32 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 |
| 19048 | Contextual definition shifted the emphasis from words to whole sentences [Quine] |
| Full Idea: Contextual definition precipitated a revolution in semantics. The primary vehicle of meaning is seen no longer as the word, but as the sentence. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.69) | |
| A reaction: I think the idea is that the term is now supported entirely by its surrounding language, and not by its denotation of something in the world. |
| 19047 | Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine] |
| Full Idea: If Bentham found some term convenient but ontologically embarrassing, contextual definition enabled him in some cases to continue to enjoy the services of the term while disclaiming its denotation. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.68) | |
| A reaction: In Quine's terms this would be to withdraw the term from the periphery of the theory, where it has to meet the world, and make it part of the inner connections of the theory. He suggests that Bentham invented this technique. |
| 10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
| Full Idea: The semantic value of a determiner (an adjective) is a function from semantic values to nouns to semantic values of full noun phrases. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §3.1) | |
| A reaction: This kind of states the obvious (assuming one has a compositional view of sentences), but his point is that you can't just eliminate adjectival uses of numbers by analysing them away, as if they didn't do anything. |
| 10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
| Full Idea: Quantifiers have two functions in communication - to range over a domain of entities, and to have an inferential role (e.g. F(t)→'something is F'). In ordinary language these two come apart for singular terms not standing for any entities. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
| A reaction: This simple observations seems to me to be wonderfully illuminating of a whole raft of problems, the sort which logicians get steamed up about, and ordinary speakers don't. Context is the key to 90% of philosophical difficulties (?). See Idea 10008. |
| 9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
| Full Idea: There are three different uses of the number words: the singular-term use (as in 'the number of moons of Jupiter is four'), the adjectival (or determiner) use (as in 'Jupiter has four moons'), and the symbolic use (as in '4'). How are they related? | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §1) | |
| A reaction: A classic philosophy of language approach to the problem - try to give the truth-conditions for all three types. The main problem is that the first one implies that numbers are objects, whereas the others do not. Why did Frege give priority to the first? |
| 10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
| Full Idea: There are two ways to read to read '2 + 2 = 4', as singular ('two and two is four'), and as plural ('two and two are four'). | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.1) | |
| A reaction: Hofweber doesn't notice that this phenomenon occurs elsewhere in English. 'The team is playing well', or 'the team are splitting up'; it simply depends whether you are holding the group in though as an entity, or as individuals. Important for numbers. |
| 10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
| Full Idea: Why is arithmetic so hard to learn, and why does it seem so easy to us now? For example, subtracting 789 from 26,789. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.2) | |
| A reaction: His answer that we find thinking about objects very easy, but as children we have to learn with difficulty the conversion of the determiner/adjectival number words, so that we come to think of them as objects. |
| 10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
| Full Idea: I argue for an internalist conception of arithmetic. Arithmetic is not about a domain of entities, not even quantified entities. Quantifiers over natural numbers occur in their inferential-role reading in which they merely generalize over the instances. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
| A reaction: Hofweber offers the hope that modern semantics can disentangle the confusions in platonist arithmetic. Very interesting. The fear is that after digging into the semantics for twenty years, you find the same old problems re-emerging at a lower level. |
| 10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
| Full Idea: That 'two dogs are more than one' is clearly true, but its truth doesn't depend on the existence of dogs, as is seen if we consider 'two unicorns are more than one', which is true even though there are no unicorns. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.2) | |
| A reaction: This is an objection to crude empirical accounts of arithmetic, but the idea would be that there is a generalisation drawn from objects (dogs will do nicely), which then apply to any entities. If unicorns are entities, it will be true of them. |
| 10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
| Full Idea: Determiner uses of number words may disappear on analysis. This is inspired by Russell's elimination of the word 'the'. The number becomes blocks of first-order quantifiers at the level of semantic representation. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §2) | |
| A reaction: [compressed] The proposal comes from platonists, who argue that numbers cannot be analysed away if they are objects. Hofweber says the analogy with Russell is wrong, as 'the' can't occur in different syntactic positions, the way number words can. |
| 10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
| Full Idea: Representing arithmetic formally we do not primarily care about semantic features of number words. We are interested in capturing the inferential relations of arithmetical statements to one another, which can be done elegantly in first-order logic. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
| A reaction: This begins to pinpoint the difference between the approach of logicists like Frege, and those who are interested in the psychology of numbers, and the empirical roots of numbers in the process of counting. |
| 19049 | In scientific theories sentences are too brief to be independent vehicles of empirical meaning [Quine] |
| Full Idea: We have come to recognise that in a scientific theory even a whole sentence is ordinarily too short a text to serve as an independent vehicle of empirical meaning. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.70) |
| 19046 | Empiricism improvements: words for ideas, then sentences, then systems, then no analytic, then naturalism [Quine] |
| Full Idea: Since 1750 empiricism shows five turns for the better. First was a shift from ideas to words. Second a shift from terms to sentences. Third the shift to systems of sentences. Fourth the abandonment of analytic-synthetic dualism. Fifth was naturalism. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.67) | |
| A reaction: [compressed] Quine must be largely credited with the last two. The first four are almost entirely linguistic in character, which is characteristic of mid-twentieth-century empiricism. I would offer the recognition of explanation as central for the sixth. |
| 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 |
| 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 |
| 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 |
| 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 |
| 10004 | Our minds are at their best when reasoning about objects [Hofweber] |
| Full Idea: Our minds mainly reason about objects. Most cognitive problems we are faced with deal with particular objects, whether they are people or material things. Reasoning about them is what our minds are good at. | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.3) | |
| A reaction: Hofweber is suggesting this as an explanation of why we continually reify various concepts, especially numbers. Very plausible. It works for qualities of character, and explains our tendency to talk about universals as objects ('redness'). |
| 19050 | Holism in language blurs empirical synthetic and empty analytic sentences [Quine] |
| Full Idea: Holism blurs the supposed contrast beween the synthetic sentence, with its empirical content, and the analytic sentence, with its null content. | |
| From: Willard Quine (Five Milestones of Empiricism [1975], p.71) | |
| A reaction: This spells out nicely that Quine's rejection of the distinction is completely tied to his holistic view of language. The obvious phenomenon of compositionality (building sentence meaning in steps) counts against holism. |
| 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 |