more on this theme
|
more from this text
Single Idea 16902
[filed under theme 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
]
Full Idea
In the Peano axiomatisation, arithmetic seems primitively to involve the thought that 0 is a number.
Gist of Idea
Peano arithmetic requires grasping 0 as a primitive number
Source
Tyler Burge (Frege on Apriority (with ps) [2000], 5)
Book Ref
Burge,Tyler: 'Truth, Thought, Reason (on Frege)' [OUP 2001], p.385
A Reaction
Burge is pointing this out as a problem for Frege, for whom only the logic is primitive.
The
14 ideas
from Tyler Burge
|
9382
|
Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications'
[Burge]
|
|
16892
|
Is apriority predicated mainly of truths and proofs, or of human cognition?
[Burge]
|
|
16901
|
The equivalent algebra model of geometry loses some essential spatial meaning
[Burge]
|
|
16902
|
Peano arithmetic requires grasping 0 as a primitive number
[Burge]
|
|
9159
|
You can't simply convert geometry into algebra, as some spatial content is lost
[Burge]
|
|
17622
|
We come to believe mathematical propositions via their grounding in the structure
[Burge]
|
|
13479
|
Given that thinking aims at truth, logic gives universal rules for how to do it
[Burge]
|
|
3115
|
Are meaning and expressed concept the same thing?
[Burge, by Segal]
|
|
14349
|
If there are no finks or antidotes at the fundamental level, the laws can't be ceteris paribus
[Burge, by Corry]
|
|
8126
|
Anti-individualism says the environment is involved in the individuation of some mental states
[Burge]
|
|
8127
|
Broad concepts suggest an extension of the mind into the environment (less computer-like)
[Burge]
|
|
8129
|
Anti-individualism may be incompatible with some sorts of self-knowledge
[Burge]
|
|
8131
|
Some qualities of experience, like blurred vision, have no function at all
[Burge]
|
|
8132
|
We now have a much more sophisticated understanding of logical form in language
[Burge]
|