29 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 |
| 18696 | The vagueness of truthmaker claims makes it easier to run anti-realist arguments [Button] |
| Full Idea: The sheer lack of structure demanded by truthmaker theorists means that it is easier to run model-theoretic arguments against them than against correspondence theorists. | |
| From: Tim Button (The Limits of Reason [2013], 02.3) | |
| A reaction: Truthmaking is a vague relation, where correspondence is fairly specific. Model arguments say you can keep the sentences steady, but shuffle around what they refer to. |
| 18701 | The coherence theory says truth is coherence of thoughts, and not about objects [Button] |
| Full Idea: According to the coherence theory of truth, for our thoughts to be true is not for them to be about objects, but only for them to cohere with one another. This is rather terrifying. | |
| From: Tim Button (The Limits of Reason [2013], 14.2) | |
| A reaction: Davidson espoused this view in 1983, but then gave it up. It strikes me as either a daft view of truth, or a denial of truth. The coherence theory of justification, on the other hand, is correct. |
| 18694 | Permutation Theorem: any theory with a decent model has lots of models [Button] |
| Full Idea: The Permutation Theorem says that any theory with a non-trivial model has many distinct isomorphic models with the same domain. | |
| From: Tim Button (The Limits of Reason [2013], 02.1) | |
| A reaction: This may be the most significant claim of model theory, since Putnam has erected an argument for anti-realism on it. See the ideas of Tim Button. |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 18692 | Realists believe in independent objects, correspondence, and fallibility of all theories [Button] |
| Full Idea: External realists have three principles: Independence - the world is objects that are independent of mind, language and theory; Correspondence - truth involves some correspondence of thoughts and things; Cartesian - an ideal theory might be false. | |
| From: Tim Button (The Limits of Reason [2013], 01.1-3) | |
| A reaction: [compressed; he cites Descartes's Demon for the third] Button is setting these up as targets. I subscribe to all three, in some form or other. Of course, as a theory approaches the success implying it is 'ideal', it becomes highly likely to be accurate. |
| 18693 | Indeterminacy arguments say if a theory can be made true, it has multiple versions [Button] |
| Full Idea: Indeterminacy arguments aim to show that if there is any way to make a theory true, then there are many ways to do so. | |
| From: Tim Button (The Limits of Reason [2013], 02.1) | |
| A reaction: Button says the simplest indeterminacy argument is Putnam's Permutation Argument - that you can shuffle the objects in a formal model, without affecting truth. But do we belief that metaphysics can be settled in this sort of way? |
| 18695 | An ideal theory can't be wholly false, because its consistency implies a true model [Button] |
| Full Idea: If realists think an ideal theory could be false, then the theory is consistent, and hence complete, and hence finitely modellable, and hence it is guaranteed that there is some way to make it true. | |
| From: Tim Button (The Limits of Reason [2013], 02.2) | |
| A reaction: [compressed] This challenges the realists' supposed claim that even the most ideal of theories could possibly be false. Presumably for a theory to be 'ideal' is not all-or-nothing. Are we capable of creating a fully ideal theory? [Löwenheim-Skolem] |
| 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. |
| 18700 | Cartesian scepticism doubts what is true; Kantian scepticism doubts that it is sayable [Button] |
| Full Idea: Cartesian scepticism agonises over whether our beliefs are true or false, whereas Kantian scepticism agonises over how it is even possible for beliefs to be true or false. | |
| From: Tim Button (The Limits of Reason [2013], 07.2) | |
| A reaction: Kant's question is, roughly, 'how can our thoughts succeed in being about the world?' Kantian scepticism is the more drastic, and looks vulnerable to a turning of the tables, but asking how Kantian worries can even be expressed. |
| 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 |
| 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 |
| 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 |
| 18698 | Predictions give the 'content' of theories, which can then be 'equivalent' or 'adequate' [Button] |
| Full Idea: The empirical 'content' of a theory is all its observable predictions. Two theories with the same predictions are empirically 'equivalent'. A theory which gets it all right at this level is empirically 'adequate'. | |
| From: Tim Button (The Limits of Reason [2013], 05.1) |
| 18697 | A sentence's truth conditions are all the situations where it would be true [Button] |
| Full Idea: A sentence's truth conditions comprise an exhaustive list of the situations in which that sentence would be true. | |
| From: Tim Button (The Limits of Reason [2013], 03.4) | |
| A reaction: So to know its meaning you must know those conditions? Compare 'my cat is licking my finger' with 'dramatic events are happening in Ethiopia'. It should take an awful long time to grasp the second sentence. |
| 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 |