14 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. |
| 13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
| Full Idea: Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11 | |
| A reaction: This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out. |
| 18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
| Full Idea: Peano Arithmetic is about any system of entities that satisfies the Peano axioms. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3 | |
| A reaction: This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series. |
| 17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
| Full Idea: Peano's premises are recommended not only by the fact that arithmetic follows from them, but also by their inherent obviousness. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| Full Idea: Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 1.2) by Volker Halbach - Axiomatic Theories of Truth (2005 ver) 1.2 |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| Full Idea: Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 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. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |
| 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. |