49 ideas
| 2666 | Carneades' pinnacles of philosophy are the basis of knowledge (the criterion of truth) and the end of appetite (good) [Carneades, by Cicero] |
| Full Idea: Carneades said the two greatest things in philosophy were the criterion of truth and the end of goods, and no man could be a sage who was ignorant of the existence of either a beginning of the process of knowledge or an end of appetition. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - Academica II.09.29 | |
| A reaction: Nice, but I would want to emphasise the distinction between truth and its criterion. Admittedly we would have no truth without a good criterion, but the truth itself should be held in higher esteem than our miserable human means of grasping it. |
| 9327 | Organisms understand their worlds better if they understand themselves [Gulick] |
| Full Idea: Organisms come to better understand their worlds by coming to better understand themselves and the ways in which their own structures engage their worlds. | |
| From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §III) | |
| A reaction: Van Gulick is defending a higher-order theory of consciousness, but this strikes me as a good rationale for the target of philosophy, which has increasingly (since Descartes) focused on understanding our own minds. |
| 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. |
| 21390 | Future events are true if one day we will say 'this event is happening now' [Carneades] |
| Full Idea: We call those past events true of which at an earlier time this proposition was true: 'They are present now'; similarly, we shall call those future events true of which at some future time this proposition will be true: 'They are present now'. | |
| From: Carneades (fragments/reports [c.174 BCE]), quoted by M. Tullius Cicero - On Fate ('De fato') 9.23-8 | |
| A reaction: This is a very nice way of paraphrasing statements about the necessity of true future contingent events. It still relies, of course, on the veracity of a tensed assertion |
| 21672 | We say future things are true that will possess actuality at some following time [Carneades, by Cicero] |
| Full Idea: Just as we speak of past things as true that possessed true actuality at some former time, so we speak of future things as true that will possess true actuality at some following time. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - On Fate ('De fato') 11.27 | |
| A reaction: This ducks the Aristotle problem of where it is true NOW when you say there will be a sea-fight tomorrow, and it turns out to be true. Carneades seems to be affirming a truth when it does not yet have a truthmaker. |
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 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. |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
| 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. |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 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'. |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
| A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
| 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. |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 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? |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 15825 | Carneades denied the transitivity of identity [Carneades, by Chisholm] |
| Full Idea: Carneades denied the principle of the transitivity of identity. | |
| From: report of Carneades (fragments/reports [c.174 BCE], fr 41-42) by Roderick Chisholm - Person and Object 3.1 | |
| A reaction: Chisholm calls this 'extreme', but I assume Carneades wouldn't deny the principle in mathematics. I'm guessing that he just means that nothing ever stays quite the same. |
| 21389 | Carneades distinguished logical from causal necessity, when talking of future events [Long on Carneades] |
| Full Idea: From 'E will take place is true' it follows that E must take place. But 'must' here is logical not causal necessity. It is a considerable achievement of Carneades to have distinguished these two senses of necessity. | |
| From: comment on Carneades (fragments/reports [c.174 BCE]) by A.A. Long - Hellenistic Philosophy 3 | |
| A reaction: Personally I am inclined to think 'necessity' is univocal, and does not have two senses. What Carneades has nicely done is distinguish the two different grounds for the necessities. |
| 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. |
| 9325 | In contrast with knowledge, the notion of understanding emphasizes practical engagement [Gulick] |
| Full Idea: In contrast with standard notions of knowledge, the concept of understanding emphasizes the element of practical engagement from the outset. | |
| From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §II) | |
| A reaction: This could be the very interesting germ of a huge revolution in our approach to epistemology, which I find rather appealing. Plato's desire that knowledge should have 'logos' seems to me in the same area. It sounds rather internalist, which is good. |
| 9326 | Knowing-that is a much richer kind of knowing-how [Gulick] |
| Full Idea: Knowing-that is a much richer kind of knowing-how. | |
| From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §II) | |
| A reaction: This thought could rather rapidly revive the discredited notion of knowing-how. I think it might slot into an account of the mind in terms of levels, so that my internalist view of knowledge emerges at higher levels, built on more basic responses. |
| 9319 | Is consciousness a type of self-awareness, or is being self-aware a way of being conscious? [Gulick] |
| Full Idea: Is consciousness just a special type of self-awareness, or is being self-aware a special way of being conscious? | |
| From: Robert van Gulick (Mirror Mirror - Is That All? [2006], Intro) | |
| A reaction: This is a really good key question, which has hovered over the debate since Locke's definition of a person (as 'self-aware'). I take the self to be a mechanism of most brains, which is prior to consciousness. Maybe the two are inseparable. |
| 9320 | Higher-order theories divide over whether the higher level involves thought or perception [Gulick] |
| Full Idea: Higher-order thought (HOT) models treat metastates as thought-like, and higher-order perception (HOP) models regard them as at least quasi-perceptual and resulting from some form of inner monitoring or inner sense. | |
| From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §I) | |
| A reaction: I would understand 'thought' to at least partially involve judgements. The HOT theory (Carruthers) seems to suit epistemological foundationalists, who want truth to enter on the ground floor. This pushes me towards the HOP model (Lycan) as more plausible. |
| 9321 | Higher-order models reduce the problem of consciousness to intentionality [Gulick] |
| Full Idea: Higher-order models would effectively reduce the problem of consciousness to that of intentionality. | |
| From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §I) | |
| A reaction: This gives the bigger picture - that higher-order theories are the cutting edge of attempts to give a naturalistic, reductivist account of consciousness. That seems to be the only way to go, so we should encourage them in the enterprise. |
| 9322 | Maybe qualia only exist at the lower level, and a higher-level is needed for what-it-is-like [Gulick] |
| Full Idea: Some higher-order theorists say we have qualitative but unconscious mental states of color or pain (qualia), but there is nothing it is like to be in such a state, which needs higher-order awareness. The meta-states are devoid of qualia. | |
| From: Robert van Gulick (Mirror Mirror - Is That All? [2006], §I.5) | |
| A reaction: He calls this the 'stranded qualia' problem. Clearly one begins to sharpen Ockham's Razor at this point, if the higher-level state isn't contributing something. I don't rule out unconscious qualia. The strength of a real pain is distorted in a dream. |
| 21671 | Voluntary motion is intrinsically within our power, and this power is its cause [Carneades, by Cicero] |
| Full Idea: Voluntary motion possesses the intrinsic property of being in our power and of obeying us, and its obedience is not uncaused, for its nature is itself the cause of this. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - On Fate ('De fato') 11.25 | |
| A reaction: To say that actions arise from our 'intrinsic power' is not much of an explanation, but it is still informative - that you should study the intrinsic powers of humans if you want to explain it. |
| 21391 | Some actions are within our power; determinism needs prior causes for everything - so it is false [Carneades, by Cicero] |
| Full Idea: Now something is in our power; but if everything happens as a result of destiny all things happen as a result of antecedent causes; therefore what happens does not happen as a result of destiny. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - On Fate ('De fato') 14.31 | |
| A reaction: This invites the question of whether some things really are 'in our power'. Carneades (as expressed by Cicero) takes that for granted. Our 'power' may be antecedent causes in disguise. |
| 21674 | Even Apollo can only foretell the future when it is naturally necessary [Carneades, by Cicero] |
| Full Idea: Carneades used to say that not even Apollo could tell any future events except those whose causes were so held together that they must necessarily happen. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by M. Tullius Cicero - On Fate ('De fato') 14.32 | |
| A reaction: Carneades is opposing the usual belief in divination, where even priests can foretell contingent future events to some extent. Careneades, of course, was defending free will. |
| 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. |
| 7398 | Carneades said that after a shipwreck a wise man would seize the only plank by force [Carneades, by Tuck] |
| Full Idea: Carneades argued forcefully that in the event of a shipwreck, the wise man would be prepared to seize the only plank capable of bearing him to shore, even if that meant pushing another person off it. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by Richard Tuck - Hobbes Ch.1 | |
| A reaction: [source for this?] This thought seems to have provoked great discussion in the sixteenth century (mostly sympathetic). I can't help thinking the right answer depends on assessing your rival. Die for a hero, drown a nasty fool. |
| 21392 | People change laws for advantage; either there is no justice, or it is a form of self-injury [Carneades, by Lactantius] |
| Full Idea: The same people often changed laws according to circumstances; there is no natural law. There is no such thing as justice or, if there is, it is the height of folly, since a man injures himself in taking thought for the advantage of others. | |
| From: report of Carneades (fragments/reports [c.174 BCE]) by Lactantius - Institutiones Divinae 5.16.4 | |
| A reaction: [An argument used by Carneades on his notorious 156BCE visit to Rome, where he argued both for and against justice] This is probably the right wing view of justice. Why give other people what they want, if it is at our expense? |
| 9324 | From the teleopragmatic perspective, life is largely an informational process [Gulick] |
| Full Idea: From the teleopragmatic perspective, life itself is largely an informational process. | |
| From: Robert van Gulick (Mirror Mirror - Is That All? [2006]) | |
| A reaction: From the cynical perspective a human is just 'blood and foul smell in a bag', but that may not give you whole story. The point here is that the informational view will cover both the genetic and the mental levels of human life. True but unilluminating? |