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Single Idea 9388

[filed under theme 9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects ]

Full Idea

Of any concept, we must require that it have a sharp boundary. Of any object it must hold either that it falls under the concept or it does not. We may not allow a third case in which it is somehow indeterminate whether an object falls under a concept.

Gist of Idea

Every concept must have a sharp boundary; we cannot allow an indeterminate third case

Source

Gottlob Frege (Logic in Mathematics [1914], p.229), quoted by Ian Rumfitt - The Logic of Boundaryless Concepts p.1 n1

A Reaction

This is the voice of the classical logician, which has echoed by Russell. I'm with them, I think, in the sense that logic can only work with precise concepts. The jury is still out. Maybe we can 'precisify', without achieving total precision.

The 20 ideas from 'Logic in Mathematics'

11219 Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta]
16864 If principles are provable, they are theorems; if not, they are axioms [Frege]
16863 Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege]
16862 The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege]
16865 'Theorems' are both proved, and used in proofs [Frege]
16866 Tracing inference backwards closes in on a small set of axioms and postulates [Frege]
16867 Logic not only proves things, but also reveals logical relations between them [Frege]
16868 The essence of mathematics is the kernel of primitive truths on which it rests [Frege]
16871 A truth can be an axiom in one system and not in another [Frege]
16870 Axioms are truths which cannot be doubted, and for which no proof is needed [Frege]
16869 To create order in mathematics we need a full system, guided by patterns of inference [Frege]
16873 Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege]
16872 A thought is the sense expressed by a sentence, and is what we prove [Frege]
16874 The parts of a thought map onto the parts of a sentence [Frege]
16876 We need definitions to cram retrievable sense into a signed receptacle [Frege]
16875 We use signs to mark receptacles for complex senses [Frege]
16877 A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege]
16878 We must be clear about every premise and every law used in a proof [Frege]
16879 A sign won't gain sense just from being used in sentences with familiar components [Frege]
9388 Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege]