28 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 |
| 13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
| Full Idea: Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11 | |
| A reaction: This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out. |
| 18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
| Full Idea: Peano Arithmetic is about any system of entities that satisfies the Peano axioms. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3 | |
| A reaction: This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series. |
| 17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
| Full Idea: Peano's premises are recommended not only by the fact that arithmetic follows from them, but also by their inherent obviousness. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| Full Idea: Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 1.2) by Volker Halbach - Axiomatic Theories of Truth (2005 ver) 1.2 |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| Full Idea: Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 12066 | Aristotelian and Kripkean essentialism are very different theories [Witt] |
| Full Idea: The differences between Aristotelian essentialism and Kripke's essentialism are so fundamental and pervasive that it is a serious distortion of both views to think of essentialism as a single theory. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], Intro) | |
| A reaction: This seems to me to be very important, because there is a glib assumption that when essentialism is needed for modal logic, that we must immediately have embraced what Aristotle was saying. Aristotle was better than Kripke. |
| 12067 | An Aristotelian essence is a nonlinguistic correlate of the definition [Witt] |
| Full Idea: An Aristotelian essence is a nonlinguistic correlate of the definition of the entity in question. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], Intro) | |
| A reaction: This is a simple and necessity corrective to the simplistic idea that Aristotle thought that essences just were definitions. Aristotle believes in real essences, not linguistic essences. |
| 12082 | If unity is a matter of degree, then essence may also be a matter of degree [Witt] |
| Full Idea: By holding that the most unified beings have essences in an unqualified sense, while allowing that other beings have them in a qualified sense - we can think of unity as a matter of degree. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], 4.3) | |
| A reaction: This is Witt's somewhat unorthodox view of how we should read Aristotle. I am sympathetic, if essences are really explanatory. That means they are unstable, and would indeed be likely to come in degrees. |
| 12089 | Essences mainly explain the existence of unified substance [Witt] |
| Full Idea: The central function of essence is to explain the actual existence of a unified substance. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], 5 n1) | |
| A reaction: She is offering an interpretation of Aristotle. Since existence is an active and not a passive matter, the identity of the entity will include its dispositions etc., I presume. |
| 12102 | Essential properties of origin are too radically individual for an Aristotelian essence [Witt] |
| Full Idea: The radical individuality of essential properties of origin makes them unsuitable for inclusion in an Aristotelian essence. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], 6.2) | |
| A reaction: Nevertheless, Aristotle believes in individual essences, though these seem to be fixed by definitions, which are composed of combinations of universals. The uniqueness is of the whole definition, not of its parts. |
| 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). |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 12085 | Reality is directional [Witt] |
| Full Idea: Reality is directional. | |
| From: Charlotte Witt (Substance and Essence in Aristotle [1989], 4.5) | |
| A reaction: [Plucked from context! She attributes the view to Aristotle] This slogan beautifully summarises the 'scientific essentialist' view of reality, based not on so-called 'laws', but on the active powers of the stuffs of reality. |
| 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 |