Combining Texts

All the ideas for 'Leibniz', 'Rechnungsmethoden (dissertation)' and 'Does Moral Subjectivism Rest on a Mistake?'

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6 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
18256 Quantity is inconceivable without the idea of addition [Frege]
     Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former.
     From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit'
     A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree.
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9831 Geometry appeals to intuition as the source of its axioms [Frege]
     Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms.
     From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics
     A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged.
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
7566 The Identity of Indiscernibles is really the same as the verification principle [Jolley]
     Full Idea: Various writers have noted that the Identity of Indiscernibles is really tantamount to the verification principle.
     From: Nicholas Jolley (Leibniz [2005], Ch.3)
     A reaction: Both principles are false, because they are the classic confusion of epistemology and ontology. The fact that you cannot 'discern' a difference between two things doesn't mean that there is no difference. Things beyond verification can still be discussed.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / f. Ethical non-cognitivism
22485 Non-cognitivists give the conditions of use of moral sentences as facts about the speaker [Foot]
     Full Idea: What all these [non-cognitivist] theories try to do is to give the conditions of use of sentences such as 'It is morally objectionable to break promises', in terms of something which must be true about the speaker.
     From: Philippa Foot (Does Moral Subjectivism Rest on a Mistake? [1995], p.192)
     A reaction: A wonderfully simple and accurate analysis of this view. Compare analysing 'there is a bus coming towards you' in the same way. Sounds silly, but lots of modern philosophers see things that way.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
22486 The mistake is to think good grounds aren't enough for moral judgement, which also needs feelings [Foot]
     Full Idea: The mistake is to think that whatever 'grounds' for a moral judgement may have been given, someone may be unready, indeed unable, to make the moral judgement, because he has not got the attitude or feeling.
     From: Philippa Foot (Does Moral Subjectivism Rest on a Mistake? [1995], p.192)
     A reaction: This is roughly the Frege-Geach problem for expressivism, of how we still make moral judgements about situations where we ourselves are entirely disinterested (such as ancient historical events).
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
22487 Moral arguments are grounded in human facts [Foot]
     Full Idea: The grounding of a moral argument is ultimately in facts about human life.
     From: Philippa Foot (Does Moral Subjectivism Rest on a Mistake? [1995], p.207)
     A reaction: The best slogan I can find for summarising Foot's metaethics. The facts she refers to the basic human needs. She is right, and this almost bridges the fact-value divide (as long as you give a damn about human needs).