19 ideas
| 9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
| Full Idea: Any set with a concrete member is 'impure'. 'Pure' sets are those that are not impure, and are paradigm cases of abstract entities, such as the sort of sets apparently dealt with in Zermelo-Fraenkel (ZF) set theory. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.116) | |
| A reaction: [I am unclear whether Jubien is introducing this distinction] This seems crucial in accounts of mathematics. On the one had arithmetic can be built from Millian pebbles, giving impure sets, while logicists build it from pure sets. |
| 9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
| Full Idea: A first-order model can be viewed as a kind of ordered set, and if the domain of the model contains only concrete entities then it is a 'fundamental' model. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.117) | |
| A reaction: An important idea. Fundamental models are where the world of logic connects with the physical world. Any account of relationship between fundamental models and more abstract ones tells us how thought links to world. |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| Full Idea: It makes no sense to suppose there might be just one natural number, say seventeen. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.113) | |
| A reaction: Hm. Not convinced. If numbers are essentially patterns, we might only have the number 'twelve', because we had built our religion around anything which exhibited that form (in any of its various arrangements). Nice point, though. |
| 9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
| Full Idea: The subject-matter of (pure) mathematics is abstract structure per se. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.115) | |
| A reaction: This is the Structuralist idea beginning to take shape after Benacerraf's launching of it. Note that Jubien gets there by his rejection of platonism, whereas some structuralist have given a platonist interpretation of structure. |
| 9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
| Full Idea: If the intuition of mathematical objects were general, there would be no real debate over platonism. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111) | |
| A reaction: It is particularly perplexing when Gödel says that his perception of them is just like sight or smell, since I have no such perception. How do you individuate very large numbers, or irrational numbers, apart from writing down numerals? |
| 9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
| Full Idea: I am unable to see how the mere existence of pure abstract entities enables us to concoct appropriate models to serve as interpretations. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111) | |
| A reaction: Nice question. It is always assumed that once we have platonic realm, that everything else follows. Even if we are able to grasp the objects, despite their causal inertness, we still have to discern innumerable relations between them. |
| 9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
| Full Idea: The essential properties of mathematical entities seem to be relational, ...so we make no progress unless we can pick out some mathematical entities wihout presupposing other entities already picked out. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.112) | |
| A reaction: [compressed] Jubien is a good critic of platonism. He has identified the problem with Frege's metaphor of a 'borehole', where we discover delightful new properties of numbers simply by reaching them. |
| 16129 | Evans argues (falsely!) that a contradiction follows from treating objects as vague [Evans, by Lowe] |
| Full Idea: Evans tries to derive a contradiction from the supposition that a given identity statement is of indeterminate truth-value. (As it happens, I consider that this argument is flawed) | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978]) by E.J. Lowe - The Possibility of Metaphysics 1.3 | |
| A reaction: A priori, I wouldn't expect to be able to settle the question of whether there are any vague objects simply by following some logical derivation. Empirical examination, and conceptual analysis (or stipulation) have to be involved. |
| 16459 | Is it coherent that reality is vague, identities can be vague, and objects can have fuzzy boundaries? [Evans] |
| Full Idea: Maybe the world is vague, and vagueness is a necessary feature of any true description of it. Also identities may lack a determinate truth value because of their vagueness. Hence it is a fact that some objects have fuzzy boundaries. But is this coherent? | |
| From: Gareth Evans (Can there be Vague Objects? [1978]) | |
| A reaction: [compressed] Lewis quotes this introduction to the famous short paper, to show that Evans wasn't proposing a poor argument, but offering a reductio of the view that vagueness is 'ontic', or a feature of the world. |
| 16460 | Evans assumes there can be vague identity statements, and that his proof cannot be right [Evans, by Lewis] |
| Full Idea: The correct interpretation is that Evans trusts his reader (unwisely) to take for granted that there are vague identity statements, that a proof of the contrary cannot be right, and that the vagueness-in-describing view affords a diagnosis of the fallacy. | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978]) by David Lewis - Vague Identity: Evans misunderstood p.319 | |
| A reaction: [Lowe 199:11 is a culprit!] Lewis put this interpretation to Evans, who replied 'Yes, yes, yes!'. |
| 16457 | There clearly are vague identity statements, and Evans's argument has a false conclusion [Evans, by Lewis] |
| Full Idea: One problem with Evans's argument that there are no such thing as vague identity statements is that its conclusion is plainly false. Example: 'Princeton = Princeton Borough', where it is unsettled what region 'Princeton' denotes. | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978]) by David Lewis - Vague Identity: Evans misunderstood p.319 | |
| A reaction: Lewis endorses the view that vagueness is semantic. I certainly don't endorse Evans's argument, which hinges on a weird example of a property, as applied to Leibniz's Law. |
| 9969 | The empty set is the purest abstract object [Jubien] |
| Full Idea: The empty set is the pure abstract object par excellence. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.118 n8) | |
| A reaction: So a really good PhD on the empty set could crack the whole nature of reality. Get to work, whoever you are! |
| 14484 | If a=b is indeterminate, then a=/=b, and so there cannot be indeterminate identity [Evans, by Thomasson] |
| Full Idea: We cannot accept the existence of vague objects, according to Evans's argument that there cannot be indeterminacy of identity. ...From the assumption that it is indeterminate whether a = b, we conclude, determinately, that it's not the case that a = b. | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978]) by Amie L. Thomasson - Ordinary Objects 05.6 | |
| A reaction: I think we should keep intrinsic identity separate from identity between entities. A cloud can be clearly identified, while being a bit fuzzy. It is only when you ask whether we saw the same cloud that Evans's argument seems relevant. |
| 16224 | There can't be vague identity; a and b must differ, since a, unlike b, is only vaguely the same as b [Evans, by PG] |
| Full Idea: Two things can't be vaguely identical, because then a would have an indeterminacy which b lacks (namely, being perfectly identical to b), so by Leibniz's Law they can't be identical. | |
| From: report of Gareth Evans (Can there be Vague Objects? [1978], 4.7) by PG - Db (ideas) | |
| A reaction: [my summary of Katherine Hawley's summary (2001:118) of Evans] Hawley considers the argument to be valid. I have grave doubts about whether b's identity with b is the sort of property needed for an application of Liebniz's Law. |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
| A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
| A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
| A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |