Combining Philosophers

All the ideas for Eubulides, Jeffrey H. Sicha and Hermann Minkowski

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7 ideas

5. Theory of Logic / L. Paradox / 1. Paradox
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
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')
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 / 3. Nature of Numbers / d. Natural numbers
The essence of natural numbers must reflect all the functions they perform [Sicha]
     Full Idea: What is really essential to being a natural number is what is common to the natural numbers in all the functions they perform.
     From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)
     A reaction: I could try using natural numbers as insults. 'You despicable seven!' 'How dare you!' I actually agree. The question about functions is always 'what is it about this thing that enables it to perform this function'.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha]
     Full Idea: A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed.
     From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3)
Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha]
     Full Idea: Counting is the activity of putting an initial segment of a serially ordered string in 1-1 correspondence with some other collection of entities.
     From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2)
27. Natural Reality / C. Space / 6. Space-Time
Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski]
     Full Idea: Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
     From: Hermann Minkowski (Space and Time [1908], Intro)
     A reaction: Notice the qualification that it is a 'kind of' union. Deep confusion arises from exaggerating the analogy between space and time. Craig Bourne remarks (2006:157) that this shows independence of measurement, not of reality