Combining Philosophers

All the ideas for Brad W. Hooker, Friedrich Schiller and Gerhard Gentzen

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14 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
     Full Idea: Gentzen introduced a natural deduction calculus (NK) in 1934.
     From: report of Gerhard Gentzen (works [1938]) by Stephen Read - Thinking About Logic Ch.8
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
     Full Idea: Gentzen argued that the inferential role of a logical constant constitutes its meaning.
     From: report of Gerhard Gentzen (works [1938]) by Robert Hanna - Rationality and Logic 5.3
     A reaction: Possibly inspired by Wittgenstein's theory of meaning as use? This idea was the target of Prior's famous connective 'tonk', which has the role of implying anything you like, proving sentences which are not logical consequences.
The logical connectives are 'defined' by their introduction rules [Gentzen]
     Full Idea: The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions.
     From: Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8
     A reaction: If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here?
Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
     Full Idea: To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these.
     From: Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III
     A reaction: [1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives.
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
     Full Idea: Gentzen thought that his natural deduction gets at the heart of logical reasoning, and used the sequent calculus only as a convenient tool for proving his chief results.
     From: report of Gerhard Gentzen (Investigations into Logical Deduction [1935]) by Ian Hacking - What is Logic? §05
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
     Full Idea: Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic.
     From: report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5
     A reaction: This does not contradict Gödel's famous result, but reinforces it. The interesting question is what assumptions Gentzen felt he had to make.
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Beauty motivates morality, by harmonising feeling and reason [Schiller, by Pinkard]
     Full Idea: On Schiller's view, only beauty could shape or evince the necessary harmony between sensibility and reason (between inclination and duty) which provides the crucial motivation for the moral life.
     From: report of Friedrich Schiller (works [1794]) by Terry Pinkard - German Philosophy 1760-1860 06
     A reaction: Maybe. Reason should probably be drawn towards feelings which seem inspiring.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
Prescriptivism says 'ought' without commitment to act is insincere, or weakly used [Hooker,B]
     Full Idea: Prescriptivism holds that if you think one 'ought' to do a certain kind of act, and yet you are not committed to doing that act in the relevant circumstances, then you either spoke insincerely, or are using the word 'ought' in a weak sense.
     From: Brad W. Hooker (Prescriptivism [1995], p.640)
     A reaction: So that's an 'ought', but not a 'genuine ought', then? (No True Scotsman move). Someone ought to rescue that drowning child, but I can't be bothered.
23. Ethics / B. Contract Ethics / 2. Golden Rule
Universal moral judgements imply the Golden Rule ('do as you would be done by') [Hooker,B]
     Full Idea: Prescriptivity is especially important if moral judgements are universalizable, for then we can employ golden rule-style reasoning ('do as you would be done by').
     From: Brad W. Hooker (Prescriptivism [1995], p.640)
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
Modern utilitarians value knowledge, friendship, autonomy, and achievement, as well as pleasure [Hooker,B]
     Full Idea: Most utilitarians now think that pleasure, even if construed widely, is not the only thing desirable in itself. ...Goods also include important knowledge, friendship, autonomy, achievement and so on.
     From: Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 2)
     A reaction: That pleasure is desired is empirically verifiable, which certainly motivated Bentham. A string of other desirables each needs to be justified - but how? What would be the value of a 'friendship' if neither party got pleasure from it?
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
Rule-utilitarians prevent things like torture, even on rare occasions when it seems best [Hooker,B]
     Full Idea: For rule-utilitarians acts of murder, torture and so on, can be impermissible even in rare cases where they really would produce better consequences than any alternative act.
     From: Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 4)
     A reaction: It is basic to rule-utilitarianism that it trumps act-ulitilarianism, even when a particular act wins the utilitarian calculation. But that is hard to understand. Only long-term benefit could justify the rule - but that should win the calculation.
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Schiller speaks obsessively of freedom throughout his works [Schiller, by Berlin]
     Full Idea: Schiller constantly speaks of spiritual freedom: freedom of reason, the kingdom of freedom, our free self, inner freedom, freedom of mind, moral freedom, the free intelligence - a very favourite phrase - holy freedom, the impregnable citadel of freedom.
     From: report of Friedrich Schiller (works [1794]) by Isaiah Berlin - The Roots of Romanticism
     A reaction: Kant's philosophy and his Kingdom of Ends are an obvious source for this, but I trace the sentiment back to 'Freeborn John' Lilburne during the English Civil War. The English, thanks to Voltaire, embodied freedom in the Enlightenment.
25. Social Practice / F. Life Issues / 2. Euthanasia
Euthanasia is active or passive, and voluntary, non-voluntary or involuntary [Hooker,B]
     Full Idea: Six types of euthanasia: 1) Active voluntary (knowing my wishes), 2) Active non-voluntary (not knowing my wishes), 3) Active involuntary (against my wishes), 4) Passive voluntary, 5) Passive non-voluntary, 6) Passive involuntary.
     From: Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 5)
     A reaction: 'Active' is intervening, and 'passive' is not intervening. A helpful framework.
Euthanasia may not involve killing, so it is 'killing or not saving, out of concern for that person' [Hooker,B]
     Full Idea: Passive euthanasia is arguably not killing, and the death involved is often painful, so let us take the term 'euthanasia' to mean 'either killing or passing up opportunities to save someone, out of concern for that person'.
     From: Brad W. Hooker (Rule Utilitarianism and Euthanasia [1997], 1)
     A reaction: This sounds good, and easily settled, until you think concern for that person could have two different outcomes, depending on whether the criteria are those of the decider or of the patient. Think of religious decider and atheist patient, or vice versa.