47 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). |
22358 | Scientific objectivity lies in inter-subjective testing [Popper] |
Full Idea: The objectivity of scientific statements lies in the fact that they can be inter-subjectively tested. | |
From: Karl Popper (The Logic of Scientific Discovery [1934], p.22), quoted by Reiss,J/Spreger,J - Scientific Objectivity 2.4 | |
A reaction: Does this mean that objectivity is the same as consensus? A bunch of subjective prejudiced fools can reach a consensus. And in the middle of that bunch there can be one person who is objecfive. Sounds wrong. |
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. |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
Full Idea: In current set theory, the search is on for new axioms to determine the size of the continuum. | |
From: Penelope Maddy (Believing the Axioms I [1988], §0) | |
A reaction: This sounds the wrong way round. Presumably we seek axioms that fix everything else about set theory, and then check to see what continuum results. Otherwise we could just pick our continuum, by picking our axioms. |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
Full Idea: Most writers agree that if any sense can be made of the distinction between analytic and synthetic, then the Axiom of Extensionality should be counted as analytic. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
A reaction: [Boolos is the source of the idea] In other words Extensionality is not worth discussing, because it simply tells you what the world 'set' means, and there is no room for discussion about that. The set/class called 'humans' varies in size. |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
Full Idea: The extensional view of sets is preferable because it is simpler, clearer, and more convenient, because it individuates uniquely, and because it can simulate intensional notions when the need arises. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
A reaction: [She cites Fraenkel, Bar-Hillet and Levy for this] The difficulty seems to be whether the extensional notion captures our ordinary intuitive notion of what constitutes a group of things, since that needs flexible size and some sort of unity. |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
Full Idea: The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
A reaction: It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art. |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
Full Idea: If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
A reaction: [Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started. |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
Full Idea: The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.6) | |
A reaction: The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one? |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
Full Idea: Jordain made consistent and ill-starred efforts to prove the Axiom of Choice. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
A reaction: This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof. |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
Full Idea: Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
A reaction: This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence? |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
Full Idea: Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
A reaction: The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking. |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
Full Idea: The Iterative Conception (Zermelo 1930) says everything appears at some stage. Given two objects a and b, let A and B be the stages at which they first appear. Suppose B is after A. Then the pair set of a and b appears at the immediate stage after B. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
A reaction: Presumably this all happens in 'logical time' (a nice phrase I have just invented!). I suppose we might say that the existence of the paired set is 'forced' by the preceding sets. No transcendental inferences in this story? |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
Full Idea: The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes. | |
From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
A reaction: This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system. |
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. |
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. |
22188 | Give Nobel Prizes for really good refutations? [Gorham on Popper] |
Full Idea: Popper implies that we should be giving Nobel Prizes to scientists who use severe tests to show us what the world is not like! | |
From: comment on Karl Popper (The Logic of Scientific Discovery [1934]) by Geoffrey Gorham - Philosophy of Science 2 | |
A reaction: A lovely simple point. The refuters are important members of the scientific team, but not the leaders. |
7780 | Falsification is the criterion of demarcation between science and non-science [Popper, by Magee] |
Full Idea: According to Popper, falsification is the criterion of demarcation between science and non-science. | |
From: report of Karl Popper (The Logic of Scientific Discovery [1934]) by Bryan Magee - Popper Ch.3 | |
A reaction: If I propose something which might be falsified in a hundred years, is it science NOW? Suppose my theory appeared to be falsifiable, but (after much effort) it turned out not to be? Suppose I just see a pattern (like quark theory) in a set of facts? |
16830 | We don't only reject hypotheses because we have falsified them [Lipton on Popper] |
Full Idea: Popper's mistake is to hold that disconfirmation and elimination work exclusively through refutation. | |
From: comment on Karl Popper (The Logic of Scientific Discovery [1934]) by Peter Lipton - Inference to the Best Explanation (2nd) 05 'Explanation' | |
A reaction: The point is that we reject hypotheses even if they have not actually been refuted, on the grounds that they don't give a good explanation. I agree entirely with Lipton. |
6794 | If falsification requires logical inconsistency, then probabilistic statements can't be falsified [Bird on Popper] |
Full Idea: In Popper's sense of the word 'falsify', whereby an observation statement falsifies a hypothesis only by being logically inconsistent with it, nothing can ever falsify a probabilistic or statistical hypothesis, which is therefore unscientific. | |
From: comment on Karl Popper (The Logic of Scientific Discovery [1934]) by Alexander Bird - Philosophy of Science Ch.5 | |
A reaction: In general, no prediction can be falsified until the events occur. This seems to be Aristotle's 'sea fight' problem (Idea 1703). |
6795 | When Popper gets in difficulties, he quietly uses induction to help out [Bird on Popper] |
Full Idea: It is a feature of Popper's philosophy that when the going gets tough, induction is quietly called upon to help out. | |
From: comment on Karl Popper (The Logic of Scientific Discovery [1934]) by Alexander Bird - Philosophy of Science Ch.5 | |
A reaction: This appears to be the central reason for the decline in Popper's reputation as the saviour of science. It would certainly seem absurd to say that you know nothing when you have lots of verification but not a glimmer of falsification. |
3856 | Good theories have empirical content, explain a lot, and are not falsified [Popper, by Newton-Smith] |
Full Idea: Popper's principles are roughly that one theory is superior to another if it has greater empirical content, if it can account for the successes of the first theory, and if it has not been falsified (unlike the first theory). | |
From: report of Karl Popper (The Logic of Scientific Discovery [1934]) by W.H. Newton-Smith - The Rationality of Science I.6 |
7779 | There is no such thing as induction [Popper, by Magee] |
Full Idea: According to Popper, induction is a dispensable concept, a myth. It does not exist. There is no such thing. | |
From: report of Karl Popper (The Logic of Scientific Discovery [1934]) by Bryan Magee - Popper Ch.2 | |
A reaction: This is a nice bold summary of the Popper view - that falsification is the underlying rational activity which we mistakenly think is verification by repeated observations. Put like this, Popper seems to be wrong. We obviously learn from experiences. |
3860 | Science cannot be shown to be rational if induction is rejected [Newton-Smith on Popper] |
Full Idea: If Popper follows Hume in abandoning induction, there is no way in which he can justify the claims that there is growth of scientific knowledge and that science is a rational activity. | |
From: comment on Karl Popper (The Logic of Scientific Discovery [1934]) by W.H. Newton-Smith - The Rationality of Science III.3 |
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. |
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 |