13 ideas
17818 | How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau] |
Full Idea: We want to know How many what? You must first partition an aggregate into parts relevant to the question, where no partition is privileged. How the partitioned set is to be numbered is bound up with its unique members, and follows from logic alone. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'New Problem') | |
A reaction: [Compressed wording of Yourgrau's summary of Frege's 'relativity argument'] Concepts do the partitioning. Yourgau says this fails, because the same argument applies to the sets themselves, as well as to the original aggregates. |
17822 | Nothing is 'intrinsically' numbered [Yourgrau] |
Full Idea: Nothing at all is 'intrinsically' numbered. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'What the') | |
A reaction: Once you are faced with distinct 'objects' of some sort, they can play the role of 'unit' in counting, so his challenge is that nothing is 'intrinsically' an object, which is the nihilism explored by Unger, Van Inwagen and Merricks. Aristotle disagrees... |
17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
Full Idea: The Frege-Maddy definition of number (as the 'property' of being-three) explains why the definitions of Von Neumann, Zermelo and others work, by giving the 'principle of collection' that ties together all threes. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'A Fregean') | |
A reaction: [compressed two or three sentences] I am strongly in favour of the best definition being the one which explains the target, rather than just pinning it down. I take this to be Aristotle's view. |
17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
Full Idea: Sets could hardly serve as a foundation for number theory if we had to await detailed results in the upper reaches of the edifice before we could make our first move. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'Two') |
17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |
Full Idea: We can address a set with any question at all that admits of a numerical reply. Thus we can ask of {Carter, Reagan} 'How many feet do the members have?'. | |
From: Palle Yourgrau (Sets, Aggregates and Numbers [1985], 'On Numbering') | |
A reaction: This is his objection to the Fregean idea that once you have fixed the members of a set, you have thereby fixed the unique number that belongs with the set. |
17488 | Empiricist theories are sets of laws, which give explanations and reductions [Glennan] |
Full Idea: In the empiricist tradition theories were understood to be deductive closures of sets of laws, explanations were understood as arguments from covering laws, and reduction was understood as a deductive relationship between laws of different theories. | |
From: Stuart Glennan (Mechanisms [2008], 'Intro') | |
A reaction: A lovely crisp summary of the whole tradition of philosophy of science from Comte through to Hempel. Mechanism and essentialism are the new players in the game. |
17493 | Modern mechanism need parts with spatial, temporal and function facts, and diagrams [Glennan] |
Full Idea: Modern champions of mechanisms say models should identify both the parts and their spatial, temporal and functional organisation, ...and the practical importance of diagrams in addition to or in place of linguistic representations of mechanisms. | |
From: Stuart Glennan (Mechanisms [2008], 'Discover') | |
A reaction: Apparently chemists obtain much more refined models by using mathematics than they did by diagrams or 3D models (let alone verbal descriptions). For that reason, I'm thinking that 'model' might be a better term than 'mechanism'. |
17487 | Mechanistic philosophy of science is an alternative to the empiricist law-based tradition [Glennan] |
Full Idea: To a significant degree, a mechanistic philosophy of science can be seen as an alternative to an earlier logical empiricist tradition in philosophy of science that gave pride of place to laws of nature. | |
From: Stuart Glennan (Mechanisms [2008], 'Intro') | |
A reaction: Lovely! Someone who actually spells out what's going on here. Most philosophers are far too coy about explaining what their real game is. Mechanism is fine in chemistry and biology. How about in 'mathematical' physics, or sociology? |
17489 | Mechanisms are either systems of parts or sequences of activities [Glennan] |
Full Idea: There are two sorts of mechanisms: systems consist of collections of parts that interact to produce some behaviour, and processes are sequences of activities which produce some outcome. | |
From: Stuart Glennan (Mechanisms [2008], 'Intro') | |
A reaction: [compressed] The second one is important because it is more generic, and under that account all kinds the features of the world that need to be explained can be subsumed. E.g. hyperinflation in an economy is a 'mechanism'. |
17490 | 17th century mechanists explained everything by the kinetic physical fundamentals [Glennan] |
Full Idea: 17th century mechanists said that interactions governed by chemical, electrical or gravitational forces would have to be explicable in terms of the operation of some atomistic (or corpuscular) kinetic mechanism. | |
From: Stuart Glennan (Mechanisms [2008], 'Intro') | |
A reaction: Glennan says science has rejected this, so modern mechanists do not reduce mechanisms to anything in particular. |
17491 | Unlike the lawlike approach, mechanistic explanation can allow for exceptions [Glennan] |
Full Idea: One of the advantages of the move from nomological to mechanistic modes of explanation is that the latter allows for explanations involving exception-ridden generalizations. | |
From: Stuart Glennan (Mechanisms [2008], 'regular') | |
A reaction: The lawlike approach has endless problems with 'ceteris paribus' ('all things being equal') laws, where specifying all the other 'things' seems a bit tricky. |
4741 | A very powerful computer might have its operations restricted by the addition of consciousness [Clark,T] |
Full Idea: It seems possible that if a powerful multi-tasking computer was then given consciousness, this might restrict its operations instead of enhancing them. | |
From: Tom Clark (talk [2003]), quoted by PG - Db (ideas) | |
A reaction: A nice thought, because it challenges the usual view - that consciousness brings huge intellectual liberty to a mind, and that a mind without it is necessarily restricted. Maybe consciousness is a bottleneck. |
17494 | Since causal events are related by mechanisms, causation can be analysed in that way [Glennan] |
Full Idea: Causation can be analyzed in terms of mechanisms because (except for fundamental causal interactions) causally related events will be connected by intervening mechanisms. | |
From: Stuart Glennan (Mechanisms [2008], 'causation') | |
A reaction: This won't give us the metaphysics of causation (which concerns the fundamentals), but this strikes me as a very coherent and interesting proposal. He mentions electron interaction as non-mechanistic causation. |