56 ideas
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| Full Idea: Fand P as 'will' and 'was', G as 'always going to be', H as 'always has been', all tenses reduce to 14 cases: the past series, each implying the next, FH,H,PH,HP,P,GP, and the future series PG,G,FG,GF,F,HF, plus GH=HG implying all, FP=PF which all imply. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.8) | |
| A reaction: I have tried to translate the fourteen into English, but am not quite confident enough to publish them here. I leave it as an exercise for the reader. |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| Full Idea: In temporal logic, if the converse Barcan formula holds then nothing goes out of existence, and the direct Barcan formula holds if nothing ever comes into existence. These results highlight the intuitive absurdity of the Barcan formulas. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This is my reaction to the modal cases as well - the absurdity of thinking that no actually nonexistent thing might possibly have existed, or that the actual existents might not have existed. Williamson seems to be the biggest friend of the formulas. |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| Full Idea: From one point of view intuitionistic logic is a part of classical logic, missing one axiom, from another classical logic is a part of intuitionistic logic, missing two connectives, intuitionistic v and → | |
| From: John P. Burgess (Philosophical Logic [2009], 6.4) |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| Full Idea: The question of the completeness of the full intuitionistic logic for its intended interpretation is not yet fully resolved. | |
| From: John P. Burgess (Philosophical Logic [2009], 6.9) |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| Full Idea: The relevantist logician's → is perhaps expressible by 'if A, then B, for that reason'. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.8) |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| Full Idea: Among the more technically oriented a 'logic' no longer means a theory about which forms of argument are valid, but rather means any formalism, regardless of its applications, that resembles original logic enough to be studied by similar methods. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: There doesn't seem to be any great intellectual obligation to be 'technical'. As far as pure logic is concerned, I am very drawn to the computer approach, since I take that to be the original dream of Aristotle and Leibniz - impersonal precision. |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| Full Idea: There are topics of great philosophical interest that classical logic neglects because they are not important to mathematics. …These include distinctions of past, present and future, or of necessary, actual and possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.1) |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| Full Idea: The Cut rule (from A|-B and B|-C, infer A|-C) directly expresses the classical doctrine that entailment is transitive. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| Full Idea: Classical logic neglects counterfactual conditionals for the same reason it neglects temporal and modal distinctions, namely, that they play no serious role in mathematics. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.1) | |
| A reaction: Science obviously needs counterfactuals, and metaphysics needs modality. Maybe so-called 'classical' logic will be renamed 'basic mathematical logic'. Philosophy will become a lot clearer when that happens. |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| Full Idea: Philosophical logic is a branch of logic, a technical subject. …Its centre of gravity today lies in theoretical computer science. | |
| From: John P. Burgess (Philosophical Logic [2009], Pref) | |
| A reaction: He firmly distinguishes it from 'philosophy of logic', but doesn't spell it out. I take it that philosophical logic concerns metaprinciples which compare logical systems, and suggest new lines of research. Philosophy of logic seems more like metaphysics. |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| Full Idea: When formalising arguments it is convenient to have as many connectives as possible available.; but when proving results about formulas it is convenient to have as few as possible. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: Illuminating. The fact that you can whittle classical logic down to two (or even fewer!) connectives warms the heart of technicians, but makes connection to real life much more difficult. Hence a bunch of extras get added. |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| Full Idea: Gricean implicature theory might suggest that a disjunction is never assertable when a disjunct is (though actually the disjunction might be 'pertinent') - but the procedure is indispensable in mathematical practice. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.2) | |
| A reaction: He gives an example of a proof in maths which needs it, and an unusual conversational occasion where it makes sense. |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| Full Idea: All occurrences of variables in atomic formulas are free. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.7) |
| 3005 | 'Jocasta' needs to be distinguished from 'Oedipus's mother' because they are connected by different properties [Fodor] |
| Full Idea: If the concept 'Jocasta' needs to be distinguished from the concept 'Oedipus's mother', that's all right because the two concepts are connected with different properties. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 84) |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| Full Idea: By contrast to rigidly designating proper names, …the denotation of definite descriptions is (in general) not rigid but flexible. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.9) | |
| A reaction: This modern way of putting it greatly clarifies why Russell was interested in the type of reference involved in definite descriptions. Obviously some descriptions (such as 'the only person who could ever have…') might be rigid. |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| Full Idea: There are atomic formulas, and formulas built from the connectives, and that is all. We show that all formulas have some property, first for the atomics, then the others. This proof is 'induction on complexity'; we also use 'recursion on complexity'. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.4) | |
| A reaction: That is: 'induction on complexity' builds a proof from atomics, via connectives; 'recursion on complexity' breaks down to the atomics, also via the connectives. You prove something by showing it is rooted in simple truths. |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| Full Idea: It might be wondered how one could have any kind of proof procedure at all if transitivity of entailment is disallowed, but the sequent calculus can get around the difficulty. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) | |
| A reaction: He gives examples where transitivity of entailment (so that you can build endless chains of deductions) might fail. This is the point of the 'cut free' version of sequent calculus, since the cut rule allows transitivity. |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| Full Idea: Instead of demonstrations which are either axioms, or follow from axioms by rules, we can have one ever-growing sequence of formulas of the form 'Axioms |- ______', where the blank is filled by Axioms, then Lemmas, then Theorems, then Corollaries. | |
| From: John P. Burgess (Philosophical Logic [2009], 5.3) |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| Full Idea: The valid formulas of classical sentential logic are called 'tautologically valid', or simply 'tautologies'; with other logics 'tautologies' are formulas that are substitution instances of valid formulas of classical sentential logic. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.5) |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| Full Idea: Validity (truth by virtue of logical form alone) and demonstrability (provability by virtue of logical form alone) have correlative notions of logical possibility, 'satisfiability' and 'consistency', which come apart in some logics. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| Full Idea: Models generally deliberately leave out meaning, retaining only what is important for the determination of truth values. | |
| From: John P. Burgess (Philosophical Logic [2009], 2.2) | |
| A reaction: This is the key point to hang on to, if you are to avoid confusing mathematical models with models of things in the real world. |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| Full Idea: In practice there is no need to consider any but mathematical models, models whose universes consist of mathematical objects, since every model is isomorphic to one of these. | |
| From: John P. Burgess (Philosophical Logic [2009], 1.8) | |
| A reaction: The crucial link is the technique of Gödel Numbering, which can translate any verbal formula into numerical form. He adds that, because of the Löwenheim-Skolem theorem only subsets of the natural numbers need be considered. |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| Full Idea: The aim in setting up a model theory is that the technical notion of truth in all models should agree with the intuitive notion of truth in all instances. A model is supposed to represent everything about an instance that matters for its truth. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.2) |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| Full Idea: It is a common view that the liar sentence ('This very sentence is not true') is an instance of a truth-value gap (neither true nor false), but some dialethists cite it as an example of a truth-value glut (both true and false). | |
| From: John P. Burgess (Philosophical Logic [2009], 5.7) | |
| A reaction: The defence of the glut view must be that it is true, then it is false, then it is true... Could it manage both at once? |
| 7014 | A particle and a coin heads-or-tails pick out to perfectly well-defined predicates and properties [Fodor] |
| Full Idea: 'Is a particle and my coin is heads' and 'is a particle and my coin is tails' are perfectly well defined predicates and they pick out perfectly well defined (relational) properties of physical particles. | |
| From: Jerry A. Fodor (Psychosemantics [1987], Ch.2) | |
| A reaction: (Somewhat paraphrased). This is a very nice offering for the case that all predicates are properties, and hence that 'properties' is an entirely conventional category. It strikes me as self-evident that Fodor is not picking out 'natural' properties. |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| Full Idea: There is a problem over 'de re' modality (as contrasted with 'de dicto'), as in ∃x□x. What is meant by '"it is analytic that Px" is satisfied by a', given that analyticity is a notion that in the first instance applies to complete sentences? | |
| From: John P. Burgess (Philosophical Logic [2009], 3.9) | |
| A reaction: This is Burgess's summary of one of Quine's original objections. The issue may be a distinction between whether the sentence is analytic, and what makes it analytic. The necessity of bachelors being unmarried makes that sentence analytic. |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| Full Idea: To the extent that there is any conventional wisdom about the question, it is that S5 is correct for alethic logical modality, and S4 correct for apodictic logical modality. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.8) | |
| A reaction: In classical logic these coincide, so presumably one should use the minimum system to do the job, which is S4 (?). |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| Full Idea: Logical necessity is a genus with two species. For classical logic the truth-related notion of validity and the proof-related notion of demonstrability, coincide - but they are distinct concept. In some logics they come apart, in intension and extension. | |
| From: John P. Burgess (Philosophical Logic [2009], 3.3) | |
| A reaction: They coincide in classical logic because it is sound and complete. This strikes me as the correct approach to logical necessity, tying it to the actual nature of logic, rather than some handwavy notion of just 'true in all possible worlds'. |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| Full Idea: Three main theories of the truth of indicative conditionals are Materialism (the conditions are the same as for the material conditional), Idealism (identifying assertability with truth-value), and Nihilism (no truth, just assertability). | |
| From: John P. Burgess (Philosophical Logic [2009], 4.3) |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| Full Idea: It is contentious whether conditionals have negations, and whether 'it is not the case that if A,B' has any clear meaning. | |
| From: John P. Burgess (Philosophical Logic [2009], 4.9) | |
| A reaction: This seems to be connected to Lewis's proof that a probability conditional cannot be reduced to a single proposition. If a conditional only applies to A-worlds, it is not surprising that its meaning gets lost when it leaves that world. |
| 2990 | Contrary to commonsense, most of what is in the mind seems to be unlearned [Fodor] |
| Full Idea: Contrary to commonsense, it looks as though much of what is in the mind is unlearned. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 15) |
| 3009 | Sticklebacks have an innate idea that red things are rivals [Fodor] |
| Full Idea: God gave the male stickleback the idea that whatever is red is a rival. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p.133) |
| 3008 | Evolution suggests that innate knowledge of human psychology would be beneficial [Fodor] |
| Full Idea: If I had to design homo sapiens, I would have made commonsense knowledge of homo sapiens psychology innate; that way nobody would have to spend time learning it. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p.132) |
| 2994 | In CRTT thought may be represented, content must be [Fodor] |
| Full Idea: In the Representation Theory of Mind, programs (the 'laws of thought') may be explicitly represented, but data structures (the 'contents of thought') have to be. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 25) | |
| A reaction: Presumably this is because content is where mental events actually meet up with the reality being considered. It may be an abstract procedure, but if it doesn't plug into reality then it isn't thought, but merely activity, like that of the liver. |
| 15494 | We can't use propositions to explain intentional attitudes, because they would need explaining [Fodor] |
| Full Idea: It's not clear what the point would be of an explanation of the intentionality of attitudes which presupposes objects that are intentional intrinsically. Why not just say that the attitudes are? | |
| From: Jerry A. Fodor (Psychosemantics [1987], Ch.3) |
| 7326 | Intentionality doesn't go deep enough to appear on the physicists' ultimate list of things [Fodor] |
| Full Idea: Sooner or later the physicists will complete the catalogue of ultimate and irreducible things, with the likes of spin, charm and charge. But aboutness won't be on the list; intentionality simply doesn't go that deep. | |
| From: Jerry A. Fodor (Psychosemantics [1987], 4 Intro) | |
| A reaction: I totally agree with this, which I take to be a warning to John Searle against including something called 'intrinsic intentionality' into his ontology. Intentionality 'emerges' out of certain complex brain activity. |
| 3001 | Behaviourism has no theory of mental causation [Fodor] |
| Full Idea: Behaviourists had trouble providing a robust construal of mental causation (and hence had no logical space for a psychology of mental processes). | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 67) | |
| A reaction: If they could reduce all mental events to stimulus-response, that seems to fall within the normal procedures of physical causation. There is no problem of mental causation if your ontology is entirely physical. |
| 2993 | Any piece of software can always be hard-wired [Fodor] |
| Full Idea: For any machine that computes a function by executing an explicit algorithm, there exists a hard-wired machine that computes the same function by not executing an explicit algorithm. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 23) | |
| A reaction: It is certainly vital for functionalists to understand that software can be hardwired. Presumably we should understand a hardwired alogirthm as 'implicit'? |
| 3011 | Causal powers must be a crucial feature of mental states [Fodor] |
| Full Idea: Everybody is a functionalist, in that we all hold that mental states are individuated, at least in part, by reference to their causal powers. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p.138) | |
| A reaction: I might individuate the Prime Minister by the carnation in his buttonhole. However, even a dualist must concede that we individuate mental faculties by their role within the mind. |
| 5498 | Mind is a set of hierarchical 'homunculi', which are made up in turn from subcomponents [Fodor, by Lycan] |
| Full Idea: Fodor sees behaviour as manifestations of psychological capacities, which result from the subject being a set of interconnected 'homunculi', which in turn have subcomponents, all of it arranged in a hierarchy. | |
| From: report of Jerry A. Fodor (Psychosemantics [1987]) by William Lycan - Introduction - Ontology p.9 | |
| A reaction: This may well miss out the most interesting parts of a mind (such as awareness, and personal identity), but it sounds basically right, especially when an evolutionary history is added to the system. Parts of my mind intrude into my trains of thought. |
| 2995 | Supervenience gives good support for mental causation [Fodor] |
| Full Idea: Mind/brain supervenience is the best idea anyone has had so far about how mental causation is possible. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 30) | |
| A reaction: I would have thought that mind brain identity was a much better idea (see Idea 3440). Supervenience seems to prove that 'mental causation' occurs, but doesn't explain it. |
| 2991 | Hume's associationism offers no explanation at all of rational thought [Fodor] |
| Full Idea: With Associationism there proved to be no way to get a rational mental life to emerge from the sorts of causal relations among thoughts that the 'laws of association' recognised. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 18) | |
| A reaction: This might not be true if you add the concept of evolution, which has refined the associations to generate truth (which is vital for survival). |
| 3002 | If mind is just physical, how can it follow the rules required for intelligent thought? [Fodor] |
| Full Idea: Central state identity theorists had trouble providing for the nomological possibility of rational machines (and hence no space for a non-biological, e.g. computational, theory of intelligence). | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 67) | |
| A reaction: I surmise that a more externalist account of the physical mind might do the trick, by explaining intelligence in terms of an evolved relationship between brain and environment. |
| 2992 | We may be able to explain rationality mechanically [Fodor] |
| Full Idea: We are on the verge of solving a great mystery about the mind: how is rationality mechanically possible? | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 20) | |
| A reaction: Optimistic, given that AI has struggled to implement natural languages, mainly because common sense knowledge seems too complex to encode. Can a machine determine logical forms of sentences? |
| 2988 | Folk psychology is the only explanation of behaviour we have [Fodor] |
| Full Idea: Commonsense belief/desire psychology explains vastly more of the facts about behaviour than any of the alternative theories available. It could hardly fail to; there are no alternative theories available. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p.x) | |
| A reaction: The alternative view wouldn't expect a clear-cut theory, because it deals with the endless complexity of brain events. The charge is that Fodor and co oversimplify their account, in their desperation for a 'theory'. |
| 3010 | Belief and desire are structured states, which need mentalese [Fodor] |
| Full Idea: A defence of the language of thought has to be an argument that believing and desiring are typically structured states. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p.136) | |
| A reaction: A structure is one thing, and a language is another. Both believings and desirings can be extremely vague, to the point where the owner is unsure what is believed or desired. They can, of course, be extremely precise. |
| 2999 | Obsession with narrow content leads to various sorts of hopeless anti-realism [Fodor] |
| Full Idea: People who ask what the narrow content of the thought that water is wet is (for example) get what they deserve: phenomenalism, verificationism, 'procedural' semantics, or scepticism, according to temperament. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 51) | |
| A reaction: The question is whether content IS narrow. We could opt for broad content because then we wouldn't have to worry about scepticism, but I doubt whether we would then sleep well at night. |
| 3012 | Do identical thoughts have identical causal roles? [Fodor] |
| Full Idea: If thoughts have their causal roles in virtue of their contents, then two thoughts with identical contents ought to be identical in their causal roles. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p.140) | |
| A reaction: A pencil would presumably have the same causal role if it wrote a love poem or hate mail. But a pencil is also good for scratching your back. 'Causal role' can be a rather vacuous idea. |
| 2998 | Grice thinks meaning is inherited from the propositional attitudes which sentences express [Fodor] |
| Full Idea: According to Gricean theories of meaning, the meaning of a sentence is inherited from the propositional attitudes that the sentence is conventionally used to express. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 50) | |
| A reaction: Since the propositional attitudes contain propositions, this seems like a very plausible idea. If an indexical like 'I' is involved, the meaning of the sentence is not the same as its 'conventional' use. |
| 3006 | Whatever in the mind delivers falsehood is parasitic on what delivers truth [Fodor] |
| Full Idea: The mechanisms that deliver falsehoods are somehow parasitic on the ones that deliver truths. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p.107) | |
| A reaction: In the case of a sentence and its negation it is not clear which one is 'parasitic', because that can usually be reversed by paraphrasing. Historically, I very much hope that truth-speaking came first. |
| 3007 | Many different verification procedures can reach 'star', but it only has one semantic value [Fodor] |
| Full Idea: Verification procedures connect terms with their denotations in too many ways. Different routes to 'star' do not determine different semantic values for 'star'. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p.125) | |
| A reaction: This fairly conclusively shows that meaning is not 'the method of verification' - but that wasn't a difficult target to hit. |
| 3004 | The meaning of a sentence derives from its use in expressing an attitude [Fodor] |
| Full Idea: The meaning of a sentence derives from its use in expressing an attitude. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 79) | |
| A reaction: Among other things. It can also arrive from a desire to remember something. A sentence can also acquire meaning compositionally (by assembling) with no use or aim. |
| 3000 | Meaning holism is a crazy doctrine [Fodor] |
| Full Idea: Meaning holism really is a crazy doctrine. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 60) | |
| A reaction: Yes. What is not crazy is a contextualist account of utterances, and a recognition of the contextual and relational ingredient in the meanings of most of our sentences. |
| 3003 | Very different mental states can share their contents, so content doesn't seem to be constructed from functional role [Fodor] |
| Full Idea: It's an embarrassment for attempts to construct content from functional role that quite different sorts of mental states can nevertheless share their contents. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 70) | |
| A reaction: That is, presumably, one content having two different roles. Two contents with the same role is 'multiple realisability'. Pain can tell me I'm damaged, or reveal that my damaged nerves are healing. Problem? |
| 2996 | Mental states may have the same content but different extensions [Fodor] |
| Full Idea: The identity of the content of mental states does not ensure the identity of their extensions. | |
| From: Jerry A. Fodor (Psychosemantics [1987], p. 45) | |
| A reaction: Obviously if I am thinking each day about 'my sheep', that won't change if I am unaware that one of them died this morning. …Because I didn’t have the precise number of sheep in mind. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |