more on this theme
|
more from this text
Single Idea 13866
[filed under theme 18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
]
Full Idea
Before we can conclude that φ expresses a sortal concept, we need to ensure that 'is the same φ as' generates statements of genuine identity rather than of some other equivalence relation.
Clarification
Equivalence relations are transitive, symmetric and transitive
Gist of Idea
A concept is only a sortal if it gives genuine identity
Source
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i)
Book Ref
Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.3
Related Idea
Idea 13865
'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C]
The
38 ideas
from Crispin Wright
10142
|
The attempt to define numbers by contextual definition has been revived
[Wright,C, by Fine,K]
|
9868
|
An expression refers if it is a singular term in some true sentences
[Wright,C, by Dummett]
|
7804
|
Wright has revived Frege's discredited logicism
[Wright,C, by Benardete,JA]
|
17441
|
Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are
[Wright,C, by Heck]
|
10140
|
We derive Hume's Law from Law V, then discard the latter in deriving arithmetic
[Wright,C, by Fine,K]
|
8692
|
Frege has a good system if his 'number principle' replaces his basic law V
[Wright,C, by Friend]
|
17440
|
Wright says Hume's Principle is analytic of cardinal numbers, like a definition
[Wright,C, by Heck]
|
9878
|
Contextually defined abstract terms genuinely refer to objects
[Wright,C, by Dummett]
|
13863
|
Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms
[Wright,C]
|
13862
|
There are five Peano axioms, which can be expressed informally
[Wright,C]
|
17853
|
Number truths are said to be the consequence of PA - but it needs semantic consequence
[Wright,C]
|
17854
|
What facts underpin the truths of the Peano axioms?
[Wright,C]
|
13861
|
Number theory aims at the essence of natural numbers, giving their nature, and the epistemology
[Wright,C]
|
13860
|
We can only learn from philosophers of the past if we accept the risk of major misrepresentation
[Wright,C]
|
13867
|
Instances of a non-sortal concept can only be counted relative to a sortal concept
[Wright,C]
|
13869
|
Number platonism says that natural number is a sortal concept
[Wright,C]
|
13870
|
We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism
[Wright,C]
|
13868
|
Sortal concepts cannot require that things don't survive their loss, because of phase sortals
[Wright,C]
|
13865
|
'Sortal' concepts show kinds, use indefinite articles, and require grasping identities
[Wright,C]
|
13866
|
A concept is only a sortal if it gives genuine identity
[Wright,C]
|
13873
|
Treating numbers adjectivally is treating them as quantifiers
[Wright,C]
|
13877
|
Singular terms in true sentences must refer to objects; there is no further question about their existence
[Wright,C]
|
17857
|
We can accept Frege's idea of object without assuming that predicates have a reference
[Wright,C]
|
13882
|
A milder claim is that understanding requires some evidence of that understanding
[Wright,C]
|
13883
|
The best way to understand a philosophical idea is to defend it
[Wright,C]
|
13884
|
The idea that 'exist' has multiple senses is not coherent
[Wright,C]
|
13885
|
If apparent reference can mislead, then so can apparent lack of reference
[Wright,C]
|
13890
|
Entities fall under a sortal concept if they can be used to explain identity statements concerning them
[Wright,C]
|
13888
|
If numbers are extensions, Frege must first solve the Caesar problem for extensions
[Wright,C]
|
13893
|
It is 1-1 correlation of concepts, and not progression, which distinguishes natural number
[Wright,C]
|
13892
|
One could grasp numbers, and name sizes with them, without grasping ordering
[Wright,C]
|
13894
|
Sameness of number is fundamental, not counting, despite children learning that first
[Wright,C]
|
13899
|
The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals
[Wright,C]
|
13896
|
The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes
[Wright,C]
|
13895
|
The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems
[Wright,C]
|
13898
|
If we can establish directions from lines and parallelism, we were already committed to directions
[Wright,C]
|
7320
|
Holism cannot give a coherent account of scientific methodology
[Wright,C, by Miller,A]
|
12189
|
Logical necessity involves a decision about usage, and is non-realist and non-cognitive
[Wright,C, by McFetridge]
|