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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]
|
19263
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Imagine an object's properties varying; the ones that won't vary are the essential ones
[Husserl, by Vaidya]
|
22221
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We know another's mind via bodily expression, while also knowing it is inaccessible
[Husserl, by Bernet]
|
22220
|
The phenomena of memory are given in the present, but as being past
[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]
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