18 ideas
| 15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
| Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3) | |
| A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
| 15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
| Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.3) |
| 15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
| Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
| A reaction: [He cites Fagin and Halpern 1988 for this] |
| 15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
| Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
| 11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
| Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
| From: Melvin Fitting (Intensional Logic [2007], §1) |
| 14352 | '¬', '&', and 'v' are truth functions: the truth of the compound is fixed by the truth of the components [Jackson] |
| Full Idea: It is widely agreed that '¬', '&', and 'v' are 'truth functions': the truth value of a compound sentence formed using them is fully determined by the truth value or values of the component sentences. | |
| From: Frank Jackson (Conditionals [2006], 'Equiv') | |
| A reaction: A candidate for not being a truth function might be a conditional →, where the arrow adds something over and above the propositions it connects. The relationship has an additional truth value? Does A depend on B? |
| 11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
| Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
| From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
| A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
| 14360 | Possible worlds for subjunctives (and dispositions), and no-truth for indicatives? [Jackson] |
| Full Idea: Subjunctive conditionals are intimately connected with dispositional properties and causation. ...Consequently, a position some find attractive is that possible worlds theory applies to subjunctives, while the no-truth theory applies to indicatives. | |
| From: Frank Jackson (Conditionals [2006], 'Indicative') | |
| A reaction: My intuitions are to reject this and favour a unified account, where both sorts of conditionals are mappings of the relationships among the facts of actuality. Nice slogan! |
| 14353 | Modus ponens requires that A→B is F when A is T and B is F [Jackson] |
| Full Idea: Modus ponens is intuitively valid, but in A,A→B|B if A is true and B is false that must be because A→B is false. So A→B is false when A is true and B is false. | |
| From: Frank Jackson (Conditionals [2006], 'Equiv') | |
| A reaction: This is his first step in showing how the truth functional account of A→B acquires its truth table. If you are giving up the truth functional view of conditionals, presumably you are not also going to give up modus ponens? |
| 14354 | When A and B have the same truth value, A→B is true, because A→A is a logical truth [Jackson] |
| Full Idea: (A→A) is a logical truth, so some conditionals with antecedent and consequent the same truth value are true. But if '→' is a truth function, that will be true for all cases. Hence whenever A and B are alike in truth value, (A→B) is true. | |
| From: Frank Jackson (Conditionals [2006], 'Equiv') | |
| A reaction: His second step in demonstrating the truth table for →, assuming it is truth functional. |
| 14355 | (A&B)→A is a logical truth, even if antecedent false and consequent true, so it is T if A is F and B is T [Jackson] |
| Full Idea: (A&B)→A is a logical truth, but A can be true and B false, so that (A&B) is false. So some conditionals with false antecedent and true consequent are true. If → is a truth function, then whenever A is false and B is true (A→B) is true. | |
| From: Frank Jackson (Conditionals [2006], 'Equiv') | |
| A reaction: This is his third and final step in showing the truth table of → if it is truth functional. |
| 14358 | In the possible worlds account of conditionals, modus ponens and modus tollens are validated [Jackson] |
| Full Idea: In the possible worlds account modus ponens is validated (the closest world, the actual, is a B-world just if B is true), and modus tollens is validated (if B is false, the actual world is not an A-world, so A is false). | |
| From: Frank Jackson (Conditionals [2006], 'Famous') | |
| A reaction: [see Jackson for slightly fuller versions] This looks like a minimal requirement for a decent theory of conditionals, so Jackson explains the attractions of the possible worlds view very persuasively. |
| 14359 | Only assertions have truth-values, and conditionals are not proper assertions [Jackson] |
| Full Idea: In the no-truth theory of conditionals they have justified assertion or acceptability conditions but not truth conditions. ...The motivation is that only assertions have truth values, and conditionals are arguments, not proper assertions. | |
| From: Frank Jackson (Conditionals [2006], 'No-truth') | |
| A reaction: Once I trim this idea down to its basics, it suddenly looks very persuasive. Except that I am inclined to think that conditional truths do state facts about the world - perhaps as facts about how more basic truths are related to each other. |
| 14357 | Possible worlds account, unlike A⊃B, says nothing about when A is false [Jackson] |
| Full Idea: In the possible worlds account of conditionals A⊃B is not sufficient for A→B. If A is false then A⊃B is true, but here nothing is implied about whether the world most like the actual world except that A is true is or is not a B-world. | |
| From: Frank Jackson (Conditionals [2006], 'Possible') | |
| A reaction: The possible worlds account seems to be built on Ramsey's idea of just holding A true and seeing what you get. Being committed to B being automatically true if A is false seems highly counterintuitive. |
| 14356 | We can't insist that A is relevant to B, as conditionals can express lack of relevance [Jackson] |
| Full Idea: One addition to the truth functional account of conditionals is that A be somehow relevant to B. However, sometimes we use conditionals to express lack of relevance, as in 'If Fred works he will fail, and if Fred doesn't work he will fail'. | |
| From: Frank Jackson (Conditionals [2006], 'Possible') | |
| A reaction: This certainly seems to put paid to an attractive instant solution to the problem. |
| 15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
| Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
| From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
| A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
| 20991 | People prepare our dinner from their own self-interest, not from humanity [Smith,A] |
| Full Idea: It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest. We address ourselves, not to their humanity but to their self-love. | |
| From: Adam Smith (The Wealth of Nations [1776], p.26-7), quoted by Amartya Sen - The Idea of Justice 08 'Narrowing' | |
| A reaction: Sen passionately pleads that this not be taken out of context. It is about the motivation for the relationship of exchange, and not about morality in general, which also includes trust etc. The subsequent lines in Smith show this. |
| 20680 | Selfish profit-seeking increases collective wealth, so greed is good, and egoism is altruism [Smith,A, by Harari] |
| Full Idea: Smith's claim that the selfish human urge to increase private profits is the basis for collective wealth is one of the most revolutionary ideas in human history. …Greed is good …and egoism is altruism. | |
| From: report of Adam Smith (The Wealth of Nations [1776]) by Yuval Noah Harari - Sapiens: brief history of humankind 16 'Growing' | |
| A reaction: The central confrontation of political philosophy still seems to be Adam Smith v Karl Marx. Why can't there be altruistic non-greedy profit-seeking? Not 'I want profits' but 'we want profits'. Altruistic capitalists aim to create jobs. |