39 ideas
19275 | You cannot understand what exists without understanding possibility and necessity [Hale] |
Full Idea: I defend the thesis that questions about what kinds of things there are cannot be properly understood or adequately answered without recourse to considerations about possibility and necessity. | |
From: Bob Hale (Necessary Beings [2013], Intro) | |
A reaction: Good. I would say that this is a growing realisation in contemporary philosophy. The issue is focused when we ask what are the limitations of Quine's approach to metaphysics. If you don't see possibilities around you, you are a fool. |
19291 | A canonical defintion specifies the type of thing, and what distinguish this specimen [Hale] |
Full Idea: One might think of a full dress, or canonical, definition as specifying what type of thing it is, and what distinguishes it from everything else within its type. | |
From: Bob Hale (Necessary Beings [2013], 06.4) | |
A reaction: Good! At last someone embraces the Aristotelian ideas that definitions are a) quite extensive and detailed (unlike lexicography), and b) they aim to get right down to the individual. In that sense, an essence is captured by a definition. |
19301 | With a negative free logic, we can dispense with the Barcan formulae [Hale] |
Full Idea: I reject both Barcan and Converse Barcan by adopting a negative free logic. | |
From: Bob Hale (Necessary Beings [2013], 11.3) | |
A reaction: See section 9.2 of Hale's book, where he makes his case. I can't evaluate this bold move, though I don't like the Barcan Formulae. We can anticipate objections to Hale: are you prepared to embrace the unexpected consequences of your new logic? |
19297 | The two Barcan principles are easily proved in fairly basic modal logic [Hale] |
Full Idea: If the Brouwersche principle, p ⊃ □◊p is adjoined to a standard quantified vesion of the weakest modal logic K, then one can prove both the Barcan principle, and its converse. | |
From: Bob Hale (Necessary Beings [2013], 09.2) | |
A reaction: The Brouwersche principle (that p implies that p must be possible) sounds reasonable, but the Barcan principles strike me as false, so something has to give. They are theorems of S5. Hale proposes giving up classical logic. |
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. |
19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
Full Idea: Contrary to what Quine supposes, it is neither necessary nor desirable to interpret bound higher-order variables as ranging over sets. Sets are a species of object. They should range over entities of a completely different type: properties and relations. | |
From: Bob Hale (Necessary Beings [2013], 08.2) | |
A reaction: This helpfully clarifies something which was confusing me. If sets are objects, then 'second-order' logic just seems to be the same as first-order logic (rather than being 'set theory in disguise'). I quantify over properties, but deny their existence! |
19289 | Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale] |
Full Idea: An old objection to conventionalism claims that it confuses sentences with propositions, confusing what makes sentences mean what they do with what makes them (as propositions) true. | |
From: Bob Hale (Necessary Beings [2013], 05.2) | |
A reaction: The conventions would presumably apply to the sentences, but not to the propositions. Since I think that focusing on propositions solves a lot of misunderstandings in modern philosophy, I like the sound of this. |
19298 | Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale] |
Full Idea: In contrast with axiomatic systems, in natural deductions systems of logic neither the premises nor the conclusions of steps in a derivation need themselves be logical truths or theorems of logic. | |
From: Bob Hale (Necessary Beings [2013], 09.2 n7) | |
A reaction: Not sure I get that. It can't be that everything in an axiomatic proof has to be a logical truth. How would you prove anything about the world that way? I'm obviously missing something. |
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. |
19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
Full Idea: The existence of the natural numbers is not a matter of pure logic - it cannot be proved in pure logic. It can be proved in second-order logic plus Hume's principle. Truths of arithmetic are not logic - they depend on the nature of natural numbers. | |
From: Bob Hale (Necessary Beings [2013], 07.4) | |
A reaction: Hume's principles needs entities which can be matched to one another, so a certain ontology is needed to get neo-logicism off the ground. |
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! |
19281 | Interesting supervenience must characterise the base quite differently from what supervenes on it [Hale] |
Full Idea: Any intereresting supervenience thesis requires that the class of facts on which the allegedly supervening facts supervene be characterizable independently, without use or presupposition of the notions involved in stating the supervening facts. | |
From: Bob Hale (Necessary Beings [2013], 03.4.1) | |
A reaction: There might be intermediate cases here, since having descriptions which are utterly unconnected (at any level) might be rather challenging. |
19278 | There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p [Hale] |
Full Idea: There is no clear gap between its being a fact that p and its being true that p, no obvious way to individuate the fact a true statement records other than via that statement's truth-conditions. | |
From: Bob Hale (Necessary Beings [2013], 03.2) | |
A reaction: Typical of philosophers of language. The concept of a fact is of something mind-independent; the concept of a truth is of something mind-dependent. They can't therefore be the same thing (by the contrapositive of the indiscernability of identicals!). |
19302 | If a chair could be made of slightly different material, that could lead to big changes [Hale] |
Full Idea: How shall we prevent a sorites taking us to the conclusion that a chair might have originated in a completely disjoint lot of wood, or even in some other material altogether? | |
From: Bob Hale (Necessary Beings [2013], 11.3.7) | |
A reaction: This seems a good criticism of Kripke's implausible claim that his lectern is necessarily (or essentially) made of the piece of wood it is made of. Could his lectern have had a small piece of plastic inserted in it? |
19290 | Absolute necessities are necessarily necessary [Hale] |
Full Idea: I argue that any absolute necessity is necessarily necessary. | |
From: Bob Hale (Necessary Beings [2013], 05.5.2) | |
A reaction: This requires the principle of S4 modal logic, that necessity implies necessary necessity. He argues that S5 is the logical of absolute necessity. |
19286 | 'Absolute necessity' is when there is no restriction on the things which necessitate p [Hale] |
Full Idea: The strength of the claim that p is 'absolutely necessary' derives from the fact that in its expression as a universally quantified counterfactual ('everything will necessitate p'), the quantifier ranges over all propositions whatever. | |
From: Bob Hale (Necessary Beings [2013], 04.1) | |
A reaction: Other philosophers don't seem to use the term 'absolute necessity', but it seems a useful concept, in contrast to conditional or local necessities. You can't buy chocolate on the sun. |
19288 | Logical and metaphysical necessities differ in their vocabulary, and their underlying entities [Hale] |
Full Idea: The difference between logical and metaphysical necessities lies, not in the range of possibilities for which they hold, but - at the linguistic level - in the kind of vocabulary essential to their expression, and the kinds of entities that explain them. | |
From: Bob Hale (Necessary Beings [2013], 04.5) | |
A reaction: I don't think much of the idea that the difference is just linguistic, and I don't like the idea of 'entities' as grounding them. I see logical necessities as arising from natural deduction rules, and metaphysical ones coming from the nature of reality. |
19285 | Logical necessity is something which is true, no matter what else is the case [Hale] |
Full Idea: We can identify the belief that the proposition that p is logically necessary, where p may be of any logical form, with the belief that, no matter what else was the case, it would be true that p. | |
From: Bob Hale (Necessary Beings [2013], 04.1) | |
A reaction: I find this surprising. I take it that logical necessity must be the consequence of logic. That all squares have corners doesn't seem to be a matter of logic. But then he seems to expand logical necessity to include conceptual necessity. Why? |
19287 | Maybe each type of logic has its own necessity, gradually becoming broader [Hale] |
Full Idea: We can distinguish between narrower and broader kinds of logical necessity. There are, for example, the logical necessities of propostional logic, those of first-order logic, and so on. Maybe they are necessities expressed using logical vocabulary. | |
From: Bob Hale (Necessary Beings [2013], 04.5) | |
A reaction: Hale goes on to prefer a view that embraces conceptual necessities. I think in philosophy we should designate the necessities according to their sources. This might clarify a currently rather confused situation. First-order includes propositional logic. |
19282 | It seems that we cannot show that modal facts depend on non-modal facts [Hale] |
Full Idea: I think we may conclude that there is no significant version of modal supervenience which both commands acceptance and implies that all modal facts depend asymmetrically on non-modal ones. | |
From: Bob Hale (Necessary Beings [2013], 03.4.3) | |
A reaction: This is the conclusion of a sustained and careful discussion, recorded here for interest. I'm inclined to think that there are very few, if any, non-modal facts in the world, if those facts are accurately characterised. |
19276 | The big challenge for essentialist views of modality is things having necessary existence [Hale] |
Full Idea: Whether the essentialist theory can account for all absolute necessities depends in part on whether the theory can explain the necessities of existence (of certain objects, properties and entities). | |
From: Bob Hale (Necessary Beings [2013], Intro) | |
A reaction: Hale has a Fregean commitment to all sorts of abstract objects, and then finds difficulty in explaining them from his essentialist viewpoint. His book didn't convince me. I'm more of a nominalist, me, so I sleep better at nights. |
19293 | Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures [Hale] |
Full Idea: The point of the essentialist theory is not to provide a reductive explanation of necessities. It is, rather, to locate a base class of necessities - those which directly reflect the natures of things - in terms of which the remainder may be explained. | |
From: Bob Hale (Necessary Beings [2013], 06.6) | |
A reaction: My picture is of most of the necessities being directly explained by the natures of things, rather than a small core of natures generating all the derived ones. All the necessities of squares derive from the nature of the square. |
19294 | If necessity derives from essences, how do we explain the necessary existence of essences? [Hale] |
Full Idea: If the essentialist theory of necessity is to be adequate, it must be able to explain how the existence of certain objects - such as the natural numbers - can itself be absolutely necessary. | |
From: Bob Hale (Necessary Beings [2013], 07.1) | |
A reaction: Hale and his neo-logicist pals think that numbers are 'objects', and they necessarily exist, so he obviously has a problem. I don't see any alternative for essentialists to treating the existing (and possible) natures as brute facts. |
19279 | What are these worlds, that being true in all of them makes something necessary? [Hale] |
Full Idea: We need an explanation of what worlds are that makes clear why being true at all of them should be necessary and sufficient for being necessary (and true at one of them suffices for being possible). | |
From: Bob Hale (Necessary Beings [2013], 03.3.2) | |
A reaction: Hale is introducing combinatorial accounts of worlds, as one possible answer to this. Hale observes that all the worlds might be identical to our world. It is always assumed that the worlds are hugely varied. But maybe worlds are constrained. |
19299 | Possible worlds make every proposition true or false, which endorses classical logic [Hale] |
Full Idea: The standard conception of worlds incorporates the assumption of bivalence - every proposition is either true or false. But it is infelicitous to build into one's basic semantic machinery a principle endorsing classical logic against its rivals. | |
From: Bob Hale (Necessary Beings [2013], 10.3) | |
A reaction: No wonder Dummett (with his intuitionist logic) immediately spurned possible worlds. This objection must be central to many recent thinkers who have begun to doubt possible worlds. I heard Kit Fine say 'always kick possible worlds where you can'. |
19300 | The molecules may explain the water, but they are not what 'water' means [Hale] |
Full Idea: What it is to be (pure) water is to be explained in terms of being composed of H2O molecules, but this is not what the word 'water' means. | |
From: Bob Hale (Necessary Beings [2013], 11.2) | |
A reaction: Hale says when the real and verbal definitions match, we can know the essence a priori. If they come apart, presumably we need a posteriori research. Interesting. It is certainly dubious to say a stuff-word means its chemical composition. |
7357 | People who control others with fluent language often end up being hated [Kongzi (Confucius)] |
Full Idea: Of what use is eloquence? He who engages in fluency of words to control men often finds himself hated by them. | |
From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], V.5) | |
A reaction: I don't recall Socrates making this very good point to any of the sophists (such as Gorgias). The idea that if you battle or connive your way to dominance over others then you are successful is false. Life is a much longer game than that. |
7358 | All men prefer outward appearance to true excellence [Kongzi (Confucius)] |
Full Idea: I have yet to meet a man as fond of excellence as he is of outward appearances. | |
From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], IX.18) | |
A reaction: Interestingly, this cynical view of the love of virtue is put by Plato into the mouths of Glaucon and Adeimantus (in Bk II of 'Republic', e.g. Idea 12), and not into the mouth of Socrates, who goes on to defend the possibility of true virtue. |
7362 | Humans are similar, but social conventions drive us apart (sages and idiots being the exceptions) [Kongzi (Confucius)] |
Full Idea: In our natures we approximate one another; habits put us further and further apart. The only ones who do not change are sages and idiots. | |
From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XVII.2) | |
A reaction: I find most of Confucius rather uninteresting, but this is a splendid remark about the influence of social conventions on human nature. Sages can achieve universal morality if they rise above social convention, and seek the true virtues of human nature. |
7360 | Do not do to others what you would not desire yourself [Kongzi (Confucius)] |
Full Idea: Do not do to others what you would not desire yourself. Then you will have no enemies, either in the state or in your home. | |
From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XII.2) | |
A reaction: The Golden Rule, but note the second sentence. Logically, it leads to the absurdity of not giving someone an Elvis record for Christmas because you yourself don't like Elvis. Kant (Idea 3733) and Nietzsche (Idea 4560) offer good criticisms. |
7359 | Excess and deficiency are equally at fault [Kongzi (Confucius)] |
Full Idea: Excess and deficiency are equally at fault. | |
From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XI.16) | |
A reaction: This is the sort of wisdom we admire in Aristotle (and in any sensible person), but it may also be the deepest motto of conservatism, and it is a long way from romantic philosophy, and the clarion call of Nietzsche to greater excitement in life. |
7363 | The virtues of the best people are humility, maganimity, sincerity, diligence, and graciousness [Kongzi (Confucius)] |
Full Idea: He who in this world can practise five things may indeed be considered Man-at-his-best: humility, maganimity, sincerity, diligence, and graciousness. | |
From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XVII.5) | |
A reaction: A very nice list. Who could resist working with a colleague who had such virtues? Who could go wrong if they married a person who had them? I can't think of anything important that is missing. |
7361 | Men of the highest calibre avoid political life completely [Kongzi (Confucius)] |
Full Idea: Men of the highest calibre avoid political life completely. | |
From: Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE], XIV.37) | |
A reaction: Plato notes that such people tend to avoid political life (and a left sheltering, as if from a wild storm!), but he thinks they should be dragged into the political arena for the common good. Confucius seems to approve of the avoidance. Plato is right. |
23393 | Confucianism assumes that all good developments have happened, and there is only one Way [Norden on Kongzi (Confucius)] |
Full Idea: The two major limitations of Confucianism are that it assumes that all worthwhile cultural, social and ethical innovation has already occurred, and that it does not recognise the plurality of worthwhile ways of life. | |
From: comment on Kongzi (Confucius) (The Analects (Lunyu) [c.511 BCE]) by Bryan van Norden - Intro to Classical Chinese Philosophy 3.III | |
A reaction: In modern liberal terms that is about as conservative as it is possible to get. We think of it as the state of mind of an old person who can only long for the way things were when they were young. But 'hold fast to that which is good'! |