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All the ideas for 'Philosophy of Mathematics', 'Introduction to 'Personal Identity'' and 'The Sense of Reality'

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9 ideas

1. Philosophy / B. History of Ideas / 1. History of Ideas
The great moments are the death of Aristotle, Machiavelli, and Romanticism [Berlin, by Watson]
     Full Idea: Berlin says there were three great turning points: after the death of Aristotle (when Greek schools focused on the inner life of individuals, instead of as social beings), Machiavelli's division of political and individual virtues, and Romanticism.
     From: report of Isaiah Berlin (The Sense of Reality [1996], p.168-9) by Peter Watson - Ideas Intro
     A reaction: I have the impression that Machiavelli introduced a new hard-boiled ethics, which dominated the sixteenth century, but in the seventeenth and eighteenth century they fought back, and Machiavellianism turned out to be just a phase.
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
     Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.4)
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
     Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.2)
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
     Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds.
     From: Leon Horsten (Philosophy of Mathematics [2007], §5.3)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
     Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept.
     From: Leon Horsten (Philosophy of Mathematics [2007], §2.3)
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
Maybe we should see persons in four dimensions, with stages or time-slices at an instant [Martin/Barresi]
     Full Idea: Some recent philosophers have argued that we should replace the three-dimensional view of persons with a four-dimensional view according to which only time-slices, or 'stages', of persons exist at short intervals of time.
     From: R Martin / J Barresi (Introduction to 'Personal Identity' [2003], p.3)
     A reaction: At first glance this seems to neatly eliminate lots of traditional worries. But why would I want to retain my identity, if someone threatened to brainwash me. I also want to disown my inadequate earlier selves. Interesting, though. Lewis.
Maybe personal identity is not vital in survival, and other continuations would suffice [Martin/Barresi]
     Full Idea: A modern question is whether personal identity is primarily what matters in survival; that is, people might cease and be continued by others whose continuation the original people would value as much.
     From: R Martin / J Barresi (Introduction to 'Personal Identity' [2003], p.3)
     A reaction: When put like this, the proposal seems hard to grasp. It only makes sense if you don't really believe in a thing called 'personal identity'. I don't see how you can believe in it without also believing that for you it has central importance.
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
Locke's intrinsic view of personal identity has been replaced by an externalist view [Martin/Barresi]
     Full Idea: In modern times the Lockean intrinsic relations view of personal identity has been superseded by an extrinsic relations view (also called the 'closest-continuer' or 'externalist' view).
     From: R Martin / J Barresi (Introduction to 'Personal Identity' [2003], p.1)
     A reaction: Sounds sweeping. My suspicion is that there is a raging fashion for externalist views of everything (justification, content etc.), but this will pass. I take Parfit to be the source of the modern views.
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
For Aristotle the psyche perishes with the body (except possibly 'nous') [Martin/Barresi]
     Full Idea: In Aristotle's view, with the possible exception of 'nous' the psyche and all its parts come into being at the same time as its associated body; it is inseparable from the body, and perishes along with it.
     From: R Martin / J Barresi (Introduction to 'Personal Identity' [2003], p.8)
     A reaction: It is suggested that he thought there was only one 'nous', which all humans share (p.9). If he wants to claim that one part is immortal, he doesn't have much evidence. If psyche is the form of the body, it is bound to perish.