44 ideas
| 16539 | A definition of a circle will show what it is, and show its generating principle [Lowe] |
| Full Idea: If the definition of a circle is based on 'locus of a point', this tells us what a circle is, and it does so by revealing its generating principle, what it takes for a circle to come into being. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: Lowe says that real definitions, as essences, do not always have to spell out a 'generating principle', but they do in this case. Another approach would be to try to map dependence relations between truths about circles, and see what is basic. |
| 16540 | Defining an ellipse by conic sections reveals necessities, but not the essence of an ellipse [Lowe] |
| Full Idea: Defining an ellipse in terms of the oblique intersection of a cone and a plane (rather than in terms of the sum of the distance between the foci) gives us a necessary property, but not the essence, because the terms are extrinsic to its nature. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: [compressed wording] Helpful and illuminating. If you say some figure is what results when one thing intersects another, that doesn't tell you what the result actually is. Geometrical essences may be a bit vague, but they are quite meaningful. |
| 16548 | An essence is what an entity is, revealed by a real definition; this is not an entity in its own right [Lowe] |
| Full Idea: An entity's essence is just what that entity is, revealed by its real definition. This isn't a distinct entity, but either the entity itself, or (my view) no entity at all. ..We should not reify essence, as that leads to an infinite regress of essences. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: The regress problem is a real one, if we wish to treat an essence as some proper and distinct part of an entity. If it is a mechanism, for example, the presumably a mechanism has an essence. No, it doesn't! Levels of explanation! |
| 16549 | Simple things like 'red' can be given real ostensive definitions [Lowe] |
| Full Idea: Is it true that we cannot say, non-circularly, what red is? We cannot find a complex synonym for it, but I think we can provide red with an ostensive real definition. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: I'm not quite sure how 'real' this definition would be, if it depends on observers (some of whom may be colourblind). In what sense is this act of ostensions a 'definition'? You must distinguish the colour from the texture or shape. |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| Full Idea: Naïve set theory is based on the principles that any formula defines a set, and that coextensive sets are identical. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.2) | |
| A reaction: The second principle is a standard axiom of ZFC. The first principle causes the trouble. |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| Full Idea: In classical semantics the function of singular terms is to refer, and that of quantifiers, to range over appropriate domains of entities. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 7.1) |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| Full Idea: Considered in isolation, the axioms of group theory are not assertions but comprise an implicit definition of some abstract structure, | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.5) | |
| A reaction: The traditional Euclidean approach is that axioms are plausible assertions with which to start. The present idea sums up the modern approach. In the modern version you can work backwards from a structure to a set of axioms. |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| Full Idea: Mathematics investigates the deductive consequences of axiomatic theories, but it also needs its own foundational axioms in order to provide models for its various axiomatic theories. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.1) | |
| A reaction: This is a problem which faces the deductivist (if-then) approach. The deductive process needs its own grounds. |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| Full Idea: If the 2nd Incompleteness Theorem undermines Hilbert's attempt to use a weak theory to prove the consistency of a strong one, it is still possible to prove the consistency of one theory, assuming the consistency of another theory. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.6) | |
| A reaction: Note that this concerns consistency, not completeness. |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| Full Idea: Philosophical structuralism holds that mathematics is the study of abstract structures, or 'patterns'. If mathematics is the study of all possible patterns, then it is inevitable that the world is described by mathematics. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 11.1) | |
| A reaction: [He cites the physicist John Barrow (2010) for this] For me this is a major idea, because the concept of a pattern gives a link between the natural physical world and the abstract world of mathematics. No platonism is needed. |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| Full Idea: Modern logic requires that logical truths be true in all models, including ones devoid of any mathematical objects. It follows immediately that the existence of mathematical objects can never be a matter of logic alone. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 2) | |
| A reaction: Hm. Could there not be a complete set of models for a theory which all included mathematical objects? (I can't answer that). |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| Full Idea: Game Formalism seeks to banish all semantics from mathematics, and Term Formalism seeks to reduce any such notions to purely syntactic ones. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.3) | |
| A reaction: This approach was stimulated by the need to justify the existence of the imaginary number i. Just say it is a letter! |
| 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. |
| 16545 | The essence of lumps and statues shows that two objects coincide but are numerically distinct [Lowe] |
| Full Idea: It is a metaphysically necessary truth, obtaining in virtue of the essences of such objects (of what a bronze statue and a lump of bronze are) that when it exists a bronze statue coincides with a lump of bronze, which is numerically distinct from it. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: I think it is nonsense to treat the lump and statue as two objects. It is essential that a statue be made of a lump, and essential that a lump have a shape, so to treat the lump and the shape as two different objects is a failure to grasp the essence. |
| 16546 | The essence of a bronze statue shows that it could be made of different bronze [Lowe] |
| Full Idea: It is a metaphysical possibility, obtaining in virtue of the essences of such objects, that the same bronze statue should coincide with different lumps of bronze at different times. (..they have different persistence conditions). | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: If the fame of a statue were that it had been made by melting down the shield of Achilles (say), then the bronze it was made of would be its most important feature. Essences are more contextual than Lowe might wish. |
| 16551 | Grasping an essence is just grasping a real definition [Lowe] |
| Full Idea: All that grasping an essence amounts to is understanding a real definition, that is, understanding a special kind of proposition. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 7) | |
| A reaction: He refuses to 'reify' an essence, and says it is not an entity, so he seems to think that the definition is the essence, but Aristotle and I take the essence to be what is picked out by the correct definition - not the definition itself. |
| 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. |
| 16542 | Explanation can't give an account of essence, because it is too multi-faceted [Lowe] |
| Full Idea: Explanation is a multifaceted one, with many species (logical, mathematical, causal, teleological, and psychological), ..so it is not a notion fit to be appealed to in order to frame a perspicuous account of essence. That is one species of explanation. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: This directly attacks the core of my thesis! His parenthetical list does not give types of explanation. If I say this explanation is 'psychological', that says nothing about what explanation is. All of his instances could rest on essences. |
| 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. |
| 16552 | If we must know some entity to know an essence, we lack a faculty to do that [Lowe] |
| Full Idea: If knowledge of essence were by acquaintance of a special kind of entity, we would doubt our ability to grasp the essence of things. For what faculty could be involved in this special kind of acquaintance? | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 7) | |
| A reaction: This is Lockean empirical scepticism about essences, but I take the view that sometimes you can be acquainted with an essence, but more often you correctly infer it from you acquaintance - and this is just what scientists do. |
| 16533 | Logical necessities, based on laws of logic, are a proper sub-class of metaphysical necessities [Lowe] |
| Full Idea: If logically necessary truths are consequences of the laws of logic, then I think they are only a proper sub-class of the class of metaphysically necessary truths. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 1) | |
| A reaction: The problem for this is unusual and bizarre systems of logic, or systems that contradict one another. This idea is only plausible if you talk about the truths derived from some roughly 'classical' core of logic. 'Tonk' won't do it! |
| 16531 | 'Metaphysical' necessity is absolute and objective - the strongest kind of necessity [Lowe] |
| Full Idea: By 'metaphysical' necessity I mean necessity of the strongest possible kind - absolute necessity - and I take it to be an objective kind of necessity, rather than being something mind-dependent. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 1) | |
| A reaction: See Bob Hale for the possibility that 'absolute' and 'metaphysical' necessity might come apart. I think I believe in metaphysical necessity, but I'm uneasy about 'absolute' necessity. That may be discredited by the sceptics. |
| 16532 | 'Epistemic' necessity is better called 'certainty' [Lowe] |
| Full Idea: 'Epistemic' necessity is more properly to be called 'certainty'. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 1) | |
| A reaction: Sounds wrong. Surely I can be totally certain of a contingent truth? |
| 16543 | If an essence implies p, then p is an essential truth, and hence metaphysically necessary [Lowe] |
| Full Idea: If we can truly affirm that it is part of the essence of some entity that p is the case, then p is an essential truth and so a metaphysically necessary truth. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: This feels too quick. He is trying to expound the idea (which I like) that necessity derives from essences, and not vice versa. Is it a metaphysical necessity that there are no moths in my wardrobe, because mothballs have driven them away? Maybe. |
| 16544 | Metaphysical necessity is either an essential truth, or rests on essential truths [Lowe] |
| Full Idea: A metaphysically necessary truth is a truth which is either an essential truth or a truth that obtains in virtue of the essences of two or more distinct things. Hence all metaphysical necessity is grounded in essence. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: Lowe is endeavouring to give an exposition of the approach advocated by Kit Fine. I divide necessities 'because of' things (such as essences) from necessities 'for' things, such as situations or events. |
| 16538 | We could give up possible worlds if we based necessity on essences [Lowe] |
| Full Idea: If we explicate the notion of metaphysical necessity in terms of the notion of essence, rather than vice versa, this may enable us to dispense with the language of possible worlds as a means of explicating modal statements. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: This is the approach I favour, though I am not convinced that the two approaches are in competition, since essentialism gives the driving force for necessity, whereas possible worlds map the logic and semantics of it. |
| 16534 | 'Intuitions' are just unreliable 'hunches'; over centuries intuitions change enormously [Lowe] |
| Full Idea: I suspect that 'intuitions' and 'hunches' are pretty much the same thing, and pretty useless as sources of knowledge. …Things that seemed intuitively true to our forebears a century or two ago often by no means seem intuitively true to us now. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 2) | |
| A reaction: I don't accept this. Intuitions change a lot over the centuries because the reliable knowledge which informs intuitions has also changed a lot. Arguments and evidence may nail individual truths, but coherence must rest on intuition. |
| 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. |
| 16535 | A concept is a way of thinking of things or kinds, whether or not they exist [Lowe] |
| Full Idea: The nearest I can get to a quick definition is to say that a concept is a way of thinking of some thing or kind of things, whether or not a really existent thing or kind of things. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 2) | |
| A reaction: The focus on 'things' seems rather narrow. Are relations things? He makes concepts sound adverbial, so that there is thinking going on, and then we add 'ways' of doing it. Thinking depends on concepts, not concepts on thinking. |
| 16550 | Direct reference doesn't seem to require that thinkers know what it is they are thinking about [Lowe] |
| Full Idea: It may be objected that currently prevailing causal or 'direct' theories of reference precisely deny that a thinker must know what it is the he or she is thinking about in order to be able to think about it. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 7) | |
| A reaction: Lowe says that at least sometimes we have to know that we are thinking about, so this account of reference can't be universally true. My solution is to pull identity and essence apart. You only need identity, not essence, for reference. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 16547 | H2O isn't necessary, because different laws of nature might affect how O and H combine [Lowe] |
| Full Idea: It is not metaphysically necessary that water is composed of H2O molecules, because the natural laws governing the chemical behaviour of hydrogen and oxygen atoms could have been significantly different, so they might not have composed that substance. | |
| From: E.J. Lowe (What is the Source of Knowledge of Modal Truths? [2013], 6) | |
| A reaction: I fear this may be incoherent, as science. See Bird on why salt must dissolve in water. There can't (I suspect) be a law which keeps O and H the same, and yet makes them combine differently. |
| 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? |
| 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) |