Combining Philosophers

All the ideas for Eubulides, Michael Faraday and Nicholas P. White

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6 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17813	Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
	Full Idea: The Löwenheim-Skolem theorem tells us that any theory with a true interpretation has a model in the natural numbers.
	From: Nicholas P. White (What Numbers Are [1974], V)

5. Theory of Logic / L. Paradox / 1. Paradox

6007	If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
	Full Idea: The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person.
	From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
	A reaction: Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976).

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox

6006	If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
	Full Idea: The liar paradox of Eubulides says 'if you state that you are lying, and state the truth, then you are lying'.
	From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
	A reaction: (also Cic. Acad. 2.95) Don't say it, then. These kind of paradoxes of self-reference eventually lead to Russell's 'barber' paradox and his Theory of Types.

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')

6008	Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
	Full Idea: The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap.
	From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School
	A reaction: (also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213).

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17812	Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
	Full Idea: Statements involving finite cardinalities can be made without treating numbers as objects at all, simply by using quantification and identity to define numerically definite quantifiers in the manner of Frege.
	From: Nicholas P. White (What Numbers Are [1974], IV)
	A reaction: [He adds Quine 1960:268 as a reference]

27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields

15314	Faraday's single field of variable forces introduces a criterion of Unity into what is ultimate [Faraday, by Harré/Madden]
	Full Idea: In Faraday lines of force picture the directional structure of powers,...so the fundamental entity is a single, unified field. ...A new criterion of the ultimate has stepped in: Unity. The universal field is still the final explanation, but not invariant.
	From: report of Michael Faraday (Experimental Researches in Electricity [1859]) by Harré,R./Madden,E.H. - Causal Powers 9.II.B
	A reaction: Almost Parmenides, except that the field is not invariant. But that was always the ancient objection to the One - that it offered no explanation of change.