49 ideas
| 1798 | He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius] |
| Full Idea: He studied philosophy on the principle of suspending his judgement on all points. | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.3 | |
| A reaction: In what sense was Pyrrho a philosopher, then? He must have asserted SOME generalised judgments. |
| 1800 | Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, by Diog. Laertius] |
| Full Idea: The Sceptics say that they only employ reason as an instrument, because it is impossible to overturn the authority of reason, without employing reason. | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.8 |
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| Full Idea: Fand P as 'will' and 'was', G as 'always going to be', H as 'always has been', all tenses reduce to 14 cases: the past series, each implying the next, FH,H,PH,HP,P,GP, and the future series PG,G,FG,GF,F,HF, plus GH=HG implying all, FP=PF which all imply. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.8) | |
| A reaction: I have tried to translate the fourteen into English, but am not quite confident enough to publish them here. I leave it as an exercise for the reader. |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| Full Idea: In temporal logic, if the converse Barcan formula holds then nothing goes out of existence, and the direct Barcan formula holds if nothing ever comes into existence. These results highlight the intuitive absurdity of the Barcan formulas. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This is my reaction to the modal cases as well - the absurdity of thinking that no actually nonexistent thing might possibly have existed, or that the actual existents might not have existed. Williamson seems to be the biggest friend of the formulas. |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| Full Idea: From one point of view intuitionistic logic is a part of classical logic, missing one axiom, from another classical logic is a part of intuitionistic logic, missing two connectives, intuitionistic v and → | |
| From: John P. Burgess (Philosophical Logic [2009], 6.4) |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| Full Idea: The question of the completeness of the full intuitionistic logic for its intended interpretation is not yet fully resolved. | |
| From: John P. Burgess (Philosophical Logic [2009], 6.9) |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| Full Idea: The relevantist logician's → is perhaps expressible by 'if A, then B, for that reason'. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.8) |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| Full Idea: Among the more technically oriented a 'logic' no longer means a theory about which forms of argument are valid, but rather means any formalism, regardless of its applications, that resembles original logic enough to be studied by similar methods. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: There doesn't seem to be any great intellectual obligation to be 'technical'. As far as pure logic is concerned, I am very drawn to the computer approach, since I take that to be the original dream of Aristotle and Leibniz - impersonal precision. |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| Full Idea: There are topics of great philosophical interest that classical logic neglects because they are not important to mathematics. …These include distinctions of past, present and future, or of necessary, actual and possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.1) |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| Full Idea: Classical logic neglects counterfactual conditionals for the same reason it neglects temporal and modal distinctions, namely, that they play no serious role in mathematics. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.1) | |
| A reaction: Science obviously needs counterfactuals, and metaphysics needs modality. Maybe so-called 'classical' logic will be renamed 'basic mathematical logic'. Philosophy will become a lot clearer when that happens. |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| Full Idea: The Cut rule (from A|-B and B|-C, infer A|-C) directly expresses the classical doctrine that entailment is transitive. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| Full Idea: Philosophical logic is a branch of logic, a technical subject. …Its centre of gravity today lies in theoretical computer science. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: He firmly distinguishes it from 'philosophy of logic', but doesn't spell it out. I take it that philosophical logic concerns metaprinciples which compare logical systems, and suggest new lines of research. Philosophy of logic seems more like metaphysics. |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| Full Idea: When formalising arguments it is convenient to have as many connectives as possible available.; but when proving results about formulas it is convenient to have as few as possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: Illuminating. The fact that you can whittle classical logic down to two (or even fewer!) connectives warms the heart of technicians, but makes connection to real life much more difficult. Hence a bunch of extras get added. |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| Full Idea: Gricean implicature theory might suggest that a disjunction is never assertable when a disjunct is (though actually the disjunction might be 'pertinent') - but the procedure is indispensable in mathematical practice. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.2) | |
| A reaction: He gives an example of a proof in maths which needs it, and an unusual conversational occasion where it makes sense. |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| Full Idea: All occurrences of variables in atomic formulas are free. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.7) |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| Full Idea: By contrast to rigidly designating proper names, …the denotation of definite descriptions is (in general) not rigid but flexible. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This modern way of putting it greatly clarifies why Russell was interested in the type of reference involved in definite descriptions. Obviously some descriptions (such as 'the only person who could ever have…') might be rigid. |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| Full Idea: There are atomic formulas, and formulas built from the connectives, and that is all. We show that all formulas have some property, first for the atomics, then the others. This proof is 'induction on complexity'; we also use 'recursion on complexity'. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: That is: 'induction on complexity' builds a proof from atomics, via connectives; 'recursion on complexity' breaks down to the atomics, also via the connectives. You prove something by showing it is rooted in simple truths. |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| Full Idea: It might be wondered how one could have any kind of proof procedure at all if transitivity of entailment is disallowed, but the sequent calculus can get around the difficulty. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) | |
| A reaction: He gives examples where transitivity of entailment (so that you can build endless chains of deductions) might fail. This is the point of the 'cut free' version of sequent calculus, since the cut rule allows transitivity. |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| Full Idea: Instead of demonstrations which are either axioms, or follow from axioms by rules, we can have one ever-growing sequence of formulas of the form 'Axioms |- ______', where the blank is filled by Axioms, then Lemmas, then Theorems, then Corollaries. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| Full Idea: The valid formulas of classical sentential logic are called 'tautologically valid', or simply 'tautologies'; with other logics 'tautologies' are formulas that are substitution instances of valid formulas of classical sentential logic. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.5) |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| Full Idea: Validity (truth by virtue of logical form alone) and demonstrability (provability by virtue of logical form alone) have correlative notions of logical possibility, 'satisfiability' and 'consistency', which come apart in some logics. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| Full Idea: In practice there is no need to consider any but mathematical models, models whose universes consist of mathematical objects, since every model is isomorphic to one of these. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.8) | |
| A reaction: The crucial link is the technique of Gödel Numbering, which can translate any verbal formula into numerical form. He adds that, because of the Löwenheim-Skolem theorem only subsets of the natural numbers need be considered. |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| Full Idea: Models generally deliberately leave out meaning, retaining only what is important for the determination of truth values. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.2) | |
| A reaction: This is the key point to hang on to, if you are to avoid confusing mathematical models with models of things in the real world. |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| Full Idea: The aim in setting up a model theory is that the technical notion of truth in all models should agree with the intuitive notion of truth in all instances. A model is supposed to represent everything about an instance that matters for its truth. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.2) |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| Full Idea: It is a common view that the liar sentence ('This very sentence is not true') is an instance of a truth-value gap (neither true nor false), but some dialethists cite it as an example of a truth-value glut (both true and false). | |
| From: John P. Burgess (Philosophical Logic [2009], 5.7) | |
| A reaction: The defence of the glut view must be that it is true, then it is false, then it is true... Could it manage both at once? |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| Full Idea: There is a problem over 'de re' modality (as contrasted with 'de dicto'), as in ∃x□x. What is meant by '"it is analytic that Px" is satisfied by a', given that analyticity is a notion that in the first instance applies to complete sentences? | |
| From: John P. Burgess (Philosophical Logic [2009], 3.9) | |
| A reaction: This is Burgess's summary of one of Quine's original objections. The issue may be a distinction between whether the sentence is analytic, and what makes it analytic. The necessity of bachelors being unmarried makes that sentence analytic. |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| Full Idea: To the extent that there is any conventional wisdom about the question, it is that S5 is correct for alethic logical modality, and S4 correct for apodictic logical modality. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.8) | |
| A reaction: In classical logic these coincide, so presumably one should use the minimum system to do the job, which is S4 (?). |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| Full Idea: Logical necessity is a genus with two species. For classical logic the truth-related notion of validity and the proof-related notion of demonstrability, coincide - but they are distinct concept. In some logics they come apart, in intension and extension. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) | |
| A reaction: They coincide in classical logic because it is sound and complete. This strikes me as the correct approach to logical necessity, tying it to the actual nature of logic, rather than some handwavy notion of just 'true in all possible worlds'. |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| Full Idea: Three main theories of the truth of indicative conditionals are Materialism (the conditions are the same as for the material conditional), Idealism (identifying assertability with truth-value), and Nihilism (no truth, just assertability). | |
| From: John P. Burgess (Philosophical Logic [2009], 4.3) |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| Full Idea: It is contentious whether conditionals have negations, and whether 'it is not the case that if A,B' has any clear meaning. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.9) | |
| A reaction: This seems to be connected to Lewis's proof that a probability conditional cannot be reduced to a single proposition. If a conditional only applies to A-worlds, it is not surprising that its meaning gets lost when it leaves that world. |
| 6595 | If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin] |
| Full Idea: Against the Stoics, the Pyrrhonians argued that if someone presents a criterion of truth, then it will be important to determine whether it is the correct criterion. | |
| From: report of Pyrrho (reports [c.325 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.4 | |
| A reaction: Hence Davidson says that attempts to define truth are 'folly'. If something has to be taken as basic, then truth seems a good candidate (since, for example, logical operators could not otherwise be defined by means of 'truth' tables). |
| 6593 | The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin] |
| Full Idea: The attacks of the Pyrrhonian sceptics are directed against the dogmas of the 'professors', not against the beliefs of the common people pursuing the business of daily life. | |
| From: report of Pyrrho (reports [c.325 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.4 | |
| A reaction: This may be because they thought that ordinary people were too confused to be worth attacking, rather than because they lived in a state of beautifully appropriate beliefs. Naïve realism is certainly worth attacking. |
| 6592 | Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin] |
| Full Idea: The ancient Academic sceptics charged the Pyrrhonian sceptics with 'negative dogmatism' when they claimed that a certain kind of knowledge is impossible. | |
| From: report of Pyrrho (reports [c.325 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.4 | |
| A reaction: It is this kind of point which should push us towards some sort of rationalism, because certain a priori 'dogmas' seem to be indispensable to get any sort of discussion off the ground. The only safe person is Cratylus (see Idea 578). |
| 1801 | Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius] |
| Full Idea: First mode: animals vary in their feelings and judgements (of food, for example). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 1802 | Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius] |
| Full Idea: Second mode: individual men vary in responses and feelings (heat and cold, for example). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 1807 | Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius] |
| Full Idea: Seventh mode: perception varies according to viewing distance and angle (the sun, and a dove's neck). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 1810 | Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius] |
| Full Idea: Tenth mode: perceptions and judgements depend on comparison (light/heavy, above/below). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 1805 | Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius] |
| Full Idea: Fifth mode: judgements vary according to local custom, law and culture (Persians marry their daughters). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 1808 | Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius] |
| Full Idea: Eighth mode: perceptions of things depend on their magnitude or quantity (food and wine). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 1803 | Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius] |
| Full Idea: Third mode: things like an apple vary according to which sense perceives them (yellow, sweet, and fragrant). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 1809 | Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius] |
| Full Idea: Ninth mode: we perceive things according to what we expect (earthquakes and sunshine). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 1804 | Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius] |
| Full Idea: Fourth mode: perceivers vary in their mental and physical state (such as the mad and the sick). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 1806 | Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius] |
| Full Idea: Sixth mode: the perception of an object depends on surrounding conditions (sunlight and lamplight). | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.Py.9 |
| 22375 | Moral judgements need more than the relevant facts, if the same facts lead to 'x is good' and 'x is bad' [Foot] |
| Full Idea: It is suggested that anyone who has considered all the facts which could bear on his moral position has ipso facto produced a 'well founded' moral judgement, ...How 'x is good' can be well founded when 'x is bad' is equally well founded is hard to see. | |
| From: Philippa Foot (Moral Arguments [1958], p.96) | |
| A reaction: This seems to be a warning to particularists, if they hope that moral judgements just emerge from the facts. It doesn't rule out physicalist naturalism about morality, if the attitudes we bring to the facts have arisen out of further facts. |
| 22378 | We can't affirm a duty without saying why it matters if it is not performed [Foot] |
| Full Idea: I do not know what could be meant by saying it was someone's duty to do something unless there was an attempt to show why it mattered if this sort of thing was not done. | |
| From: Philippa Foot (Moral Arguments [1958], p.105) | |
| A reaction: The Kantian idea assumes that duty is an absolute, and yet each duty rests on a particular maxim which is going to be universalised. So why should that maxim be universalised, and not some other? |
| 22377 | Whether someone is rude is judged by agreed criteria, so the facts dictate the value [Foot] |
| Full Idea: Whether a man is speaking of behaviour as rude or not rude, he must use the same criteria as anyone else. ...We have here an example of a non-evaluative premise from which an evaluative conclusion can be deduced. | |
| From: Philippa Foot (Moral Arguments [1958], p.104) | |
| A reaction: We would now call 'rude' a 'thick' ethical concept (where 'good' is 'thin'). Her powerful point is, I take it, that evidence is always relevant to judgements of thick concepts, so there is no fact-value gap. 'Rude' has criteria, but 'good' may not. |
| 22376 | Facts and values are connected if we cannot choose what counts as evidence of rightness [Foot] |
| Full Idea: To show that facts and values are connected we must show that some things do and some things don't count in favour of a moral conclusion, and that no one can choose what counts as evidence for rightness or wrongness. | |
| From: Philippa Foot (Moral Arguments [1958], p.99) | |
| A reaction: But what sort of facts might do the job? I can only think of right functioning and health as facts which seem to imply value. Pleasure and misery don't quite get there. |
| 3062 | There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius] |
| Full Idea: The idea of cause is relative to that of which it is the cause, and so has no real existence. …Also cause must either be body causing body, or incorporeal causing incorporeal, and neither of these is possible. | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.11.11 |
| 3063 | Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius] |
| Full Idea: Motion is not moved in the place in which it is is, and it is impossible that it should be moved in the place in which it is not, so there is no such thing as motion. | |
| From: report of Pyrrho (reports [c.325 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.11.11 |