19 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. |
| 16137 | Earlier views of Aristotle were dominated by 'Categories' [Frede,M] |
| Full Idea: For centuries 'Categories' and 'De Interpretatione' (+ Porphyry's 'Isagoge') formed the core of the philosophical corpus still being seriously studied. It is hardly surprising that our received view of Aristotle was coloured substantially by 'Categories'. | |
| From: Michael Frede (Title, Unity, Authenticity of the 'Categories' [1983], I) | |
| A reaction: He adds that doubts remain about the authenticity of the second part, and the whole thing bears marks of having been edited. |
| 23249 | The early philosophers thought that reason has its own needs and desires [Frede,M] |
| Full Idea: It is part of the notion of reason according to these philosophers [Socrates, Plato, Aristotle, Stoics] that reason has its own needs and desires. | |
| From: Michael Frede (Intro to 'Rationality in Greek Thought' [1996], p.5) | |
| A reaction: This sounds as if reason is treated as a separate person within a person. Anyone solving a logical puzzle feels that reason has its own compulsion. 'Boulesis' is the desire characteristic of reason. |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| Full Idea: Many axioms have been proposed, not on the grounds that they can be directly known, but rather because they produce a desired body of previously recognised results. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.5.1) | |
| A reaction: This is the perennial problem with axioms - whether we start from them, or whether we deduce them after the event. There is nothing wrong with that, just as we might infer the existence of quarks because of their results. |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
| Full Idea: Mathematical realism is the doctrine that mathematical objects exist, that much contemporary mathematics is true, and that the existence and truth in question is independent of our constructions, beliefs and proofs. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.12.9) | |
| A reaction: As thus defined, I would call myself a mathematical realist, but everyone must hesitate a little at the word 'exist' and ask, how does it exist? What is it 'made of'? To say that it exists in the way that patterns exist strikes me as very helpful. |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| Full Idea: In maths the primary subject-matter is not mathematical objects but structures in which they are arranged; our constants and quantifiers denote atoms, structureless points, or positions in structures; they have no identity outside a structure or pattern. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.1) | |
| A reaction: This seems to me a very promising idea for the understanding of mathematics. All mathematicians acknowledge that the recognition of patterns is basic to the subject. Even animals recognise patterns. It is natural to invent a language of patterns. |
| 6303 | Sets are positions in patterns [Resnik] |
| Full Idea: On my view, sets are positions in certain patterns. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.5) | |
| A reaction: I have always found the ontology of a 'set' puzzling, because they seem to depend on prior reasons why something is a member of a given set, which cannot always be random. It is hard to explain sets without mentioning properties. |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| Full Idea: An objection is that structuralism fails to explain why certain mathematical patterns are unified wholes while others are not; for instance, some think that an ontological account of mathematics must explain why a triangle is not a 'random' set of points. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.4) | |
| A reaction: This is an indication that we are not just saying that we recognise patterns in nature, but that we also 'see' various underlying characteristics of the patterns. The obvious suggestion is that we see meta-patterns. |
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| Full Idea: If we take mathematics at its word, there are too many mathematical objects for it to be plausible that they are all mental or physical objects. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: No one, of course, has ever claimed that they are, but this is a good starting point for assessing the ontology of mathematics. We are going to need 'rules', which can deduce the multitudinous mathematical objects from a small ontology. |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| Full Idea: I argue that mathematical knowledge has its roots in pattern recognition and representation, and that manipulating representations of patterns provides the connection between the mathematical proof and mathematical truth. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], One.1) | |
| A reaction: The suggestion that patterns are at the basis of the ontology of mathematics is the most illuminating thought I have encountered in the area. It immediately opens up the possibility of maths being an entirely empirical subject. |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| Full Idea: Of the equivalence relationships which occur between patterns, congruence is the strongest, equivalence the next, and mutual occurrence the weakest. None of these is identity, which would require the same position. | |
| From: Michael D. Resnik (Maths as a Science of Patterns [1997], Three.10.3) | |
| A reaction: This gives some indication of how an account of mathematics as a science of patterns might be built up. Presumably the recognition of these 'degrees of strength' cannot be straightforward observation, but will need an a priori component? |
| 16157 | Insurance on the original ship would hardly be paid out if the plank version was wrecked! [Frede,M] |
| Full Idea: No insurance company, presented with a policy written for 'Theoris' [the original ship] would pay for damages suffered if the ship contructed from the old planks had been shipwrecked. | |
| From: Michael Frede (Individuals in Aristotle [1978]) | |
| A reaction: A very nicely dramatic way of presenting what is taken to be the usual reading of the basic case - that the original identity tracks the continuity of the original structure, not the matter. |
| 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. |
| 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. |
| 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. |
| 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. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |