two modes of Being emerge [Husserl]
21220 The physical given, unlike the mental given, could be non-existing [Husserl]
22212 Pure consciousness is a sealed off system of actual Being [Husserl]
22213 Absolute reality is an absurdity [Husserl]
22214 We never meet the Ego, as part of experience, or as left over from experience [Husserl]
22215 Phenomenology describes consciousness, in the light of pure experiences [Husserl]
21217 Phenomenology needs absolute reflection, without presuppositions [Husserl]
15570 Phenomenology is the science of essences - necessary universal structures for art, representation etc. [Husserl, by Polt]
7614 Bracketing subtracts entailments about external reality from beliefs [Husserl, by Putnam]
6893 Phenomenology aims to describe experience directly, rather than by its origins or causes [Husserl, by Mautner]
21216 Husserl says we have intellectual intuitions (of categories), as well as of the senses [Husserl, by Velarde-Mayol]
17444 Husserl said counting is more basic than Frege's one-one correspondence [Husserl, by Heck]
21214 We clarify concepts (e.g. numbers) by determining their psychological origin [Husserl, by Velarde-Mayol]
9819 Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl]
9851 Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl]
9837 0 is not a number, as it answers 'how many?' negatively [Husserl, by Dummett]
9575 Husserl identifies a positive mental act of unification, and a negative mental act for differences [Husserl, by Frege]
9576 Multiplicity in general is just one and one and one, etc. [Husserl]
3348 If phenomenology is deprived of the synthetic a priori, it is reduced to literature [Benardete,JA on Husserl]