38 ideas
| 16137 | Earlier views of Aristotle were dominated by 'Categories' [Frede,M] |
| Full Idea: For centuries 'Categories' and 'De Interpretatione' (+ Porphyry's 'Isagoge') formed the core of the philosophical corpus still being seriously studied. It is hardly surprising that our received view of Aristotle was coloured substantially by 'Categories'. | |
| From: Michael Frede (Title, Unity, Authenticity of the 'Categories' [1983], I) | |
| A reaction: He adds that doubts remain about the authenticity of the second part, and the whole thing bears marks of having been edited. |
| 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. |
| 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. |
| 2730 | Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R] |
| Full Idea: Taking the proposition that gold is malleable to be necessary does not commit one to considering it analytic. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], IV p.116) |
| 2715 | Beliefs are based on perception, memory, introspection or reason [Audi,R] |
| Full Idea: The four basic kinds of belief are rooted in perception, memory, introspective consciousness, and reason. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], Intr.p.7) |
| 2735 | Could you have a single belief on its own? [Audi,R] |
| Full Idea: Could one have just a single belief? | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.198) |
| 2736 | We can make certain of what we know, so knowing does not entail certainty [Audi,R] |
| Full Idea: The possibility of making certain of what we already know suggests that knowing a proposition does not entail its being certain. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.220) |
| 2721 | If you gradually remove a book's sensory properties, what is left at the end? [Audi,R] |
| Full Idea: If you imagine subtracting a book's sensory properties one by one, what is left of it? | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.42) |
| 2722 | Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R] |
| Full Idea: Where the sense-datum theory is an indirect realism, phenomenalism is a direct irrealism. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.43) |
| 2728 | The concepts needed for a priori thought may come from experience [Audi,R] |
| Full Idea: I may well need experience to acquire the concepts needed for knowledge of the a priori, such as the concept of a colour. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], IV p.103) |
| 2727 | Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R] |
| Full Idea: The proposition that nothing is red and green all over at once is not analytic, but it is rationally graspable, so it seems to be an a priori synthetic proposition. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], IV p.100) |
| 2717 | How could I see a field and believe nothing regarding it? [Audi,R] |
| Full Idea: How could I see a field and believe nothing regarding it? | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.20) |
| 2716 | To see something as a field, I obviously need the concept of a field [Audi,R] |
| Full Idea: The propositional belief which portrays what I see in front of me AS a field requires my having a concept of one. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.17) | |
| A reaction: To me this immediately invites the question of what a cow or horse experiences when they look at a familiar field. They know how to leave and enter it, and register its boundaries and qualities. Concepts? |
| 2719 | Sense data imply representative realism, possibly only representing primary qualities [Audi,R] |
| Full Idea: A sense-datum theory might be called a representative realism because it conceives perception as a relation in which sense-data represent perceived external (hence real) objects to us. For Locke they were resemblances only of primary qualities. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.33) |
| 2720 | Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R] |
| Full Idea: The sense-datum theory is mainly to explain hallucinations and illusions, though there might be other theories, such as the 'adverbial' theory. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.36) |
| 2718 | Perception is first simple, then objectual (with concepts) and then propositional [Audi,R] |
| Full Idea: Simple perceiving gives rise to objectual perceiving (attaching concepts to the object), which gives rise to propositional perceiving. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], I p.23) |
| 2729 | Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R] |
| Full Idea: Rationalists virtually always assert or imply that, in addition to knowledge of analytic truths, there is knowledge of synthetic a priori truths. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], IV p.105) |
| 2741 | The principles of justification have to be a priori [Audi,R] |
| Full Idea: The crucial principles of justification are a priori. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], X p.311) |
| 2725 | To remember something is to know it [Audi,R] |
| Full Idea: Remembering something is so entails knowing that it is so. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], II p.68) | |
| A reaction: Clearly I can say I "remember" x, but be wrong. Presumably we then say that I didn't really remember, which requires success, like "I know". It is true (as with "know") that as soon as I say that the something is false, I can't claim to remember it. |
| 2724 | I might remember someone I can't recall or image, by recognising them on meeting [Audi,R] |
| Full Idea: If I can neither recall nor image Jane I can still remember her, for on seeing her I might recognise her, and might remember, and even recall, our last meeting. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], II p.66) | |
| A reaction: Hm. I can hardly claim to remember her if I have no concept of her, and don't recall our last meeting. If seeing her triggers recognition, I would say that I NOW remember her, but I didn't before. Memory is more conscious than Audi claims. |
| 2731 | Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R] |
| Full Idea: There are four possible kinds of epistemic chain: infinite and unanchored, circular and unanchored, anchored in a belief which is not knowledge, and anchored in a belief which is bedrock knowledge. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.183) | |
| A reaction: About right, though I don't think 'chain' is the right word for what is proposed if justification is to be coherent. The justifications float like lilies in the pond of reason, and a Self (Monet?) seems needed to assess the picture |
| 2739 | Internalism about justification implies that there is a right to believe something [Audi,R] |
| Full Idea: Internalists about justification tend to conceive of it as a matter of having a right to believe something. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.234) | |
| A reaction: I'm an internalist, but I don't understand this, unless it refers to the social aspect of justification. Can I grant myself internal rights? I can justify my belief to other people. |
| 2732 | Maths may be consistent with observations, but not coherent [Audi,R] |
| Full Idea: That 7+5=12 and that carrots are nourishing are mutually consistent, but do not exhibit coherence. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.192) | |
| A reaction: This shows how difficult it would be to define 'coherent'. Is 'carrots are nourishing' coherent with 'fish are nourishing'? Is the battle of Hastings coherent with the battle of Waterloo? |
| 2733 | It is very hard to show how much coherence is needed for justification [Audi,R] |
| Full Idea: It is very difficult to specify when an explanatory relation generates enough coherence to create justification. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.193) | |
| A reaction: I take coherence to be the key concept in epistemology, and quite impossible to define. This is why the 'space of reasons' is a useful concept. It is a courtroom, in which each case is different. |
| 2734 | A consistent madman could have a very coherent belief system [Audi,R] |
| Full Idea: A schizophrenic who thinks he is Napoleon, if he has a completely consistent story with enough interlocking details, may have a belief system that is superbly coherent. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VII p.194) | |
| A reaction: This is an exaggeration, but the fact is that one isolated lie is totally coherent, so coherence can only emerge when a system is large. Sense experience must be central to coherence. |
| 2738 | Consistent accurate prediction looks like knowledge without justified belief [Audi,R] |
| Full Idea: If someone consistently prophesied the winners of horse races, it appears that this man knows who will win the races, but surely he does not have justified beliefs as to who will win? | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.229) | |
| A reaction: This is where internalists and externalists (notably reliabilists) sharply part company. IF a reliable clairvoyant appeared, we would eventually accept them as a knower. But they DON'T appear, because knowledge needs justification! |
| 2740 | A reliability theory of knowledge seems to involve truth as correspondence [Audi,R] |
| Full Idea: If one favours a reliability theory of knowledge (which is externalist) the correspondence theory of truth seems the most appropriate. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.243) | |
| A reaction: Sounds right. Coherence implies some sort of internal assessment, whereas correspondence just needs to plugged into the facts. I like coherence justification and correspondence truth. |
| 2737 | 'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R] |
| Full Idea: Reliabilism cannot specify how reliable a process must be before it grounds knowledge, and it cannot specify what is reliable in the first place. 'Reliable' may become circular, and may mean 'justified'. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], VIII p.225) | |
| A reaction: The first time you ever read an instrument, or talk to a stranger, you have no indication of reliability. Circularity looks like a big problem. Knowledge must precede reliability? |
| 2726 | We can be ignorant about ourselves, for example, our desires and motives [Audi,R] |
| Full Idea: We can have false beliefs, or some degree of ignorance, about our own mental lives. For example, about our own dispositions, such as not believing that we have a certain ignoble desire. | |
| From: Robert Audi (Epistemology: contemporary introduction [1998], III p.83) | |
| A reaction: This idea, that we don't know ourselves, has become a commonplace of recent philosophy, but I am unconvinced. Mostly we know only too well that we harbour a base desire, and we feel a creeping sense of shame. Total ignorance is very rare. |