39 ideas
| 20801 | A wise man's chief strength is not being tricked; nothing is worse than error, frivolity or rashness [Zeno of Citium, by Cicero] |
| Full Idea: Zeno held that the wise man's chief strength is that he is careful not to be tricked, and sees to it that he is not deceived; for nothing is more alien to the conception that we have of the seriousness of the wise man than error, frivolity or rashness. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica II.66 | |
| A reaction: I presume that this concerns being deceived by other people, and also being deceived by evidence. I suggest that the greatest ability of the wise person is the accurate assessment of evidence. |
| 1771 | When shown seven versions of the mowing argument, he paid twice the asking price for them [Zeno of Citium, by Diog. Laertius] |
| Full Idea: When shown seven species of dialectic in the mowing argument, he asked the price, and when told 'a hundred drachmas', he gave two hundred, so devoted was he to learning. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.20 | |
| A reaction: Wonderful. I have a watertight proof that pleasure is not the good, which I will auction on the internet. |
| 20770 | Philosophy has three parts, studying nature, character, and rational discourse [Zeno of Citium, by Diog. Laertius] |
| Full Idea: They say that philosophical theory is tripartite. For one part of it concerns nature [i.e. physics], another concerns character [i.e. ethics], and another concerns rational discourse [i.e. logic] | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.39 | |
| A reaction: Surely 'nature' included biology, and shouldn't be glossed as 'physics'? And I presume that 'rational discourse' is 'logos', rather than 'logic'. Interesting to see that ethics just is the study of character (and not of good and bad actions). |
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| Full Idea: Late nineteenth century mathematicians said that, although plus, minus and 0 could not be precisely defined, they could be partially 'implicitly defined' as a group. This nonsense was rejected by Frege and others, as expressed in Russell 1903. | |
| From: Wilfrid Hodges (Model Theory [2005], 2) | |
| A reaction: [compressed] This is helpful in understanding what is going on in Frege's 'Grundlagen'. I won't challenge Hodges's claim that such definitions are nonsense, but there is a case for understanding groups of concepts together. |
| 6022 | Someone who says 'it is day' proposes it is day, and it is true if it is day [Zeno of Citium, by Diog. Laertius] |
| Full Idea: Someone who says 'It is day' seems to propose that it is day; if, then, it is day, the proposition advanced comes out true, but if not, it comes out false. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.65 | |
| A reaction: Those who find Tarski's theory annoyingly vacuous should note that the ancient Stoics thought the same point worth making. They seem to have clearly favoured some minimal account of truth, according to this. |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
| Full Idea: In first-order languages the completeness theorem tells us that T |= φ holds if and only if there is a proof of φ from T (T |- φ). Since the two symbols express the same relationship, theorist often just use |- (but only for first-order!). | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: [actually no spaces in the symbols] If you are going to study this kind of theory of logic, the first thing you need to do is sort out these symbols, which isn't easy! |
| 10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
| Full Idea: If every structure which is a model of a set of sentences T is also a model of one of its sentences φ, then this is known as the model-theoretic consequence relation, and is written T |= φ. Not to be confused with |= meaning 'satisfies'. | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: See also Idea 10474, which gives the other meaning of |=, as 'satisfies'. The symbol is ALSO used in propositional logical, to mean 'tautologically implies'! Sort your act out, logicians. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| Full Idea: The symbol in 'I |= S' reads that if the interpretation I (about word meaning) happens to make the sentence S state something true, then I 'is a model for' S, or I 'satisfies' S. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: Unfortunately this is not the only reading of the symbol |= [no space between | and =!], so care and familiarity are needed, but this is how to read it when dealing with models. See also Idea 10477. |
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| Full Idea: Model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Tarski's truth definition as a paradigm. | |
| From: Wilfrid Hodges (Model Theory [2005], Intro) | |
| A reaction: My attention is caught by the fact that natural languages are included. Might we say that science is model theory for English? That sounds like Quine's persistent message. |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| Full Idea: A 'structure' in model theory is an interpretation which explains what objects some expressions refer to, and what classes some quantifiers range over. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: He cites as examples 'first-order structures' used in mathematical model theory, and 'Kripke structures' used in model theory for modal logic. A structure is also called a 'universe'. |
| 10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
| Full Idea: The models in model-theory are structures, but there is also a common use of 'model' to mean a formal theory which describes and explains a phenomenon, or plans to build it. | |
| From: Wilfrid Hodges (Model Theory [2005], 5) | |
| A reaction: Hodges is not at all clear here, but the idea seems to be that model-theory offers a set of objects and rules, where the common usage offers a set of descriptions. Model-theory needs homomorphisms to connect models to things, |
| 7555 | Zeno achieved the statement of the problems of infinitesimals, infinity and continuity [Russell on Zeno of Citium] |
| Full Idea: Zeno was concerned with three increasingly abstract problems of motion: the infinitesimal, the infinite, and continuity; to state the problems is perhaps the hardest part of the philosophical task, and this was done by Zeno. | |
| From: comment on Zeno (Citium) (fragments/reports [c.294 BCE]) by Bertrand Russell - Mathematics and the Metaphysicians p.81 | |
| A reaction: A very nice tribute, and a beautiful clarification of what Zeno was concerned with. |
| 10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
| Full Idea: First-order logic is hopeless for discriminating between one infinite cardinal and another. | |
| From: Wilfrid Hodges (Model Theory [2005], 4) | |
| A reaction: This seems rather significant, since mathematics largely relies on first-order logic for its metatheory. Personally I'm tempted to Ockham's Razor out all these super-infinities, but mathematicians seem to make use of them. |
| 20860 | Whatever participates in substance exists [Zeno of Citium, by Stobaeus] |
| Full Idea: Zeno says that whatever participates in substance exists. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by John Stobaeus - Anthology 2.05a | |
| A reaction: This seems Aristotelian, implying that only objects exist. Unformed stuff would not normally qualify as a 'substance'. So does mud exist? See the ideas of Henry Laycock. |
| 21397 | Perception an open hand, a fist is 'grasping', and holding that fist is knowledge [Zeno of Citium, by Long] |
| Full Idea: Zeno said perceptions starts like an open hand; then the assent by our governing-principle is partly closing the hand; then full 'grasping' is like making a fist; and finally knowledge is grasping the fist with the other hand. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by A.A. Long - Hellenistic Philosophy 4.3.1 | |
| A reaction: [In Cicero, Acad 2.145] It sounds as if full knowledge requires meta-cognition - knowing that you know. |
| 20799 | A grasp by the senses is true, because it leaves nothing out, and so nature endorses it [Zeno of Citium, by Cicero] |
| Full Idea: He thought that a grasp made by the senses was true and reliable, …because it left out nothing about the object that could be grasped, and because nature had provided this grasp as a standard of knowledge, and a basis for understanding nature itself. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.42 | |
| A reaction: Sounds like Williamson's 'knowledge first' claim - that the basic epistemic state is knowledge, which we have when everything is working normally. I like Zeno's idea that a 'grasp' leaves nothing out about the object. Compare nature with Descartes' God. |
| 20797 | If a grasped perception cannot be shaken by argument, it is 'knowledge' [Zeno of Citium, by Cicero] |
| Full Idea: What had been grasped by sense-perception, he called this itself a 'sense-perception', and if it was grasped in such a way that it could not be shaken by argument he called it 'knowledge'. And between knowledge and ignorance he placed the 'grasp'. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.41 | |
| A reaction: This seems to say that a grasped perception is knowledge if there is no defeater. |
| 21398 | A presentation is true if we judge that no false presentation could appear like it [Zeno of Citium, by Cicero] |
| Full Idea: I possess a standard enabling me to judge presentations to be true when they have a character of a sort that false ones could not have. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica II.18.58 | |
| A reaction: [This is a spokesman in Cicero for the early Stoic view] No sceptic will accept this, but it is pretty much how I operate. If you see something weird, like a leopard wandering wild in Hampshire, you believe it once you have eliminated possible deceptions. |
| 1770 | When a slave said 'It was fated that I should steal', Zeno replied 'Yes, and that you should be beaten' [Zeno of Citium, by Diog. Laertius] |
| Full Idea: When a slave who was being beaten for theft said, 'It was fated that I should steal', Zeno replied, 'Yes, and that you should be beaten.' | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.19 |
| 3799 | A dog tied to a cart either chooses to follow and is pulled, or it is just pulled [Zeno of Citium, by Hippolytus] |
| Full Idea: Zeno and Chrysippus say everything is fated with the following model: when a dog is tied to a cart, if it wants to follow it is pulled and follows, making its spontaneous act coincide with necessity, but if it does not want to follow it will be compelled. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Hippolytus - Refutation of All Heresies §1.21 | |
| A reaction: A nice example, but it is important to keep the distinction clear between freedom and free will. The dog lacks freedom as it is dragged along, but it is still free to will that it is asleep in its kennel. |
| 21402 | Incorporeal substances can't do anything, and can't be acted upon either [Zeno of Citium, by Cicero] |
| Full Idea: Zeno held that an incorporeal substance was incapable of any activity, whereas anything capable of acting, or being acted upon in any way, could not be incorporeal. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.11.39 | |
| A reaction: This is substance dualism kicked into the long grass by Zeno, long before Descartes defended dualism, and was swiftly met with exactly the same response. The interaction problem. |
| 20816 | A body is required for anything to have causal relations [Zeno of Citium, by Cicero] |
| Full Idea: Zeno held (contrary to Xenocrates and others) that it was impossible for anything to be effected that lacked a body, and indeed that whatever effected something or was affected by something must be body. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.39 | |
| A reaction: This seems to make stoics thoroughgoing physicalists, although they consider the mind to be made of refined fire, rather than of flesh. |
| 1773 | A sentence always has signification, but a word by itself never does [Zeno of Citium, by Diog. Laertius] |
| Full Idea: A sentence is always significative of something, but a word by itself has no signification. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.28 | |
| A reaction: This is the Fregean dogma. Words obviously can signify, but that is said to be parasitic on their use in sentences. It feels like a false dichotomy to me. Much sentence meaning is compositional. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 20841 | Zeno said live in agreement with nature, which accords with virtue [Zeno of Citium, by Diog. Laertius] |
| Full Idea: Zeno first (in his book On Human Nature) said that the goal was to live in agreement with nature, which is to live according to virtue. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.87 | |
| A reaction: The main idea seems to be Aristotelian - that the study of human nature reveals what our virtues are, and following them is what nature requires. Nature is taken to be profoundly rational. |
| 1774 | Since we are essentially rational animals, living according to reason is living according to nature [Zeno of Citium, by Diog. Laertius] |
| Full Idea: As reason is given to rational animals according to a more perfect principle, it follows that to live correctly according to reason, is properly predicated of those who live according to nature. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.Ze.52 | |
| A reaction: This is the key idea for understanding what the stoics meant by 'live according to nature'. The modern idea of rationality doesn't extend to 'perfect principles', however. |
| 20863 | The goal is to 'live in agreement', according to one rational consistent principle [Zeno of Citium, by Stobaeus] |
| Full Idea: Zeno says the goal of life is 'living in agreement', which means living according to a single and consonant rational principle, since those who live in conflict are unhappy. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by John Stobaeus - Anthology 2.06a | |
| A reaction: If there is a 'single' principle, is it possible to state it? To live by consistent principles sets the bar incredibly high, as any professional philosopher can tell you. |
| 2662 | Zeno saw virtue as a splendid state, not just a source of splendid action [Zeno of Citium, by Cicero] |
| Full Idea: Zeno held that not merely the exercise of virtue, as his predecessors held, but the mere state of virtue is in itself a splendid thing, although nobody possesses virtue without continuously exercising it. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by M. Tullius Cicero - Academica I.10.38 |
| 21395 | One of Zeno's books was 'That Which is Appropriate' [Zeno of Citium, by Long] |
| Full Idea: Zeno of Citium wrote a (lost) book entitled 'That Which is Appropriate'. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by A.A. Long - Hellenistic Philosophy 4.1 | |
| A reaction: I cite this because I take it to be about what in Aristotle called 'the mean' - to emphasise that the mean is not what is average, or midway between the extremes, but what is a balanced response to each situation |
| 5964 | Zeno says there are four main virtues, which are inseparable but distinct [Zeno of Citium, by Plutarch] |
| Full Idea: Zeno (like Plato) admits a plurality of specifically different virtues, namely prudence, courage, sobriety, justice, which he takes to be inseparable but yet distinct and different from one another. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Plutarch - 70: Stoic Self-contradictions 1034c | |
| A reaction: In fact, the virtues are 'supervenient' on one another, which is the doctrine of the unity of virtue. Zeno is not a pluralist in the way Aristotle is - who says there are other goods apart from the virtues. |
| 20822 | There is no void in the cosmos, but indefinite void outside it [Zeno of Citium, by Ps-Plutarch] |
| Full Idea: Zeno and his followers say that there is no void within the cosmos but an indefinite void outside it. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Pseudo-Plutarch - On the Doctrine of the Philosophers 884a | |
| A reaction: Only atomists (such as Epicureans) need void within the cosmos, as space within which atoms can move. What would they make of modern 'fields'? Posidonius later said there was sufficient, but not infinite, void. |
| 2648 | Things are more perfect if they have reason; nothing is more perfect than the universe, so it must have reason [Zeno of Citium] |
| Full Idea: That which has reason is more perfect than that which has not. But there is nothing more perfect than the universe; therefore the universe is a rational being. | |
| From: Zeno (Citium) (fragments/reports [c.294 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') II.20 |
| 20811 | Since the cosmos produces what is alive and rational, it too must be alive and rational [Zeno of Citium] |
| Full Idea: Nothing which lacks life and reason can produce from itself something which is alive and rational; but the cosmos can produce from itself things which are alive and rational; therefore the cosmos is alive and rational. | |
| From: Zeno (Citium) (fragments/reports [c.294 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') 2.22 | |
| A reaction: Eggs and sperm don't seem to be rational, but I don't suppose they count. I note that this is presented as a formal proof, when actually it is just an evaluation of evidence. Logic as rhetoric, I would say. |
| 20810 | Rational is better than non-rational; the cosmos is supreme, so it is rational [Zeno of Citium] |
| Full Idea: That which is rational is better than that which is not rational; but there is nothing better than the cosmos; therefore, the cosmos is rational. | |
| From: Zeno (Citium) (fragments/reports [c.294 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') 2.21 | |
| A reaction: This looks awfully like Anselm's ontological argument to me. The cosmos was the greatest thing that Zeno could conceive. |
| 2649 | If tuneful flutes grew on olive trees, you would assume the olive had some knowledge of the flute [Zeno of Citium] |
| Full Idea: If flutes playing tunes were to grow on olive trees, would you not infer that the olive must have some knowledge of the flute? | |
| From: Zeno (Citium) (fragments/reports [c.294 BCE]), quoted by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') II.22 |
| 20807 | The cosmos and heavens are the substance of god [Zeno of Citium, by Diog. Laertius] |
| Full Idea: Zeno says that the entire cosmos and the heaven are the substance of god. | |
| From: report of Zeno (Citium) (fragments/reports [c.294 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.148 |