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Single Idea 9135

[filed under theme 5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic ]

Full Idea

As philosophers gradually freed themselves from the assumption that all words are names, ..they realised that generalizations really use variables rather than names of abstract entities.

Gist of Idea

We now see that generalizations use variables rather than abstract entities

Source

Roy Sorensen (Vagueness and Contradiction [2001], 8.4)

Book Ref

Sorensen,Roy: 'Vagueness and Contradiction' [OUP 2004], p.132

A Reaction

This looks like a key thought in trying to understand abstraction - though I don't think you can shake it off that easily. (For all x)(x-is-a-bird then x-has-wings) seems to require a generalised concept of a bird to give a value to the variable.

The 20 ideas from 'Vagueness and Contradiction'

9119 No attempt to deny bivalence has ever been accepted [Sorensen]
9116 Vague words have hidden boundaries [Sorensen]
9118 The colour bands of the spectrum arise from our biology; they do not exist in the physics [Sorensen]
9121 Illusions are not a reason for skepticism, but a source of interesting scientific information [Sorensen]
9137 Banning self-reference would outlaw 'This very sentence is in English' [Sorensen]
9139 If nothing exists, no truthmakers could make 'Nothing exists' true [Sorensen]
9140 Which toothbrush is the truthmaker for 'buy one, get one free'? [Sorensen]
9122 God cannot experience unwanted pain, so God cannot understand human beings [Sorensen]
9125 Denying problems, or being romantically defeated by them, won't make them go away [Sorensen]
9124 We are unable to perceive a nose (on the back of a mask) as concave [Sorensen]
9126 Bayesians build near-certainty from lots of reasonably probable beliefs [Sorensen]
9128 It is propositional attitudes which can be a priori, not the propositions themselves [Sorensen]
9130 Attributing apriority to a proposition is attributing a cognitive ability to someone [Sorensen]
9129 I can buy any litre of water, but not every litre of water [Sorensen]
9131 Two long understandable sentences can have an unintelligible conjunction [Sorensen]
9132 An offer of 'free coffee or juice' could slowly shift from exclusive 'or' to inclusive 'or' [Sorensen]
9133 Propositions are what settle problems of ambiguity in sentences [Sorensen]
9134 The negation of a meaningful sentence must itself be meaningful [Sorensen]
9135 We now see that generalizations use variables rather than abstract entities [Sorensen]
9136 The paradox of analysis says that any conceptual analysis must be either trivial or false [Sorensen]