50 ideas
| 14052 | Begin philosophy when you are young, and keep going when you are old [Epicurus] |
| Full Idea: Let no one delay the study of philosophy while young nor weary of it when old; for no one is either too young or too old for the health of the soul. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 122) | |
| A reaction: I agree with this on both accounts. I think the correct age to begin the study of philosophy is four, and it is vital to continue its study up to the point where you can no longer remember your own name. 'Health of the soul' sounds right too. |
| 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) |
| 9406 | A class is natural when everybody can spot further members of it [Quinton] |
| Full Idea: To say that a class is natural is to say that when some of its members are shown to people they pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: He concedes a number of problems with his view, but I admire his attempt to at least begin to distinguish the natural (real!) classes from the ersatz ones. A mention of causal powers would greatly improve his story. |
| 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? |
| 15730 | Extreme nominalists say all classification is arbitrary convention [Quinton] |
| Full Idea: Pure, extreme nominalism sees all classification as the product of arbitrary convention. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I'm not sure what the word 'arbitrary' is doing there. Nominalists are not daft, and if they can classify any way they like, they are not likely to choose an 'arbitrary' system. Pragmatism tells the right story here. |
| 15728 | The naturalness of a class depends as much on the observers as on the objects [Quinton] |
| Full Idea: The naturalness of a class depends as essentially on the nature of the observers who classify as it does on the nature of the objects that they classify. ...It depends on our perceptual apparatus, and on our relatively mutable needs and interests. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: This seems to translate 'natural' as 'natural for us', which is not much use to scientists, who spend quite a lot of effort combating folk wisdom. Do desirable sports cars constitute a natural class? |
| 9407 | Properties imply natural classes which can be picked out by everybody [Quinton] |
| Full Idea: To say there are properties is to say there are natural classes, classes introduction to some of whose members enables people to pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: Aristotle would like this approach, but it doesn't find many friends among modern logician/philosophers. We should go on to ask why people agree on these things. Causal powers will then come into it. |
| 15729 | Uninstantiated properties must be defined using the instantiated ones [Quinton] |
| Full Idea: Properties that have no concrete instances must be defined in terms of those that have. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I wonder what the dodo used to smell like? |
| 8520 | An individual is a union of a group of qualities and a position [Quinton, by Campbell,K] |
| Full Idea: Quinton proposes that an individual is a union of a group of qualities and a position. | |
| From: report of Anthony Quinton (The Nature of Things [1973], Pt I) by Keith Campbell - The Metaphysic of Abstract Particulars §5 | |
| A reaction: This seems the obvious defence of a bundle account of objects against the charge that indiscernibles would have to be identical. It introduces, however, 'positions' into the ontology, but maybe that price must be paid. Materialism needs space. |
| 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. |
| 14062 | Sooner follow mythology, than accept the 'fate' of natural philosophers [Epicurus] |
| Full Idea: It would be better to follow the stories told about the gods than to be a slave to the fate of the natural philosophers. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 134) | |
| A reaction: At this point in history there is a blurring between autonomous decisions and what we now call free will, and also between fate and determinism, which we try to keep distinct. |
| 1837 | We should not refer things to irresponsible necessity, but either to fortune or to our own will [Epicurus] |
| Full Idea: The best men have no belief in necessity (set up by some as mistress of all), but refer some things to fortune, some to ourselves, because necessity is irresponsible, and fortune is unstable, while our own will is free. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 133), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.27 |
| 1836 | Prudence is more valuable than philosophy, because it avoids confusions of the soul [Epicurus] |
| Full Idea: The greatest good in avoiding confusion of the soul is prudence [phronesis], on which account prudence is something more valuable than even philosophy. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 132), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.27 |
| 14061 | Our own choices are autonomous, and the basis for praise and blame [Epicurus] |
| Full Idea: What occurs by our own agency is autonomous, and it is to this that praise and blame are attached. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 133) | |
| A reaction: I don't think this should be understand as an assertion of free will in the modern sense. The 'swerve' of the atoms just means that decisions can arise out of us - not that they are somehow outside of nature. |
| 14055 | The wisdom that produces a good life also produces a good death [Epicurus] |
| Full Idea: The same kind of practice produces a good life and a good death. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 126) | |
| A reaction: This is the kind of old fashioned observation which we would do well to hang on to. The ideal of dying well has vanished from our culture. |
| 14054 | Fearing death is absurd, because we are not present when it occurs [Epicurus] |
| Full Idea: Death, the most frightening of bad things, is nothing to us; since when we exist, death is not yet present, and when death is present, then we do not exist. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 125) | |
| A reaction: This is a fairly accurate observation. To fear not being in this life is a bit like fearing not being in Vancouver next Tuesday. It also involves the paradox of the present moment. E.g. Idea 1904. |
| 14053 | It is absurd to fear the pain of death when you are not even facing it [Epicurus] |
| Full Idea: He is a fool who says that he fears death not because it will be painful when present but because it is painful when it is still to come. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 125) | |
| A reaction: Not very plausible, I'm afraid. It provides a good argument in favour of smoking, if the lung cancer is far in the future. Paralysing fear is daft, but some remote fears should be heeded. |
| 14057 | All pleasures are good, but it is not always right to choose them [Epicurus] |
| Full Idea: Every pleasure is a good thing, since it has a nature congenial to us, but not every one is to be chosen, just as every pain is a bad thing, but not every one is such as to be always avoided. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 129) | |
| A reaction: This kind of sensible remark would be wholly endorsed by Bentham and Mill. This fits in with the excellent distinction between what is right and what is good. |
| 14058 | Pleasure is the goal, but as lack of pain and calm mind, not as depraved or greedy pleasure [Epicurus] |
| Full Idea: When we say that pleasure is the goal we do not mean the pleasures of the profligate or the pleasures of consumption, but rather the lack of pain in the body and disturbance in the soul. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 131) | |
| A reaction: I don't really understand the aspiration to a 'calm mind'. No one likes stress, but total calmness sounds close to non-existence. The mean! There is no achievement without pain. |
| 1833 | Pleasure is the first good in life [Epicurus] |
| Full Idea: Pleasure is the beginning and end of living happily, and we recognise this as the first good. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 128) | |
| A reaction: We might enquire what we would live for if our capacities for pleasure were surgically removed. Would we still experience intellectual curiosity, or an aspiration to some cold and remote goodness? |
| 14063 | Sooner a good decision going wrong, than a bad one turning out for the good [Epicurus] |
| Full Idea: It is better for a good decision not to turn out right in action than for a bad decision to turn out right because of chance. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 135) | |
| A reaction: This sounds right, and on the whole the law agrees. Notice that what we need is a 'good decision', and not just to 'mean well'. The well-meaning fool is wicked. I am opposed to consequentialism, and agree with this idea. |
| 14059 | The best life is not sensuality, but rational choice and healthy opinion [Epicurus] |
| Full Idea: It is not drinking bouts or enjoying boys and women or consuming fish which produces the pleasant life, but sober calculation which searches out reasons for every choice, and drives out opinions which produce turmoil of the soul. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 132) | |
| A reaction: This more or less sums up what I would call the philosophical life. Spontaneity is good, and some pleasures are killed by excessive thought, but on the whole actions are always better if good reasons are found, and error brings chaos. |
| 1835 | True pleasure is not debauchery, but freedom from physical and mental pain [Epicurus] |
| Full Idea: When we say that pleasure is the chief good, we do not mean debauchery, but freedom of the body from pain, and of the soul from confusion…. which requires sober contemplation. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 131), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.27 | |
| A reaction: I'm not clear how lack of pain and confusion counts as pleasure. Also the concepts of debauchery held by the puritan and the sybarite are wildly different. |
| 14056 | We only need pleasure when we have the pain of desire [Epicurus] |
| Full Idea: We are in need of pleasure only when we are in pain because of the absence of pleasure, and when we are not in pain, then we no longer need pleasure. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 128) | |
| A reaction: This Buddhist aspiration to eliminate desire has no appeal for me. It just sounds like a recipe for boredom, and an aversion to risk-taking. Start by asking what is best in life; it inevitably involves pleasure of some sort. Anyway, desire isn't painful. |
| 14060 | Prudence is the greatest good, and more valuable than philosophy, because it produces virtue [Epicurus] |
| Full Idea: Prudence is the principle of the rational life and is the greatest good. That is why prudence is more valuable than philosophy, for prudence is the source of all the other virtues. | |
| From: Epicurus (Letter to Menoeceus [c.291 BCE], 132) | |
| A reaction: ['prudence' will be Greek 'phronesis']The interest of this is that it is almost copied straight out of Aristotle's Ethics. Epicurus was an opponent of the Peripatetics, but greatly influenced by them. |