33 ideas
| 15163 | The interest of quantified modal logic is its metaphysical necessity and essentialism [Soames] |
| Full Idea: The chief philosophical interest in quantified modal logic lies with metaphysical necessity, essentialism, and the nontrivial modal de re. | |
| From: Scott Soames (Philosophy of Language [2010], 3.1) |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 15158 | Indefinite descriptions are quantificational in subject position, but not in predicate position [Soames] |
| Full Idea: The indefinite description in 'A man will meet you' is naturally treated as quantificational, but an occurrence in predicative position, in 'Jones is not a philosopher', doesn't have a natural quantificational counterpart. | |
| From: Scott Soames (Philosophy of Language [2010], 1.23) |
| 15157 | Recognising the definite description 'the man' as a quantifier phrase, not a singular term, is a real insight [Soames] |
| Full Idea: Recognising the definite description 'the man' as a quantifier phrase, rather than a singular term, is a real insight. | |
| From: Scott Soames (Philosophy of Language [2010], 1.22) | |
| A reaction: 'Would the man who threw the stone come forward' seems like a different usage from 'would the man in the black hat come forward'. |
| 15156 | The universal and existential quantifiers were chosen to suit mathematics [Soames] |
| Full Idea: Since Frege and Russell were mainly interested in formalizing mathematics, the only quantifiers they needed were the universal and existential one. | |
| From: Scott Soames (Philosophy of Language [2010], 1.22) |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 17377 | All descriptive language is classificatory [Dupré] |
| Full Idea: Classification pervades any descriptive use of language whatever. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: This is because, as Aristotle well knew, language consists almost entirely of universals (apart from the proper names). Language just is classification. |
| 17376 | We should aim for a classification which tells us as much as possible about the object [Dupré] |
| Full Idea: The most important desideratum of a classificatory scheme is that assigning an object to a particular classification tell us as much as possible about that object. | |
| From: John Dupré (The Disorder of Things [1993], Ch 1) | |
| A reaction: We should probably say that the aim is a successful explanation, rather than a heap of information. If we are totally baffled by a particular type of object, it is presumably important to group the instances together, to focus the bafflement. |
| 17390 | Natural kinds don't need essentialism to be explanatory [Dupré] |
| Full Idea: The importance of natural kinds for explanation does not depend on a doctrine of essences. | |
| From: John Dupré (The Disorder of Things [1993], 3) | |
| A reaction: He suggest as the alternative that laws do the explaining, employing natural kinds. He allows that individual essences might be explanatory. |
| 17388 | It seems that species lack essential properties, so they can't be natural kinds [Dupré] |
| Full Idea: It is widely agreed among biologists that no essential property can be found to demarcate species, so that if an essential property is necessary for a natural kind, species are not natural kinds. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: This uses 'essential' to mean 'necessary', but I would use 'essential' to mean 'deeply explanatory'. Biological species are, nevertheless, dubious members of an ontological system. Vegetables are the problem. |
| 17389 | A species might have its essential genetic mechanism replaced by a new one [Dupré] |
| Full Idea: Contradicting one of the main points of essentialism, there is no reason in principle why a species should not survive the demise of its current genetic mechanisms (some other species coherence gradually taking over). | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: I would say that this meant that the species had a new essence, because I don't take what is essential to be the same as what is necessary. The new genetics would replace the old as the basic explanation of the species. |
| 15162 | We understand metaphysical necessity intuitively, from ordinary life [Soames] |
| Full Idea: Our understanding of metaphysical necessity is intuitive - drawn from our ordinary thought and talk. | |
| From: Scott Soames (Philosophy of Language [2010], 3.1) | |
| A reaction: This, of course, is a good reason for analytic philosophers to dislike metaphysical necessity. |
| 15161 | There are more metaphysically than logically necessary truths [Soames] |
| Full Idea: The set of metaphysically necessary truths is larger than the set of logically necessary truths. | |
| From: Scott Soames (Philosophy of Language [2010], 3.1) | |
| A reaction: Likewise, the set of logically possible truths is much larger than the set of metaphysically possible truths. If a truth is logically necessary, it will clearly be metaphysically necessary. Er, unless it is necessitated by daft logic... |
| 17374 | The possibility of prediction rests on determinism [Dupré] |
| Full Idea: Determinism is the metaphysical underlay of the possibility of prediction. | |
| From: John Dupré (The Disorder of Things [1993], Intro) | |
| A reaction: Not convinced. There might be micro-indeterminacies which iron out into macro-regularities. |
| 17378 | Presumably molecular structure seems important because we never have the Twin Earth experience [Dupré] |
| Full Idea: It is surely the absence of experiences like the one Putnam describes that makes it reasonable to attach to molecular structure at least most of the importance that Putnam ascribes to it. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: That is, whenever we experience water-like stuff, it always turns out to have the same molecular structure. Twin Earth is a nice thought experiment, except that XZY is virtually inconceivable. |
| 15152 | To study meaning, study truth conditions, on the basis of syntax, and representation by the parts [Soames] |
| Full Idea: The systematic study of meaning requires a framework for specifying the truth conditions of sentences on the basis of their syntactic structure, and the representational contents of their parts. | |
| From: Scott Soames (Philosophy of Language [2010], Intro) | |
| A reaction: Soames presents this as common sense, on the first page of his book, and it is hard to disagree. Representation will shade off into studying the workings of the mind. Fodor seems a good person to start with. |
| 15153 | Tarski's account of truth-conditions is too weak to determine meanings [Soames] |
| Full Idea: The truth conditions provided by Tarski's theories (based on references of subsentential constituents) are too weak to determine meanings, because they lacked context-sensitivity and various forms of intensionality. | |
| From: Scott Soames (Philosophy of Language [2010], Intro) | |
| A reaction: Interesting. This suggests that stronger modern axiomatic theories of truth might give a sufficient basis for a truth conditions theory of meaning. Soames says possible worlds semantics was an attempt to improve things. |
| 15154 | We should use cognitive states to explain representational propositions, not vice versa [Soames] |
| Full Idea: Instead of explaining the representationality of sentences and cognitive states in terms of propositions, we must explain the representationality of propositions in terms of the representationality of the relevant cognitive states. | |
| From: Scott Soames (Philosophy of Language [2010], Intro) | |
| A reaction: Music to my ears. I am bewildered by this Russellian notion of a 'proposition' as some abstract entity floating around in the world waiting to be expressed. The vaguer word 'facts' (and false facts?) will cover that. It's Frege's fault. |
| 17381 | Phylogenetics involves history, and cladism rests species on splits in lineage [Dupré] |
| Full Idea: The phylogenetic conception of classification reflects the facts of evolutionary history. Cladism insists that every taxonomic distinction should reflect an evolutionary event of lineage bifurcation. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: Devitt attacks cladism nicely. It rules out species change without bifurcation, and it insists on species change even in a line which remains unchanged after a split. |
| 17385 | Kinds don't do anything (including evolve) because they are abstract [Dupré] |
| Full Idea: A kind, being an abstract object, cannot do anything, including evolve. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: Maybe. We might have an extensional view of the kind, so that 'gold' is the set of extant gold atoms. But possible gold atoms are also gold, and defunct ones too. Virtually every word in English is abtract if you think about it long enough. |
| 17380 | Wales may count as fish [Dupré] |
| Full Idea: The claim that whales are not fish is a debatable one | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: A very nice challenge to an almost unquestioned orthodoxy. |
| 17375 | Natural kinds are decided entirely by the intentions of our classification [Dupré] |
| Full Idea: The question of which natural kind a thing belongs to ....can be answered only in relation to some specification of the goal underlying the intent to classify the object. | |
| From: John Dupré (The Disorder of Things [1993], Intro) | |
| A reaction: I don't think I believe this. The situation is complex, and our intents are relevant, but to find an intent which no longer classifies tigers into the same category is wilful silliness. |
| 17379 | Borders between species are much less clear in vegetables than among animals [Dupré] |
| Full Idea: The richest source of illustrations is the vegetable kingdom, where specific differences tend to be much less clear than among animals, and considerable developmental plasticity is the rule. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: Nice. Just as the idea that laws of nature are mathematical suits physics, but founders on biology, so natural kinds founder in an area of biology to which we pay less attention. He cites prickly pears and lilies. I'm thinking oranges, satsumas etc. |
| 17382 | Cooks, unlike scientists, distinguish garlic from onions [Dupré] |
| Full Idea: It would be a severe culinary misfortune if no distinction were drawn between garlic and onions, a distinction that is not reflected in scientific taxonomy. | |
| From: John Dupré (The Disorder of Things [1993], 1) | |
| A reaction: Not every persuasive. We distinguish some cows from others because they taste better, but no one thinks that is a serious way in which to classify cows. |
| 17384 | Even atoms of an element differ, in the energy levels of their electrons [Dupré] |
| Full Idea: Even if we claim that it is really isotopes not atoms that are the natural kinds (thus divorcing chemistry from ordinary language), atoms are said to differ with respect to such features as energy levels of the electrons. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: So we can't just pick out the features of one atom, and say that is the essence. Essence always involves some selection. I say the essence arises from the explanation of the atom's behaviour. |
| 17387 | Ecologists favour classifying by niche, even though that can clash with genealogy [Dupré] |
| Full Idea: To the extent that the occupants of a particular niche do not coincide with the members of a particular genealogical line, a possibility widely acknowledged to occur, ecologists must favour a method of classification lacking genealogical grounding. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: Zoo keepers probably classify by cages, or which zoo owns what, but that doesn't mean that they reject genealogy. Don't assume ecologists are rejecting any underlying classification that differs from theirs. Compare classification by economists. |
| 17386 | The theory of evolution is mainly about species [Dupré] |
| Full Idea: Species are what the theory of evolution is centrally about. | |
| From: John Dupré (The Disorder of Things [1993], 2) |
| 17383 | Species are the lowest-level classification in biology [Dupré] |
| Full Idea: Species are, by definition, the lowest-level classificatory unit, or basal taxonomic unit, for biological organisms. | |
| From: John Dupré (The Disorder of Things [1993], 2) | |
| A reaction: I think this is the 'infima species' for Aristotelians. What about 'male' and 'female' in each species? |