37 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) |
| 13331 | Part and whole contribute asymmetrically to one another, so must differ [Fine,K] |
| Full Idea: The whole identity of a part is relevant to whether it is a part, but the identity of the whole makes a part a part. The whole part belongs to the whole as a part. The standard account in terms of time-slices fails to respect this part/whole asymmetry. | |
| From: Kit Fine (Things and Their Parts [1999], §2) | |
| A reaction: Hard to follow, but I think the asymmetry is that the wholeness of the part contributes to the wholeness of the whole, while the wholeness of the whole contributes to the parthood of the part. Wholeness does different jobs in different directions. OK? |
| 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) |
| 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? |
| 13332 | Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K] |
| Full Idea: It is the hierarchical conception of sets and their members, rather than the linear conception of set and subset or of aggregate and component, that provides us with the better model for the structure of part-whole in its application to material things. | |
| From: Kit Fine (Things and Their Parts [1999], §5) | |
| A reaction: His idea is to give some sort of internal structure. He says of {a,b,c,d} that we can create subsets {a,b} and {c,d} from that. But {{a,b},{c,d}} has given member sets, and he is looking for 'natural' divisions between the members. |
| 13333 | The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K] |
| Full Idea: The wood is, as it were, a relatively unstructured version of the tree, just as the set {a,b,c,d} is an unstructured counterpart of the set {{a,b},{c,d}}. | |
| From: Kit Fine (Things and Their Parts [1999], §5) | |
| A reaction: He is trying to give a modern logicians' account of the Aristotelian concept of 'form' (as applied to matter). It is part of the modern project that objects must be connected to the formalism of mereology or set theory. If it works, are we thereby wiser? |
| 13326 | A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K] |
| Full Idea: First, a thing can be a part in a way that is relative to a time, for example, that a newly installed carburettor is now part of my car, whereas earlier it was not. (This will be called a 'temporary' part). | |
| From: Kit Fine (Things and Their Parts [1999], Intro) | |
| A reaction: [Cf Idea 13327 for the 'second' concept of part] I'm immediately uneasy. Being a part seems to be a univocal concept. He seems to be distinguishing parts which are necessary for identity from those which aren't. Fine likes to define by example. |
| 13327 | A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K] |
| Full Idea: Second, an object can be a part of another in a way that is not relative to time ('timeless'). It is not appropriate to ask when it is a part. Thus pants and jacket are parts of the suit, atoms of a water molecule, and two pints part of a quart of milk. | |
| From: Kit Fine (Things and Their Parts [1999], Intro) | |
| A reaction: [cf Idea 13326 for the other concept of 'part'] Again I am uneasy that 'part' could have two meanings. A Life Member is a member in the same way that a normal paid up member is a member. |
| 13329 | An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K] |
| Full Idea: In the 'aggregative' understanding of a sum, it is spread out in time, so that exists whenever any of its components exists (just as it is located at any time wherever any of its components are located). | |
| From: Kit Fine (Things and Their Parts [1999], §1) | |
| A reaction: This works particularly well for something like an ancient forest, which steadily changes its trees. On that view, though, the ship which has had all of its planks replaced will be the identical single sum of planks all the way through. Fine agrees. |
| 13330 | An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K] |
| Full Idea: In the 'compound' notion of sum, the mereological sum is spread out only in space, not also in time. For it to exist at a time, all of its components must exist at the time. | |
| From: Kit Fine (Things and Their Parts [1999], §1) | |
| A reaction: It is hard to think of anything to which this applies, apart from for a classical mereologist. Named parts perhaps, like Tom, Dick and Harry. Most things preserve sum identity despite replacement of parts by identical components. |
| 13328 | Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K] |
| Full Idea: I develop a version of hylomorphism, in which the theory of 'rigid embodiment' provides an account of the timeless relation of part, and the theory of 'variable embodiment' is an account of the temporary relation. We must accept two new kinds of whole. | |
| From: Kit Fine (Things and Their Parts [1999], Intro) | |
| A reaction: [see Idea 13326 and Idea 13327 for the two concepts of 'part'] This is easier to take than the two meanings for 'part'. Since Aristotle, everyone has worried about true wholes (atoms, persons?) and looser wholes (houses). |
| 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. |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |