37 ideas
13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
Full Idea: There are four 'perfect syllogisms': Barbara (every M is P, every S is M, so every S is P); Celarent (no M is P, every S is M, so no S is P); Darii (every M is P, some S is M, so some S is P); Ferio (no M is P, some S is M, so some S is not P). | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
A reaction: The four names are mnemonics from medieval universities. |
13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
Full Idea: It has often been claimed (e.g. by Leibniz) that a single rule governs all syllogistic validity, called 'dictum de omni et null', which says that what is affirmed or denied of any whole is affirmed or denied of any part of that whole. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
A reaction: This seems to be the rule which is captured by Venn Diagrams. |
13915 | Syllogistic can't handle sentences with singular terms, or relational terms, or compound sentences [Engelbretsen/Sayward] |
Full Idea: Three common kinds of sentence cannot be put into syllogistic ('categorical') form: ones using singular terms ('Mars is red'), ones using relational terms ('every painter owns some brushes'), and compound sentences. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) |
13916 | Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward] |
Full Idea: Term logic begins with expressions and two 'term functors'. Any simple letter is a 'term', any term prefixed by a minus ('-') is a 'negative term', and any pair of terms flanking a plus ('+') is a 'compound term'. Parenthese are used for grouping. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8) | |
A reaction: [see Engelbretsen and Sayward for the full formal system] |
13850 | In modern logic all formal validity can be characterised syntactically [Engelbretsen/Sayward] |
Full Idea: One of the key ideas of modern formal logic is that all formally valid inferences can be specified in strictly syntactic terms. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.2) |
13849 | Classical logic rests on truth and models, where constructivist logic rests on defence and refutation [Engelbretsen/Sayward] |
Full Idea: Classical logic rests on the concepts of truth and falsity (and usually makes use of a semantic theory based on models), whereas constructivist logic accounts for inference in terms of defense and refutation. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Intro) | |
A reaction: My instincts go with the classical view, which is that inferences do not depend on the human capacity to defend them, but sit there awaiting revelation. My view isn't platonist, because I take the inferences to be rooted in the physical world. |
13851 | Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward] |
Full Idea: Unlike ∨, →, ↔, and ∀, the sign = is not eliminable from a logic. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], Ch.3) |
13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |
Full Idea: A set of axioms is said to be ω-incomplete if, for some universal quantification, each of its instances is derivable from those axioms but the quantification is not thus derivable. | |
From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 7) |
21382 | Things get smaller without end [Anaxagoras] |
Full Idea: Of the small there is no smallest, but always a smaller. | |
From: Anaxagoras (fragments/reports [c.460 BCE], B03), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras II | |
A reaction: Anaxagoras seems to be speaking of the physical world (and probably writing prior to the emergence of atomism, which could have been a rebellion against he current idea). |
481 | Nothing is created or destroyed; there is only mixing and separation [Anaxagoras] |
Full Idea: No thing comes into being or passes away, but it is mixed together or separated from existing things. Thus it would be correct if coming into being was called 'mixing', and passing away 'separation-off''. | |
From: Anaxagoras (fragments/reports [c.460 BCE], B17), quoted by Simplicius - On Aristotle's 'Physics' 163.20 |
21822 | Anaxagoras's concept of supreme Mind has a simple First and a multiple One [Anaxagoras, by Plotinus] |
Full Idea: Anaxagoras, in his assertion of a Mind pure and unmixed, affirms a simplex First and a sundered One, though writing long ago he failed in precision. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plotinus - The Enneads 5.1.09 | |
A reaction: The crunch question is whether the supreme One or Mind is part of Being, or is above and beyond Being. Plotinus claims that Anaxagoras was on his side (with Plato, against Parmenides). |
17995 | Basic is the potentially perceptible, then comes the contrary qualities, and finally the 'elements' [Anaxagoras] |
Full Idea: We must recognise three 'originative sources': first that which is potentially perceptible body, secondly the contrarities (e.g hot and cold), and thirdly Fire, Water, and the like. Only thirdly, however, for these bodies change into one another. | |
From: Anaxagoras (fragments/reports [c.460 BCE]), quoted by Aristotle - The History of Animals 529a34 | |
A reaction: The 'potentially perceptible' seems to be matter. The surprise here is that the contraries are more basic than the elements, rather than being properties of them. Reality is modes of matter, it seems. |
19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
Full Idea: The proposition that understanding does not involve knowledge is widespread (for example, in discussions of what philosophy aims at), but hardly withstands scrutiny. If you do not know how a jet engine works, you do not understand how it works. | |
From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.24) | |
A reaction: This seems a bit disingenuous. As in 'Theaetetus', knowing the million parts of a jet engine is not to understand it. More strongly - how could knowledge of an infinity of separate propositional truths amount to understanding on their own? |
19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
Full Idea: An essential prerequisite for useful discussion of the relation between knowledge and understanding is systematic explicitness about what is to be known or understood. | |
From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.25) | |
A reaction: This is better. I say what needs to be known for understanding is the essence of the item under discussion (my PhD thesis!). Obviously understanding needs some knowledge, but I take it that epistemology should be understanding-first. That is the main aim. |
19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
Full Idea: If we say our cognitive aim is to get knowledge, the opposing views are the naturalistic view that what matters is just true belief (or just 'getting by'), or that there are rival epistemic goods such as understanding and wisdom. | |
From: Dougherty,T/Rysiew,P (Experience First (and reply) [2014], p.17) | |
A reaction: [compressed summary] I'm a fan of understanding. The accumulation of propositional knowledge would relish knowing the mass of every grain of sand on a beach. If you say the propositions should be 'important', other values are invoked. |
20802 | Snow is not white, and doesn't even appear white, because it is made of black water [Anaxagoras, by Cicero] |
Full Idea: Anaxagoras not only denied that snow was white, but because he knew that the water from which it was composed was black, even denied that it appeared white to himself. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by M. Tullius Cicero - Academica II.100 | |
A reaction: Not ridiculous. Can you deny that red and yellow balls look orange from a distance? A failure of discrimination on your part. It sounds okay to say 'what I am really perceiving is red and yellow'. [see 'Anaxagoras' poem by D.H.Lawrence!] |
13257 | The senses are too feeble to determine the truth [Anaxagoras] |
Full Idea: Owing to the feebleness of the sense, we are not able to determine the truth. | |
From: Anaxagoras (fragments/reports [c.460 BCE], B21), quoted by Patricia Curd - Anaxagoras 5.1 | |
A reaction: Anaxagoras offers a corresponding elevation of the power of mind (Idea 13256), so I now realise that he is, along with Pythagoras and Parmenides, one of the fathers of rationalism in philosophy. They probably overrate reason. |
19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
Full Idea: Much theorizing about justification conflates issues of justified belief with issues of justified/blameless believers. | |
From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.12) | |
A reaction: [They cite Kent Bach 1985] Presumably the only thing that really justifies a belief is the truth, or the actual facts. You could then say 'p is a justified belief, though no one actually believes it'. E.g. the number of stars is odd. |
19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
Full Idea: If knowledge is indeed unanalyzable, that could be seen as a liberation of justification to assume importance in its own right. | |
From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.11) | |
A reaction: [They cite Kvanvig 2003:192 and Greco 2010:9-] See Scruton's Idea 3897. I suspect that we should just give up discussing 'knowledge', which is a woolly and uninformative term, and focus on where the real epistemological action is. |
22761 | We reveal unreliability in the senses when we cannot discriminate a slow change of colour [Anaxagoras, by Sext.Empiricus] |
Full Idea: Our lack of sureness in the senses is shown if we take two colours, back and white, and pour one into the other drop by drop, we are unable to distinguish the gradual alterations although they subsist as actual facts. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Sextus Empiricus - Against the Logicians (two books) I.090 | |
A reaction: [Sextus calls Anaxagoras 'the greatest of the physicists'] I'm not sure what this proves. People with bad eyesight can distinguish very little, but that doesn't prove scepticism. And there are things too small for anyone to see. |
13256 | Nous is unlimited, self-ruling and pure; it is the finest thing, with great discernment and strength [Anaxagoras] |
Full Idea: Nous is unlimited and self-ruling and has been mixed with no thing, but is alone itself by itself. ...For it is the finest of all things and the purest, and indeed it maintains all discernment about everything and has the greatest strength. | |
From: Anaxagoras (fragments/reports [c.460 BCE], B12), quoted by Patricia Curd - Anaxagoras 3.3 | |
A reaction: Anaxagoras seems to have been a pioneer in elevating the status of the mind, which is a prop to the rationalist view, and encourages dualism. More naturalistic accounts are, in my view, much healthier. |
13784 | Mind is self-ruling, pure, ordering and ubiquitous [Anaxagoras, by Plato] |
Full Idea: Anaxagoras says that mind is self-ruling, mixes with nothing else, orders the things that are, and travels through everything. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plato - Cratylus 413c | |
A reaction: This elevation of the mind in the natural scheme of things by Anaxagoras looks increasingly significant in western culture to me. Without this line of thought, Descartes and Kant are inconceivable. |
5118 | Anaxagoras says mind remains pure, and so is not affected by what it changes [Anaxagoras, by Aristotle] |
Full Idea: Anaxagoras says that intellect (which is a cause of change) is not affected by or mixed in with anything else; for this is the only way in which it can cause change, while being itself changeless, and control things without mixing with them. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Physics 256b24 | |
A reaction: I suggest that this is the germ of the original concept of freewill - of the mind as somehow outside the causal processes of the world, so that it can initiate change without itself being affected by other causes. Aristotle says he's right; I disagree. |
19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
Full Idea: Entailment is modelled in formal semantics as set inclusion. 'Cat' entails 'mammal' because the cats are a subset of the mammals. | |
From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.10) | |
A reaction: I would have thought that this was only one type of entailment. 'Travelling to Iceland entails flying'. Travelling includes flying, the reverse of cats/mammals, to a very complex set-theoretic account is needed. Interesting. |
18231 | Anaxagoras said a person would choose to be born to contemplate the ordered heavens [Anaxagoras] |
Full Idea: When Anaxagoras was asked what it was for which a person would choose to be born rather than not, he said it would be to apprehend the heavens and the order in the whole universe. | |
From: Anaxagoras (fragments/reports [c.460 BCE], 1216), quoted by Aristotle - Eudemian Ethics 8 'Finality' | |
A reaction: [Anaxagoras, quoted by Aristotle, quoted by Korsgaard, quoted by me, and then quoted by you, perhaps] |
631 | For Anaxagoras the Good Mind has no opposite, and causes all movement, for a higher reason [Anaxagoras, by Aristotle] |
Full Idea: Anaxagoras says the good is a principle as the source of movement, in the form of Mind. However it does it for the sake of something else, which is a further factor. And he allows no opposite to the good Mind. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Metaphysics 1075b |
22727 | Mind creates the world from a mixture of pure substances [Anaxagoras, by ] |
Full Idea: Anaxagoras assumed that Mind, which is God, is the efficient principle, and the multi-mixture of homoeomeries is the material principle. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by - I.6 | |
A reaction: The choice of homoeomeries as basic is a good one. They are much better candidates than materials which are made of parts of a quite different kind, where the parts are a better candidate than the whole. |
550 | Anaxagoras said that the number of principles was infinite [Anaxagoras, by Aristotle] |
Full Idea: Anaxagoras said that the number of principles was infinite. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Metaphysics 984a |
21383 | The ultimate constituents of reality are the homoeomeries [Anaxagoras, by Vlastos] |
Full Idea: Anaxagoras contrasts with other thinkers in the formula that his 'elements' were not the air of Anaximenes or the fire of Heraclitus or the roots of Empedocles or the atoms of Leucippus, but the infinite variety of homoiomereia. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Gregory Vlastos - The Physical Theory of Anaxagoras III | |
A reaction: Not sure about the 'roots' of Empedocles. Anaxagoras is particularly thinking of the basic stuffs that make up the body, such as hair, bone and blood. It is plausible to reduce everything to stuffs that seem to have no further structure. |
13208 | Anaxagoreans regard the homoeomeries as elements, which compose earth, air, fire and water [Anaxagoras, by Aristotle] |
Full Idea: The followers of Anaxagoras regard the 'homoeomeries' as 'simple' and elements, whilst they affirm that Earth, Fire, Water and Air are composite; for each of these is (according to them) a 'common seminary' of all the homoeomeries. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 314a28 | |
A reaction: Compare Idea 13207. Aristotle is amused that the followers of Empedocles and of Anaxagoras have precisely opposite views on this subject. |
367 | Anaxagoras says mind produces order and causes everything [Anaxagoras, by Plato] |
Full Idea: Anaxagoras asserted that it is mind that produces order and is the cause of everything. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plato - Phaedo 097d |
21381 | Germs contain microscopic organs, which become visible as they grow [Anaxagoras] |
Full Idea: In the germ there are hair, nails, arteries, sinews, bones, which are not manifest because of the smallness of their parts, but become distinct little by little as they grow. For how could hair come from not-hair, or flesh from non-flesh. | |
From: Anaxagoras (fragments/reports [c.460 BCE], B10), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras I | |
A reaction: Compare Aristotle's apparent view that the physical world has no microscopic structure, and Democritus's view that hair can come from not-hair by the organisation of atoms. Is this the first suggestion that we need to know what is microscopic? |
22726 | When things were unified, Mind set them in order [Anaxagoras] |
Full Idea: All things were together, and Mind came and set them in order. | |
From: Anaxagoras (fragments/reports [c.460 BCE]) | |
A reaction: This is presumably the source for the passionate belief of Plato in the importance of order. Existence seems like chaos, with order residing beneath it, but we can wonder whether if we go even deeper it is chaos again. |
2629 | Anaxagoras was the first to say that the universe is directed by an intelligence [Anaxagoras, by Cicero] |
Full Idea: Anaxagoras, pupil of Anaximenes, was the first to maintain that the form and motion of the universe was determined and directed by the power and purpose of an infinite intelligence. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.26 |
480 | Past, present and future, and the movements of the heavens, were arranged by Mind [Anaxagoras] |
Full Idea: Whatever was then in existence which is not now, and all things that now exist, and whatever shall exist - all were arranged by Mind, as also the revolution followed now by the stars, the sun and the moon. | |
From: Anaxagoras (fragments/reports [c.460 BCE], B12), quoted by Simplicius - On Aristotle's 'Physics' 164.24 |
5956 | Anaxagoras was charged with impiety for calling the sun a lump of stone [Anaxagoras, by Plutarch] |
Full Idea: Anaxagoras was charged with impiety because he called the sun a lump of stone. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Plutarch - 14: Superstition §9 | |
A reaction: The point is that he was supposed to say that the sun is a god. |
7488 | Anaxagoras was the first recorded atheist [Anaxagoras, by Watson] |
Full Idea: Anaxagoras was the first recorded atheist. | |
From: report of Anaxagoras (fragments/reports [c.460 BCE]) by Peter Watson - Ideas Ch.25 | |
A reaction: He was a very lively character, right in the middle of the Athenian golden age. |