Combining Texts

All the ideas for 'fragments/reports', 'Structure and Ontology' and 'Notes on Comments by Fardella'

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6 ideas

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).

9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual

13160	To exist and be understood, a multitude must first be reduced to a unity [Leibniz]
	Full Idea: A plurality of things can neither be understood nor can exist unless one first understands the thing that is one, that to which the multitude necessarily reduces.
	From: Gottfried Leibniz (Notes on Comments by Fardella [1690], Prop 3)
	A reaction: Notice that it is our need to understand which imposes the unity on the multitude. It is not just some random fiction, or a meaningless mechanical act of thought.

9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance

13161	Substances are everywhere in matter, like points in a line [Leibniz]
	Full Idea: There are substances everywhere in matter, just as points are everywhere in a line.
	From: Gottfried Leibniz (Notes on Comments by Fardella [1690], Clarif)
	A reaction: Since Leibniz is unlikely to believe in the reality of the points, we must wonder whether he was really committed to this infinity of substances. The more traditional notion of substance is always called 'substantial form' by Leibniz.

18. Thought / E. Abstraction / 3. Abstracta by Ignoring

9626	A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro]
	Full Idea: A structure is the abstract form of a system, focussing on the interrelationships among the objects, and ignoring any features of them that do not affect how they relate to other objects in the system.
	From: Stewart Shapiro (Structure and Ontology [1989], 146), quoted by James Robert Brown - Philosophy of Mathematics Ch.4
	A reaction: I find this account very attractive, even though it appeals to supposedly outmoded psychological abstractionism. It seems pretty close to Aristotle's view of things. Shapiro's account must face up to Frege's worries about these matters.