13 ideas
| 23326 | In the third century Stoicism died out, replaced by Platonism, with Aristotelian ethics [Frede,M] |
| Full Idea: By the second century CE Aristotelianism and Platonism had begun to eclipse Stoicism, and by the end of the third century Stoicism had no followers. All philosophers now opted for some form of Platonism, but including Aristotle's ethical principles. | |
| From: Michael Frede (A Free Will [1997], 04) | |
| A reaction: The idea that Aristotelian ethics dominated that period is new to me. Stoic influence remained strong in Augustine, and hence in Christianity. |
| 23335 | In late antiquity nearly all philosophers were monotheists [Frede,M] |
| Full Idea: I am inclined to think that almost all philosophers in late antiquity were monotheists. | |
| From: Michael Frede (A Free Will [1997], 08) | |
| A reaction: I'm not sure when late antiquity begins, in this remark. Maybe as early as 100 CE. Epictetus talks of Zeus as if he is supreme. |
| 11022 | 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 |
| 11065 | 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. |
| 11023 | 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? |
| 11213 | 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. |
| 10067 | 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. |
| 23333 | The idea of free will achieved universal acceptance because of Christianity [Frede,M] |
| Full Idea: There is no doubt that the notion of a free will found almost universal acceptance owing to the influence of Christianity. | |
| From: Michael Frede (A Free Will [1997], 07) | |
| A reaction: This is presumably because a free will not only elevates us above the animals, qualifying us for immortality, but also gives us absolute and ultimate responsibility for our lives, which thus justifies either salvation or damnation. |
| 23337 | The Stoics needed free will, to allow human choices in a divinely providential cosmos [Frede,M] |
| Full Idea: The Stoics said that everything happens according to a divine providential plan, so they had to explain how this was compatible with human choices. They tried to do this with their doctrine of freedom and a free will. | |
| From: Michael Frede (A Free Will [1997], 10) | |
| A reaction: Epictetus made our ability to choose central to moral life, so he particularly needed (and thus created, it seems) this doctrine. |
| 23334 | For Christians man has free will by creation in God's image (as in Genesis) [Frede,M] |
| Full Idea: The Christian view, following Genesis, is that man is created in the image of God, and this is understood as crucially involving the idea that man has a free will in the image of God's will. | |
| From: Michael Frede (A Free Will [1997], 08) | |
| A reaction: The idea of free will evidently originated with Epictetus, but was taken up by Christians because it fitted doctrinal needs. Even Epictetus saw free will as originating in Zeus. |
| 23336 | There is no will for Plato or Aristotle, because actions come directly from perception of what is good [Frede,M] |
| Full Idea: Plato and Aristotle do not have a notion of a will, since for them a willing, a desire of reason, is a direct result of one's cognitive state: once one sees something to be good, one will it. | |
| From: Michael Frede (A Free Will [1997], 09) | |
| A reaction: The point is that their decisions are 'direct', whereas the will introduces the concept of a final arbiter which weighs up the desires, reasons and drives. The historical steps were first the meta-choosing, then the will as entity, then the will as free. |
| 9425 | Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis] |
| Full Idea: Later Lewis said we must choose between the intersection of the axioms of the tied best systems. He chose for laws the axioms that are in all the tied systems (but then there may be few or no axioms in the intersection). | |
| From: comment on David Lewis (Subjectivist's Guide to Objective Chance [1980], p.124) by Stephen Mumford - Laws in Nature |
| 23313 | The Gnostic demiurge (creator) is deluded, and doesn't care about us [Frede,M] |
| Full Idea: The Gnostics thought the demiurge or creator pursues its own interests without regard for what this does to us, a being lacking in wisdom and goodness, as seen by its deluding itself into thinking that it is God, and demanding worship. | |
| From: Michael Frede (A Free Will [1997], Intro) | |
| A reaction: Frede mentions Irenaeus as a source of this view. The idea that the Great Being doesn't care about us seems a fairly accurate observation. |