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Single Idea 9837

[filed under theme 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero ]

Full Idea

Husserl contends that 0 is not a number, on the grounds that 'nought' is a negative answer to the question 'how many?'.

Gist of Idea

0 is not a number, as it answers 'how many?' negatively

Source

report of Edmund Husserl (Philosophy of Arithmetic [1894], p.144) by Michael Dummett - Frege philosophy of mathematics Ch.8

Book Ref

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.95

A Reaction

I seem to be in a tiny minority in thinking that Husserl may have a good point. One apple is different from one orange, but no apples are the same as no oranges. That makes 0 a very peculiar number. See Idea 9838.

Related Idea

Idea 9838 Treating 0 as a number avoids antinomies involving treating 'nobody' as a person [Frege, by Dummett]

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]