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Single Idea 6409
[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
]
Full Idea
The idea that there should be something like a distinction of levels among properties is captured in Ramsey's 'simple theory of types'.
Gist of Idea
The 'simple theory of types' distinguishes levels among properties
Source
report of Frank P. Ramsey (works [1928]) by A.C. Grayling - Russell
Book Ref
Grayling,A.C.: 'Russell' [OUP 1996], p.31
A Reaction
I merely report this, though it is not immediately obvious how anyone would decide which 'level' a type belonged on.
The
23 ideas
from Frank P. Ramsey
3750
|
"It is true that x" means no more than x
[Ramsey]
|
18818
|
Sentence meaning is given by the actions to which it would lead
[Ramsey]
|
13427
|
Either 'a = b' vacuously names the same thing, or absurdly names different things
[Ramsey]
|
13426
|
Formalists neglect content, but the logicists have focused on generalizations, and neglected form
[Ramsey]
|
13425
|
Formalism is hopeless, because it focuses on propositions and ignores concepts
[Ramsey]
|
13428
|
Reducibility: to every non-elementary function there is an equivalent elementary function
[Ramsey]
|
13430
|
Infinity: there is an infinity of distinguishable individuals
[Ramsey]
|
13334
|
Contradictions are either purely logical or mathematical, or they involved thought and language
[Ramsey]
|
22328
|
I just confront the evidence, and let it act on me
[Ramsey]
|
22325
|
A belief is knowledge if it is true, certain and obtained by a reliable process
[Ramsey]
|
19724
|
Belief is knowledge if it is true, certain, and obtained by a reliable process
[Ramsey]
|
6894
|
Mental terms can be replaced in a sentence by a variable and an existential quantifier
[Ramsey]
|
10993
|
Ramsey's Test: believe the consequent if you believe the antecedent
[Ramsey, by Read]
|
9418
|
All knowledge needs systematizing, and the axioms would be the laws of nature
[Ramsey]
|
9420
|
Causal laws result from the simplest axioms of a complete deductive system
[Ramsey]
|
14279
|
Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge
[Ramsey]
|
19143
|
Ramsey gave axioms for an uncertain agent to decide their preferences
[Ramsey, by Davidson]
|
13766
|
'If' is the same as 'given that', so the degrees of belief should conform to probability theory
[Ramsey, by Ramsey]
|
8494
|
Obviously 'Socrates is wise' and 'Socrates has wisdom' express the same fact
[Ramsey]
|
8495
|
The distinction between particulars and universals is a mistake made because of language
[Ramsey]
|
8493
|
We could make universals collections of particulars, or particulars collections of their qualities
[Ramsey]
|
6409
|
The 'simple theory of types' distinguishes levels among properties
[Ramsey, by Grayling]
|
3212
|
Beliefs are maps by which we steer
[Ramsey]
|