33 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 |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 21500 | We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI] |
| Full Idea: When the whole range of empirical beliefs is taken into account, all of them more or less dependent on memorial knowledge, we find that those which are most credible can be assured by their mutual support, or 'congruence'. | |
| From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 334), quoted by Erik J. Olsson - Against Coherence 3.1 | |
| A reaction: Lewis may be over-confident about this, and is duly attacked by Olson, but it seems to me roughly correct. How do you assess whether some unusual element in your memory was a dream or a real experience? |
| 21501 | If we doubt memories we cannot assess our doubt, or what is being doubted [Lewis,CI] |
| Full Idea: To doubt our sense of past experience as founded in actuality, would be to lose any criterion by which either the doubt itself or what is doubted could be corroborated. | |
| From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 358), quoted by Erik J. Olsson - Against Coherence 3.3.1 | |
| A reaction: Obviously scepticism about memory can come in degrees, but total rejection of short-term and clear memories looks like a non-starter. What could you put in its place? Hyper-rationalism? Even maths needs memory. |
| 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). |
| 6556 | If anything is to be probable, then something must be certain [Lewis,CI] |
| Full Idea: If anything is to be probable, then something must be certain. | |
| From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 186), quoted by Robert Fogelin - Walking the Tightrope of Reason Intro | |
| A reaction: Lewis makes this comment when facing infinite regress problems. It is a very nice slogan for foundationalism, which embodies the slippery slope view. Personally I feel the emotional pull of foundations, but acknowledge the very strong doubts about them. |
| 21498 | Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI] |
| Full Idea: A set of statements, or a set of supposed facts asserted, will be said to be congruent if and only if they are so related that the antecedent probability of any one of them will be increased if the remainder of the set can be assumed as given premises. | |
| From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946], 338), quoted by Erik J. Olsson - Against Coherence 2.2 | |
| A reaction: This thesis is vigorously attacked by Erik Olson, who works through the probability calculations. There seems an obvious problem without that. How else do you assess 'congruence', other than by evidence of mutual strengthening? |
| 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). |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 5828 | Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI] |
| Full Idea: "The denotation or extension of a term is the class of all actual or existent things which the term correctly applies to or names; the connotation or intension of a term is delimited by any correct definition of it." ..And intension determines extension. | |
| From: C.I. Lewis (An Analysis of Knowledge and Valuation [1946]), quoted by Stephen P. Schwartz - Intro to Naming,Necessity and Natural Kinds §II | |
| A reaction: The last part is one of the big ideas in philosophy of language, which was rejected by Putnam and co. If you were to reverse the slogan, though, (to extension determines intension) how would you identify the members of the extension? |
| 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 |