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Single Idea 18168
[filed under theme 5. Theory of Logic / E. Structures of Logic / 1. Logical Form
]
Full Idea
A 'propositional function' is generated when one of the terms of the proposition is replaced by a variable, as in 'x is wise' or 'Socrates'.
Gist of Idea
'Propositional functions' are propositions with a variable as subject or predicate
Source
Penelope Maddy (Naturalism in Mathematics [1997], I.1)
Book Ref
Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.9
A Reaction
This implies that you can only have a propositional function if it is derived from a complete proposition. Note that the variable can be in either subject or in predicate position. It extends Frege's account of a concept as 'x is F'.
The
36 ideas
with the same theme
[structure of a sentence relevant to its logical role]:
18896
|
Aristotle places terms at opposite ends, joined by a quantified copula
[Aristotle, by Sommers]
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4730
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For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality
[Aristotle, by O'Grady]
|
21400
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Stoics avoided universals by paraphrasing 'Man is...' as 'If something is a man, then it is...'
[Stoic school, by Long]
|
6020
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'Man is a rational mortal animal' is equivalent to 'if something is a man, that thing is a rational mortal animal'
[Sext.Empiricus]
|
7729
|
Frege replaced Aristotle's subject/predicate form with function/argument form
[Frege, by Weiner]
|
4975
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A thought can be split in many ways, so that different parts appear as subject or predicate
[Frege]
|
8645
|
Convert "Jupiter has four moons" into "the number of Jupiter's moons is four"
[Frege]
|
6115
|
Vagueness, and simples being beyond experience, are obstacles to a logical language
[Russell]
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7528
|
Leibniz bases everything on subject/predicate and substance/property propositions
[Russell]
|
7758
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'Elizabeth = Queen of England' is really a predication, not an identity-statement
[Russell, by Lycan]
|
6092
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In a logically perfect language, there will be just one word for every simple object
[Russell]
|
6101
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Romulus does not occur in the proposition 'Romulus did not exist'
[Russell]
|
18276
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A statement's logical form derives entirely from its constituents
[Wittgenstein]
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18743
|
Wittgenstein says we want the grammar of problems, not their first-order logical structure
[Wittgenstein, by Horsten/Pettigrew]
|
18268
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Apparent logical form may not be real logical form
[Wittgenstein]
|
22434
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Reduction to logical forms first simplifies idioms and grammar, then finds a single reading of it
[Quine]
|
8358
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There are no rules for the exact logic of ordinary language, because that doesn't exist
[Strawson,P]
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18893
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Translating into quantificational idiom offers no clues as to how ordinary thinkers reason
[Sommers]
|
7332
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There is a huge range of sentences of which we do not know the logical form
[Davidson]
|
3080
|
Logical form is the part of a sentence structure which involves logical elements
[Harman]
|
3081
|
A theory of truth in a language must involve a theory of logical form
[Harman]
|
3084
|
Our underlying predicates represent words in the language, not universal concepts
[Harman]
|
16464
|
We regiment to get semantic structure, for evaluating arguments, and understanding complexities
[Stalnaker]
|
8132
|
We now have a much more sophisticated understanding of logical form in language
[Burge]
|
6339
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Logical form is the aspects of meaning that determine logical entailments
[Horwich]
|
2544
|
Thoughts have a dual aspect: as they seem to introspection, and their underlying logical reality
[McGinn]
|
8072
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Sentences of apparent identical form can have different contextual meanings
[Devlin]
|
12220
|
Is it the sentence-token or the sentence-type that has a logical form?
[Fine,K]
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13632
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Finding the logical form of a sentence is difficult, and there are no criteria of correctness
[Shapiro]
|
18168
|
'Propositional functions' are propositions with a variable as subject or predicate
[Maddy]
|
10407
|
Logical Form explains differing logical behaviour of similar sentences
[Swoyer]
|
10373
|
Logical form can't dictate metaphysics, as it may propose an undesirable property
[Schaffer,J]
|
10754
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In proof-theory, logical form is shown by the logical constants
[Rossberg]
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18741
|
Logical formalization makes concepts precise, and also shows their interrelation
[Horsten/Pettigrew]
|
18905
|
Propositions can be analysed as pairs of terms glued together by predication
[Engelbretsen]
|
18922
|
Logical syntax is actually close to surface linguistic form
[Engelbretsen]
|