Combining Texts

All the ideas for 'Realistic Rationalism', 'Nietzsche, Genealogy, History' and 'Sets, Aggregates and Numbers'

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15 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Traditionally philosophy is an a priori enquiry into general truths about reality [Katz]
     Full Idea: The traditional conception of philosophy is that it is an a priori enquiry into the most general facts about reality.
     From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xi)
     A reaction: I think this still defines philosophy, though it also highlights the weakness of the subject, which is over-confidence about asserting necessary truths. How could the most god-like areas of human thought be about anything else?
Most of philosophy begins where science leaves off [Katz]
     Full Idea: Philosophy, or at least one large part of it, is subsequent to science; it begins where science leaves off.
     From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxi)
     A reaction: In some sense this has to be true. Without metaphysics there couldn't be any science. Rationalists should not forget, though, the huge impact which Darwin's science has (or should have) on fairly abstract philosophy (e.g. epistemology).
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
     Full Idea: We want to know How many what? You must first partition an aggregate into parts relevant to the question, where no partition is privileged. How the partitioned set is to be numbered is bound up with its unique members, and follows from logic alone.
     From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'New Problem')
     A reaction: [Compressed wording of Yourgrau's summary of Frege's 'relativity argument'] Concepts do the partitioning. Yourgau says this fails, because the same argument applies to the sets themselves, as well as to the original aggregates.
Nothing is 'intrinsically' numbered [Yourgrau]
     Full Idea: Nothing at all is 'intrinsically' numbered.
     From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'What the')
     A reaction: Once you are faced with distinct 'objects' of some sort, they can play the role of 'unit' in counting, so his challenge is that nothing is 'intrinsically' an object, which is the nihilism explored by Unger, Van Inwagen and Merricks. Aristotle disagrees...
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
     Full Idea: The Frege-Maddy definition of number (as the 'property' of being-three) explains why the definitions of Von Neumann, Zermelo and others work, by giving the 'principle of collection' that ties together all threes.
     From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'A Fregean')
     A reaction: [compressed two or three sentences] I am strongly in favour of the best definition being the one which explains the target, rather than just pinning it down. I take this to be Aristotle's view.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
     Full Idea: Sets could hardly serve as a foundation for number theory if we had to await detailed results in the upper reaches of the edifice before we could make our first move.
     From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'Two')
You can ask all sorts of numerical questions about any one given set [Yourgrau]
     Full Idea: We can address a set with any question at all that admits of a numerical reply. Thus we can ask of {Carter, Reagan} 'How many feet do the members have?'.
     From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'On Numbering')
     A reaction: This is his objection to the Fregean idea that once you have fixed the members of a set, you have thereby fixed the unique number that belongs with the set.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz]
     Full Idea: Three objections to realism in philosophy of mathematics: mathematical objects have no space/time location, and so no causal role; that such objects are determinate, but reference to numbers aren't; and that there is no abstract/concrete distinction.
     From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxix)
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz]
     Full Idea: Linguistic meaning is not rich enough to show either that all metaphysical sentences are meaningless or that all alleged synthetic a priori propositions are just analytic a priori propositions.
     From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xx)
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Experience cannot teach us why maths and logic are necessary [Katz]
     Full Idea: The Leibniz-Kant criticism of empiricism is that experience cannot teach us why mathematical and logical facts couldn't be otherwise than they are.
     From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxxi)
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
Feelings are not unchanging, but have a history (especially if they are noble) [Foucault]
     Full Idea: We believe that feelings are immutable, but every sentiment, particularly the most noble and disinterested, has a history.
     From: Michel Foucault (Nietzsche, Genealogy, History [1971], p.86), quoted by Johanna Oksala - How to Read Foucault 5
     A reaction: This is the sort of remark that makes me think Foucault is worth reading. Aristotle thought you could teach correct feelings. That implies that you can also teach incorrect feelings.
19. Language / A. Nature of Meaning / 1. Meaning
Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz]
     Full Idea: In linguistics there are two schools of thought: Bloomfieldian structuralism (favoured by Quine) conceives of sentences acoustically and meanings behaviouristically; and Chomskian generative grammar (which is silent about semantics).
     From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxiv)
     A reaction: They both appear to be wrong, so there is (or was) something rotten in the state of linguistics. Are the only options for meaning either behaviourist or eliminativist?
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
It is generally accepted that sense is defined as the determiner of reference [Katz]
     Full Idea: There is virtually universal acceptance of Frege's definition of sense as the determiner of reference.
     From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxvi)
     A reaction: Not any more, since Kripke and Putnam. It is one thing to say sense determines reference, and quite another to say that this is the definition of sense.
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz]
     Full Idea: Pace Frege, sense determines sense properties and relations, like meaningfulness and synonymy, rather than determining referential properties, like denotation and truth.
     From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxvi)
     A reaction: This leaves room for Fregean 'sense', after Kripke has demolished the idea that sense determines reference.
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
Sentences are abstract types (like musical scores), not individual tokens [Katz]
     Full Idea: Sentences are types, not utterance tokens or mental/neural tokens, and hence sentences are abstract objects (like musical scores).
     From: Jerrold J. Katz (Realistic Rationalism [2000], Int.xxvi)
     A reaction: If sentences are abstract types, then two verbally indistinguishable sentences are the same sentence. But if I say 'I am happy', that isn't the same as you saying it.