50 ideas
| 326 | For relaxation one can consider the world of change, instead of eternal things [Plato] |
| Full Idea: If, for relaxation, one gives up discussing eternal things, it is pleasant to consider likely accounts of the world of change. | |
| From: Plato (Timaeus [c.349 BCE], 59c) | |
| A reaction: To understand this, examine Plato's example of the Line at 'Republic' 509d. |
| 315 | Philosophy is the supreme gift of the gods to mortals [Plato] |
| Full Idea: Philosophy is the greatest gift the gods have ever given or ever will give to mortals. | |
| From: Plato (Timaeus [c.349 BCE], 47b) | |
| A reaction: I wonder why they gave it to us? |
| 306 | Nothing can come to be without a cause [Plato] |
| Full Idea: Nothing can come to be without a cause. | |
| From: Plato (Timaeus [c.349 BCE], 28a) |
| 13252 | Some truths have true negations [Beall/Restall] |
| Full Idea: Dialetheism is the view that some truths have true negations. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.4) | |
| A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'. |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3) | |
| A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example. |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2) | |
| A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative? |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation. |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here. |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| Full Idea: We have not abandoned classical logic in our acceptance of relevant logic. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.4) | |
| A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable. |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3) | |
| A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems. |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| Full Idea: We could reject the inference from A to itself (on grounds of circularity). | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal. |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| Full Idea: Some relevant logics reject transitivity, but we defend the classical view. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion. |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.1) | |
| A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse. |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic. |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence! |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all. |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view. |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| Full Idea: The model theory of classical predicate logic is mathematics if anything is. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1) | |
| A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics. |
| 13253 | There are several different consequence relations [Beall/Restall] |
| Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it. |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 3.2) | |
| A reaction: This why the symbol |= is often referred to as 'models'. |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic. |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.4) | |
| A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one? |
| 324 | Before the existence of the world there must have been being, space and becoming [Plato] |
| Full Idea: There were, before the world came into existence, being, space, and becoming, three distinct realities. | |
| From: Plato (Timaeus [c.349 BCE], 52d) |
| 20364 | The apprehensions of reason remain unchanging, but reasonless sensation shows mere becoming [Plato] |
| Full Idea: That which is apprehended by intelligence and reason is always in the same state, but that which is conceived by opinion with the help of sensation and without reason is always in a process of becoming and perishing, and never really is. | |
| From: Plato (Timaeus [c.349 BCE], 28a) | |
| A reaction: Lots of problems with this, of which I take the main one to be the idea that sensation is 'without reason', as if there were a sharp dichotomy in our ways of evaluating reality. Laws of nature seem to be laws of change, not of stasis. |
| 12042 | Plato's Forms were seen as part of physics, rather than of metaphysics [Plato, by Annas] |
| Full Idea: In the ancient world Plato's Theory of Forms was mostly seen as one aspect of Plato's 'physics' or theory of the world (rather than as 'metaphysics'). | |
| From: report of Plato (Timaeus [c.349 BCE]) by Julia Annas - Ancient Philosophy: very short introduction Ch.5 | |
| A reaction: This is how I also see the theory, but then I am inclined to see religion as a rather startling branch of speculative physics. Annas cites 'Timaeus' as the key text for this. |
| 307 | Something will always be well-made if the maker keeps in mind the eternal underlying pattern [Plato] |
| Full Idea: Whenever the maker of anything keeps his eye on the eternally unchanging and uses it as his pattern for the form and function of his product the result must be good. | |
| From: Plato (Timaeus [c.349 BCE], 28b) |
| 318 | In addition to the underlying unchanging model and a changing copy of it, there must also be a foundation of all change [Plato] |
| Full Idea: In addition to an eternal unchanging model and a visible and changing copy of reality, there must be a third part, the receptacle and nurse of all becoming and change. | |
| From: Plato (Timaeus [c.349 BCE], 49b) | |
| A reaction: cf Aristotle's criticism in Metaphysics |
| 321 | For knowledge and true opinion to be different there must be Forms; otherwise we are just stuck with sensations [Plato] |
| Full Idea: If intelligence and true opinion are different, then the forms must exist, but if they are the same, then what our senses perceive must be the most certain reality. | |
| From: Plato (Timaeus [c.349 BCE], 51d) |
| 317 | The universe is basically an intelligible and unchanging model, and a visible and changing copy of it [Plato] |
| Full Idea: Our basic description of the universe contained an intelligible and unchanging model, and a visible and changing copy of it. | |
| From: Plato (Timaeus [c.349 BCE], 48e) |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences. |
| 334 | Only bird-brained people think astronomy is entirely a matter of evidence [Plato] |
| Full Idea: Birds are empty-headed men who grew feathers instead of hair, because they were interested in astronomy but thought it was entirely a matter of physical evidence. | |
| From: Plato (Timaeus [c.349 BCE], 91d) |
| 5962 | Plato says the soul is ordered by number [Plato, by Plutarch] |
| Full Idea: Plato regards the substance of soul not as number but as being ordered by number. | |
| From: report of Plato (Timaeus [c.349 BCE]) by Plutarch - 68: Generation of the soul in 'Timaeus' 1023 | |
| A reaction: This remark points towards Plato's esoteric doctrines, which are some sort of mathematical metaphysics. The idea that order and numbers are in some way connected is one of the most powerful in western civilization, with undeniable appeal. |
| 330 | No one wants to be bad, but bad men result from physical and educational failures, which they do not want or choose [Plato] |
| Full Idea: No one wishes to be bad, but a bad man is bad because of some flaw in his physical makeup and failure in his education, neither of which he likes or chooses. | |
| From: Plato (Timaeus [c.349 BCE], 86e) |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates? |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4) | |
| A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality. |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I. |
| 316 | Music has harmony like the soul, and serves to reorder disharmony within us [Plato] |
| Full Idea: Music has harmonic motions like the orbits of the soul, and is not for irrational pleasure, but to reduce to order any disharmony in the revolutions within us. | |
| From: Plato (Timaeus [c.349 BCE], 47d) |
| 332 | One should exercise both the mind and the body, to avoid imbalance [Plato] |
| Full Idea: One should preserve a balance and avoid exercising the mind or body without the other; mathematicians should exercise physically, and athletes mentally. | |
| From: Plato (Timaeus [c.349 BCE], 88c) | |
| A reaction: Excellent, and very modern. Use it or lose it. It suggests that Plato had a fairly holistic view of a human being, and saw mind and body as closely integrated. |
| 328 | Everything that takes place naturally is pleasant [Plato] |
| Full Idea: Everything that takes place naturally is pleasant. | |
| From: Plato (Timaeus [c.349 BCE], 81e) | |
| A reaction: Not many people would agree with this. I recently watched a sparrowhawk eat a pigeon in my garden. This is the source of the stoic formula of living according to nature. |
| 23137 | Liberty without socialism is injustice; socialism without liberty is brutality [Bakunin] |
| Full Idea: Liberty without socialism is injustice; socialism without liberty is slavery and brutality. | |
| From: Mikhail Bakunin (works [1867], 3), quoted by Adam Gopnik - A Thousand Small Sanities 3 | |
| A reaction: [1867, but no reference] Bakunin was an anarchistic socialist. This must be the best one-line defence of socialism ever written. Gopnik quotes it as part of the anarchist critique of liberalism. So are liberty and socialism long-term compatible? |
| 322 | Intelligence is the result of rational teaching; true opinion can result from irrational persuasion [Plato] |
| Full Idea: Intelligence is produced by teaching, involves truth and reason, and cannot be moved; true opinion involves persuasion, is irrational and can be moved. | |
| From: Plato (Timaeus [c.349 BCE], 51e) |
| 331 | Bad governments prevent discussion, and discourage the study of virtue [Plato] |
| Full Idea: Under a bad government discussion, both public and private, is bad, and no courses of study are available to cure faults of character. | |
| From: Plato (Timaeus [c.349 BCE], 87b) |
| 311 | The cosmos must be unique, because it resembles the creator, who is unique [Plato] |
| Full Idea: So that our universe can resemble the perfect living creature in being unique, the universe was, is and will continue to be its maker's only creation. | |
| From: Plato (Timaeus [c.349 BCE], 31c) |
| 310 | The creator of the cosmos had no envy, and so wanted things to be as like himself as possible [Plato] |
| Full Idea: This changing cosmos was made because its maker is good, and therefore lacks envy; he therefore wished all things to be as like himself as possible. | |
| From: Plato (Timaeus [c.349 BCE], 29e) |
| 325 | We must consider the four basic shapes as too small to see, only becoming visible in large numbers [Plato] |
| Full Idea: We must think of the individual units of all four basic shapes as being far too small to be visible, and only becoming visible when massed together in large numbers. | |
| From: Plato (Timaeus [c.349 BCE], 56c) |
| 327 | There are two types of cause, the necessary and the divine [Plato] |
| Full Idea: We must distinguish two types of cause, the necessary and the divine. | |
| From: Plato (Timaeus [c.349 BCE], 68e) |
| 314 | Heavenly movements gave us the idea of time, and caused us to inquire about the heavens [Plato] |
| Full Idea: Days, months, years and solstices have caused the invention of number, given us the notion of time, and caused us to inquire into the nature of the universe. | |
| From: Plato (Timaeus [c.349 BCE], 47a) |
| 312 | Time came into existence with the heavens, so that there will be a time when they can be dissolved [Plato] |
| Full Idea: Time came into being with the heavens, so that they should be dissolved together if ever they are dissolved. | |
| From: Plato (Timaeus [c.349 BCE], 38c) |
| 309 | Clearly the world is good, so its maker must have been concerned with the eternal, not with change [Plato] |
| Full Idea: If the world is beautiful and its maker good, he had an eye on the eternal; if not, on that which is subject to change; clearly the world is the fairest of things, and he the best of causes, so it is eternal. | |
| From: Plato (Timaeus [c.349 BCE], 29a) |
| 308 | If the cosmos is an object of perception then it must be continually changing [Plato] |
| Full Idea: The cosmos is visible, tangible and corporeal, and therefore perceptible by the senses; therefore it is an object of opinion and sensation, and therefore change and coming into being. | |
| From: Plato (Timaeus [c.349 BCE], 28d) |