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All the ideas for 'Philosophy of Mathematics', 'Virtue Ethics: an Introduction' and 'Introduction to German Philosophy'

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16 ideas

2. Reason / A. Nature of Reason / 1. On Reason
20955 Art can make reason more all-inclusive, by articulating what seemed inexpressible [Bowie]
     Full Idea: The early German Romantics argued that art pointed to a more all-inclusive conception of reason, which can offer ways of articulating what is not conceptually accessible.
     From: Andrew Bowie (Introduction to German Philosophy [2003], 5 'Reason')
     A reaction: [This is Novalis, F.Schlegel, Schleiermacher, and Hölderlin] I'm in favour of expanding reason, to include assessment of situations and coherence, rather than just stepwise reasoning. Not sure that art 'articulates' something new.
2. Reason / D. Definition / 8. Impredicative Definition
10882 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
10884 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
10885 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
10881 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)
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
20950 German Idealism says our thinking and nature have the same rational structure [Bowie]
     Full Idea: German Idealism aims to demonstrate that our thinking relates to a nature which is intelligibly structured in the same way as our thinking is structured.
     From: Andrew Bowie (Introduction to German Philosophy [2003], 3 'Limits')
     A reaction: Now that's an idealism I might buy into. Frege thought his logic was mapping rational reality. My angle is that we are a product of this 'reality', so we should expect our thinking to be similarly structured. Reason is derived from nature.
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
20942 Nazis think race predetermines the self [Bowie]
     Full Idea: The Nazi idea is that the self is predetermined primarily by its race.
     From: Andrew Bowie (Introduction to German Philosophy [2003], Intro)
     A reaction: I suspect that I occasionally encounter this view, in very patriotic people. But then you meet people who feeling that their self is mainly determined by support of a football team. Note, though, 'pre-'determined. Hegel makes this idea possible?
19. Language / F. Communication / 1. Rhetoric
20946 Rhetoric is built into language, so it cannot be stripped from philosophy [Bowie]
     Full Idea: The attempt to rid philosophy of rhetoric falls prey precisely to that fact that what is involved in rhetoric is inherent in what is built into all natural languages by their genesis in the real historical world.
     From: Andrew Bowie (Introduction to German Philosophy [2003], 2 'Hamann')
     A reaction: Rhetoric can range from charming to bullying, and it is the latter which is the problem. The underlying issue is dogma versus dialectic. Some analytic philosophers have a good shot at being non-rhetorical.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
5078 Kant and Mill both try to explain right and wrong, without a divine lawgiver [Taylor,R]
     Full Idea: Kant and Mill were in total agreement in trying to give content to the distinction between moral right and wrong, without recourse to any divine lawgiver.
     From: Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.14)
     A reaction: A nice analysis, in tune with MacIntyre and others, who see such attempts as failures. It is hard, however, to deny the claims of rational principles, or of suffering, in our moral framework. I agree with Taylor's move back to virtue, but it ain't simple.
5067 Morality based on 'forbid', 'permit' and 'require' implies someone who does these things [Taylor,R]
     Full Idea: If morality is based on wrong (meaning 'forbidden'), right ('permitted'), and obligatory ('required'), we are led to ask 'Who is it that thus permits, forbids or requires that certain things be done or not done?'
     From: Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.2)
     A reaction: Clear reinforcement for Nietzsche's attack on conventional morals, which Taylor sees as a relic of medieval religious attitudes. Taylor says Kant offered a non-religious version of the same authority. I agree. Back to the Greek pursuit of excellence!
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
5079 Pleasure can have a location, and be momentary, and come and go - but happiness can't [Taylor,R]
     Full Idea: Pleasures can be located in a particular part of the body, and can be momentary, and come and go, but this is not the case with happiness.
     From: Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.16)
     A reaction: Probably no one ever thought that pleasure and happiness were actually identical - merely that pleasure is the only cause and source of happiness. These are good objections to that hypothesis. Pleasure simply isn't 'the good'.
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
5068 'Eudaimonia' means 'having a good demon', implying supreme good fortune [Taylor,R]
     Full Idea: The word 'eudaimonia' means literally 'having a good demon', which is apt, because it suggests some kind of supreme good fortune, of the sort which might be thought of as a bestowal.
     From: Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.5)
     A reaction: Beware of etymology. This implies that eudaimonia is almost entirely beyond a person's control, but Aristotle doesn't think that. A combination of education and effort can build on some natural gifts to create a fully successful life.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
5076 To Greeks it seemed obvious that the virtue of anything is the perfection of its function [Taylor,R]
     Full Idea: To the Greeks it seemed obvious that the virtue of anything is the perfection of its function.
     From: Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.10)
     A reaction: A problem case might be a work of art, but one might reply that there is no obvious perfection there because there is no clear function. For artefacts and organisms the principle seems very good. But 'Is the Cosmos good?'
23. Ethics / D. Deontological Ethics / 1. Deontology
5077 The modern idea of obligation seems to have lost the idea of an obligation 'to' something [Taylor,R]
     Full Idea: In modern moral thinking, obligation is something every responsible person is supposed to have, but it is not an obligation to the state, or society, or humanity, or even to God. It is an obligation standing by itself.
     From: Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.12)
     A reaction: This nicely pinpoints how some our moral attitudes are relics of religion. Taylor wants a return to virtue, but one could respond by opting for the social contract (with very clear obligations) or Kantian 'contractualism' (answering to rational beings).
23. Ethics / D. Deontological Ethics / 2. Duty
5066 If we are made in God's image, pursuit of excellence is replaced by duty to obey God [Taylor,R]
     Full Idea: Once people are declared to be images of God, just by virtue of minimal humanity, they have, therefore, no greater individual excellence to aspire to, and their purpose became one of obligation, that is, obedience to God's will.
     From: Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.2)
     A reaction: An interesting and plausible historical analysis. There is a second motivation for the change, though, in Grotius's desire to develop a more legalistic morality, focusing on actions rather than character. Taylor's point is more interesting, though.
5065 The ethics of duty requires a religious framework [Taylor,R]
     Full Idea: The ethics of duty cannot be sustained independently of a religious framework.
     From: Richard Taylor (Virtue Ethics: an Introduction [2002], Ch.2)
     A reaction: This is a big challenge to Kant, echoing Nietzsche's jibe that Kant just wanted to be 'obedient'. The only options are either 'natural duties', or 'duties of reason'. Reason may have a pull (like pleasure), but a 'duty'? Difficult.