37 ideas
| 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) |
| 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. |
| 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) |
| 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. |
| 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) |
| 1553 | No perceptible object is truly straight or curved [Protagoras] |
| Full Idea: No perceptible object is geometrically straight or curved; after all, a circle does not touch a ruler at a point, as Protagoras used to say, in arguing against the geometers. | |
| From: Protagoras (fragments/reports [c.441 BCE], B07), quoted by Aristotle - Metaphysics 998a1 |
| 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) |
| 17292 | Avoid 'in virtue of' for grounding, since it might imply a reflexive relation such as identity [Audi,P] |
| Full Idea: We should not use 'in virtue of' where it might express a reflexive relation, such as identity. Since grounding is a relation of determination, and closely linked to the concept of explanation, it is irreflexive and asymmetric. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.2) | |
| A reaction: E.g. he says someone isn't a bachelor in virtue of being an unmarried man, since a bachelor just is an unmarried man. I can't disagree. 'Determination' looks like the magic word, even if we don't know how it cashes out. |
| 17295 | Ground relations depend on the properties [Audi,P] |
| Full Idea: On my view, grounding relations depend on the natures of the properties involved in them. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.2) | |
| A reaction: I'm cautious about this if we don't find out more exactly what properties are (and they had better not just be predicates). Maybe properties are the only apparatus we have here, though I prefer 'powers' for the fundamentals. |
| 17297 | A ball's being spherical non-causally determines its power to roll [Audi,P] |
| Full Idea: The fact that a given thing is spherical non-causally determines the fact that it has the power to roll. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.3) | |
| A reaction: Quine won't accept this, because you have added something called a 'power' to the ball (intrinsically, it seems), over and above its observable sphericity. Does being a ball 'determine' that it can't be in two places at once? Order of explanation? |
| 17302 | Ground is irreflexive, asymmetric, transitive, non-monotonic etc. [Audi,P] |
| Full Idea: The logical principles about grounding include irreflexivity, asymmetry, transitivity, non-monotonicity, and so forth. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.8) | |
| A reaction: [It can't ground itself, there is no mutual grounding, grounds of grounds ground, and grounding judgements are not fixed] |
| 17303 | The best critique of grounding says it is actually either identity or elimination [Audi,P] |
| Full Idea: I think the most promising skeptical strategy is to insist on either identity or elimination wherever grounding is alleged to hold. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.9) | |
| A reaction: This comes after an assessment of the critiques of grounding by Oliver, Hofweber and Daly. So we don't say chemistry grounds biology, we either say biology is chemistry, or that there is no biology. Everything is just simples. Not for me. |
| 17294 | Grounding is a singular relation between worldly facts [Audi,P] |
| Full Idea: On my view, grounding is a singular relation between facts. ...Facts, on this view, are obtaining states of affairs. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.2) | |
| A reaction: He rest this claim on his 'worldly' view of facts, Idea 17293. I seem to be agreeing with him. Note that it is not between types of fact, even if there are such general truths, such as in chemistry. |
| 17300 | If grounding relates facts, properties must be included, as well as objects [Audi,P] |
| Full Idea: Taking facts to be the relata of grounding has the interesting consequence that it does not relate ordinary particulars, objects, considered apart from their properties. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.4) | |
| A reaction: It will depend on what you mean by properties, and it seems to me that something like 'powers' must be invoked, to get the active character that seems to be involved in grounding. |
| 17296 | We must accept grounding, for our important explanations [Audi,P] |
| Full Idea: The reason we must countenance grounding is that it is indispensible to certain important explanations. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.3) | |
| A reaction: I like this a lot. The first given of all philosophy is the drive to exlain. However, we mustn't go inventing features of the world, simply to give us the possibility of explaining it. The objective fact seems to be the without-which-not relation. |
| 17301 | Reduction is just identity, so the two things are the same fact, so reduction isn't grounding [Audi,P] |
| Full Idea: I deny that when p grounds q, q thereby reduces to p, and I deny that if q reduces to p, then p grounds q. ...On my view, reduction is nothing other than identity, so p is the same fact as q. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.5) | |
| A reaction: Very good. I can't disagree with any of it, and it is crystal clear. Philosophical heaven. |
| 17293 | Worldly facts are obtaining states of affairs, with constituents; conceptual facts also depend on concepts [Audi,P] |
| Full Idea: The 'worldly' view of facts says they are obtaining states of affairs, individuated by their constituents and their combination. On the 'conceptual' view, facts will differ if they pick out an object or property via different concepts. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.2) | |
| A reaction: Might it be that conceptual differences between facts are supervenient on worldly differences (with the worldly facts in charge)? |
| 1549 | Everything that exists consists in being perceived [Protagoras] |
| Full Idea: Everything that exists consists in being perceived. | |
| From: Protagoras (fragments/reports [c.441 BCE]), quoted by Didymus the Blind - Commentary on the Psalms (frags) | |
| A reaction: A striking anticipation of Berkeley's "esse est percipi" (to be is to be perceived). |
| 1545 | Protagoras was the first to claim that there are two contradictory arguments about everything [Protagoras, by Diog. Laertius] |
| Full Idea: Protagoras was the first to claim that there are two contradictory arguments about everything. | |
| From: report of Protagoras (fragments/reports [c.441 BCE], A01) by Diogenes Laertius - Lives of Eminent Philosophers 09.51 |
| 1547 | Man is the measure of all things - of things that are, and of things that are not [Protagoras] |
| Full Idea: He began one of his books as follows: 'Man is the measure of all things - of the things that are, that they are, and of the things that are not, that they are not'. | |
| From: Protagoras (fragments/reports [c.441 BCE], B01), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.51 |
| 3305 | There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras] |
| Full Idea: No purer metaphysical doctrine can possibly be found than the Protagorean thesis that to be (anything at all) is to be relative ( to something or other). | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.3 |
| 3313 | If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA on Protagoras] |
| Full Idea: Because the wind is cold to me but not you, Protagoras takes it to in itself neither cold nor not-cold. Accordingly, I very much doubt that he can allow the wind to be exactly as cold as itself. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.8 |
| 3317 | You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras] |
| Full Idea: Only if the thing that is cold to me is precisely identical with the thing that is not cold to you can Protagoras launch his argument, but then it is seen to be the thing in itself that exists absolutely speaking. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.8 |
| 247 | God is "the measure of all things", more than any man [Plato on Protagoras] |
| Full Idea: In our view it is God who is pre-eminently the "measure of all things", much more so than any "man", as they say. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by Plato - The Laws 716c |
| 606 | Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras] |
| Full Idea: When Protagoras quipped that man is the measure of all things, he had in mind, of course, the knowing or perceiving man. The grounds are that they have perception/knowledge, and these are said to be the measures of objects. Utter nonsense! | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by Aristotle - Metaphysics 1053b |
| 612 | Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras] |
| Full Idea: In fact there is no difference between Protagoreanism and saying this: if you stick your finger under your eyes and make single things seem two, then they are two, just because they seem to be two. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by Aristotle - Metaphysics 1063a06 |
| 17298 | Two things being identical (like water and H2O) is not an explanation [Audi,P] |
| Full Idea: If there is identity between water and H2O, we have neither the asymmetry nor the irreflexivity that explanations require. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.3) | |
| A reaction: Once you realise it is H2O, you understand its deeper features, which will open up new explanations. He's right, though. |
| 17299 | There are plenty of examples of non-causal explanation [Audi,P] |
| Full Idea: There are a number of explanations where it seems clear that causation is not involved at all: normative grounded in non-normative, disposition grounded in categorical, aesthetic grounded in non-aesthetic, semantic in social and psychological. | |
| From: Paul Audi (Clarification and Defense of Grounding [2012], 3.3) | |
| A reaction: Apart from dispositions, perhaps, these all seem to be experienced phenomena grounded in the physical world. 'Determination' is the preferred term for non-causal grounding. |
| 6016 | Early sophists thought convention improved nature; later they said nature was diminished by it [Protagoras, by Miller,FD] |
| Full Idea: Protagoras and Hippias evidently believed that convention was an improvement on nature, whereas later sophists such as Antiphon, Thrasymachus and Callicles seemed to contend that conventional morality was undermined because it was 'against nature'. | |
| From: report of Protagoras (fragments/reports [c.441 BCE]) by Fred D. Miller jr - Classical Political Thought | |
| A reaction: This gets to the heart of a much more interesting aspect of the nomos-physis (convention-nature) debate, rather than just a slanging match between relativists and the rest. The debate still goes on, over issues about the free market and intervention. |
| 1580 | For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik] |
| Full Idea: For Protagoras the only constraint on human behaviour is that it not interfere with social harmony, the essential condition for human survival. | |
| From: report of Protagoras (fragments/reports [c.441 BCE]) by David Roochnik - The Tragedy of Reason p.63 |
| 205 | Protagoras contradicts himself by saying virtue is teachable, but then that it is not knowledge [Plato on Protagoras] |
| Full Idea: Protagoras claimed that virtue was teachable, but now tries to show it is not knowledge, which makes it less likely to be teachable. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE]) by Plato - Protagoras 361b |
| 1659 | Protagoras seems to have made the huge move of separating punishment from revenge [Protagoras, by Vlastos] |
| Full Idea: The distinction of punishment from revenge must be regarded as one of the most momentous of the conceptual discoveries ever made by humanity in the course of its slow, tortuous, precarious, emergence from barbaric tribalism. Protagoras originated it. | |
| From: report of Protagoras (fragments/reports [c.441 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.187 |
| 532 | Successful education must go deep into the soul [Protagoras] |
| Full Idea: Education does not take root in the soul unless one goes deep. | |
| From: Protagoras (fragments/reports [c.441 BCE], B11), quoted by Plutarch - On Practice 178.25 |
| 1552 | He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily] |
| Full Idea: He used legislation to improve the condition of illiterate people, on the grounds that they lack one of life's great goods, and thought literacy should be a matter of public concern and expense. | |
| From: report of Protagoras (fragments/reports [c.441 BCE]) by Diodorus of Sicily - Universal History 12.13.3.3 |
| 1551 | He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras] |
| Full Idea: He said that he did not know whether there were gods - but this is the same as saying that he knew there were no gods. | |
| From: comment on Protagoras (fragments/reports [c.441 BCE], A23) by Diogenes (Oen) - Wall inscription 11 Chil 2 |