40 ideas
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 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. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 23634 | Accepting the existence of anything presupposes the notion of existence [Reid] |
| Full Idea: The belief of the existence of anything seems to suppose a notion of existence - a notion too abstract, perhaps, to enter into the mind of an infant. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 05) | |
| A reaction: But even a small infant has to cope with the experience of waking up from a dream. I don't see how existence can be anything other than a primitive concept in any system of ontology. |
| 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. |
| 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. |
| 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. |
| 23635 | Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid] |
| Full Idea: Self-evident propositions are those which appear evident to every man of sound understanding who apprehends the meaning of them distinctly, and attends to them without prejudice. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 10) | |
| A reaction: I suspect that there are some truths which are self-evident to dogs. There are also truths which are self-evident to experts, but not to ordinary persons of good understanding. Self-evidence is somewhat contextual. Self-evidence can be empirical. |
| 7631 | Sensation is not committed to any external object, but perception is [Reid] |
| Full Idea: Sensation, by itself, implies neither the conception nor belief of any external object. ...Perception implies a conviction and belief of something external. ...Things so different in their nature ought to be distinguished. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], II.16), quoted by Barry Maund - Perception | |
| A reaction: Maund sees this as the origin of the two-stage view of perception, followed by Chisholm, Evans, Dretske and Lowe. It implies that 'looks', 'tastes', 'sounds' etc. are ambiguous words, having either phenomenal or realist meanings. I like it. |
| 23637 | Primary qualities are the object of mathematics [Reid] |
| Full Idea: The primary qualities are the object of the mathematical sciences. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 17) | |
| A reaction: He spells out this crucial point, which is not so obvious in Locke. The sciences totally rely on the primary qualities, so it is ridiculous to reject the distinction (which Reid accepts). |
| 23638 | Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid] |
| Full Idea: The thought of a secondary quality always carries us back to the sensation which it produces.We give the same name to both, and are apt to confound them. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 17) | |
| A reaction: 'Redness', for example. Reid puts the point very nicely. Secondary qualities are not entirely mental; they pick out features of the world, but are much harder to understand than the primary qualities. The qualia question lurks. |
| 23639 | It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid] |
| Full Idea: If it be made a question whether the toothache be in the mind that feels it, or in tooth that is affected, much might be said on both sides, while it is not observed that the word has two meanings. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 18) | |
| A reaction: I'm glad Reid was struck by the weird phenomenon of the brain apparently 'projecting' a pain into a tooth. Presumably before the brain's role was known, people were unaware of this puzzle. There certainly are not two distinct experiences. |
| 6492 | Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H] |
| Full Idea: Reid is often represented by modern opponents of the empiricists as the outstanding protagonist of direct or naïve realism and common sense in the eighteenth century. | |
| From: report of Thomas Reid (Essays on Intellectual Powers 2: Senses [1785]) by Howard Robinson - Perception 1.6 | |
| A reaction: Robinson does not deny that this is Reid's view. Keith Lehrer is a great fan of Reid. Personally I think direct realism is quite clearly false, so I find myself losing interest in Reid's so-called 'common sense'. |
| 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. |
| 23641 | People dislike believing without evidence, and try to avoid it [Reid] |
| Full Idea: To believe without evidence is a weakness which every man is concerned to avoid, and which every man wishes to avoid. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 20) | |
| A reaction: It seems to be very common, though, for people to believe things on incredibly flimsy evidence, if they find the belief appealing. This is close to Clifford's Principle, but not quite as dogmatic. |
| 23642 | If non-rational evidence reaches us, it is reason which then makes use of it [Reid] |
| Full Idea: If Nature gives us information of things that concern us, by other means that by reasoning, reason itself will direct us to receive that information with thankfulness, and to make the best use of it. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 20) | |
| A reaction: This is more of a claim than an argument, but it is hard to see how anything could even be seen as evidence if some sort of rational judgement has not been made. The clever detective sees which facts are evidence. |
| 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. |
| 23640 | Only mature minds can distinguish the qualities of a body [Reid] |
| Full Idea: I think it requires some ripeness of understanding to distinguish the qualities of a body from the body; perhaps this distinction is not made by brutes, or by infants. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 19) | |
| A reaction: I'm glad the brutes get a mention in his assessment of these questions. I take such thinking to arise from what can be labelled the faculty of abstraction, which presumably only appears in a mature brain. It is second-level 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. |
| 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. |