15 ideas
| 9355 | One sort of circularity presupposes a premise, the other presupposes a rule being used [Braithwaite, by Devitt] |
| Full Idea: An argument is 'premise-circular' if it aims to establish a conclusion that is assumed as a premise of that very argument. An argument is 'rule-circular' if it aims to establish a conclusion that asserts the goodness of the rule used in that argument. | |
| From: report of R.B. Braithwaite (Scientific Explanation [1953], p.274-8) by Michael Devitt - There is no a Priori §2 | |
| A reaction: Rule circularity is the sort of thing Quine is always objecting to, but such circularities may be unavoidable, and even totally benign. All the good things in life form a mutually supporting team. |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| Full Idea: The master science can be thought of as the theory of sets with the entire range of physical objects as ur-elements. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: This sounds like Quine's view, since we have to add sets to our naturalistic ontology of objects. It seems to involve unrestricted mereology to create normal objects. |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| Full Idea: If you wonder why multiplication is commutative, you could prove it from the Peano postulates, but the proof offers little towards an answer. In set theory Cartesian products match 1-1, and n.m dots when turned on its side has m.n dots, which explains it. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: 'Turning on its side' sounds more fundamental than formal set theory. I'm a fan of explanation as taking you to the heart of the problem. I suspect the world, rather than set theory, explains the commutativity. |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| Full Idea: The standard account of the relationship between numbers and sets is that numbers simply are certain sets. This has the advantage of ontological economy, and allows numbers to be brought within the epistemology of sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Maddy votes for numbers being properties of sets, rather than the sets themselves. See Yourgrau's critique. |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| Full Idea: I propose that ...numbers are properties of sets, analogous, for example, to lengths, which are properties of physical objects. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Are lengths properties of physical objects? A hole in the ground can have a length. A gap can have a length. Pure space seems to contain lengths. A set seems much more abstract than its members. |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| Full Idea: A set of things is located where the aggregate of those things is located, ...but a number is simultaneously located at many different places (10 in my hand, and a baseball team) ...so numbers seem more like universals than particulars. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: My gut feeling is that Maddy's master idea (of naturalising sets by building them from ur-elements of natural objects) won't work. Sets can work fine in total abstraction from nature. |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| Full Idea: I am not suggesting a reduction of number theory to set theory ...There are only sets with number properties; number theory is part of the theory of finite sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], V) |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| Full Idea: The popular challenges to platonism in philosophy of mathematics are epistemological (how are we able to interact with these objects in appropriate ways) and ontological (if numbers are sets, which sets are they). | |
| From: Penelope Maddy (Sets and Numbers [1981], I) | |
| A reaction: These objections refer to Benacerraf's two famous papers - 1965 for the ontology, and 1973 for the epistemology. Though he relied too much on causal accounts of knowledge in 1973, I'm with him all the way. |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| Full Idea: Number words are not like normal adjectives. For example, number words don't occur in 'is (are)...' contexts except artificially, and they must appear before all other adjectives, and so on. | |
| From: Penelope Maddy (Sets and Numbers [1981], IV) | |
| A reaction: [She is citing Benacerraf's arguments] |
| 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. |
| 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. |