82 ideas
6979 | Serious metaphysics cares about entailment between sentences [Jackson] |
Full Idea: Serious metaphysics is committed to views about which sentences entail which other sentences. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
A reaction: This does not say that metaphysics is only about entailment, or (even worse) only about sentences. Put another way: if we wish to be wise, we must study the implications of our beliefs. Yes. |
6980 | Conceptual analysis studies whether one story is made true by another story [Jackson] |
Full Idea: Conceptual analysis is the very business of addressing when and whether a story told in one vocabulary is made true by one told in some allegedly more fundamental vocabulary. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.2) | |
A reaction: This is a view of linguistic analysis as focusing on entailments rather than on usage or truth conditions. If philosophy is the attempt to acquire a totally consistent set of beliefs (a plausible view), then Jackson is right. |
6983 | Intuitions about possibilities are basic to conceptual analysis [Jackson] |
Full Idea: Intuitions about possibilities are the bread and butter of conceptual analysis. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
A reaction: Hence the centrality of the debate over conceivability and possibility. Which seems to reduce to the relationship between 'intuition' and 'imagination'. Imagination is a very weak guide to what is possible, and intuition is very uncertain.... |
14707 | Conceptual analysis is needed to establish that metaphysical reductions respect original meanings [Jackson, by Schroeter] |
Full Idea: On the empiricist view of meaning, the relevance of conceptual analysis to metaphysics is that it establishes that a putative reduction respects the original meaning of the target expression. | |
From: report of Frank Jackson (From Metaphysics to Ethics [1998], p.28) by Laura Schroeter - Two-Dimensional Semantics 2.2.4 |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
Full Idea: Dedkind gave a rigorous proof of the principle of definition by recursion, permitting recursive definitions of addition and multiplication, and hence proofs of the familiar arithmetical laws. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 13 'Deriv' |
7005 | Something can only have a place in a preferred account of things if it is entailed by the account [Jackson] |
Full Idea: The one and only way of having a place in an account told in some set of preferred terms is by being entailed by that account - a view I will refer to as the entry by entailment thesis. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
A reaction: How do we distinguish between the original account, which seems to be just accepted, and the additions which accrue because they are entailed by it? Why does this club distinguish members from guests? |
6994 | Truth supervenes on being [Jackson] |
Full Idea: Truth supervenes on being. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
A reaction: A nice slogan for those of us who find the word 'truth' to be meaningful. |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
Full Idea: A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7 | |
A reaction: Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is! |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
Full Idea: Dedekind had an interesting proof of the Axiom of Infinity. He held that I have an a priori grasp of the idea of my self, and that every idea I can form the idea of that idea. Hence there are infinitely many objects available to me a priori. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], no. 66) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 12 'Numb' | |
A reaction: Who said that Descartes' Cogito was of no use? Frege endorsed this, as long as the ideas are objective and not subjective. |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
Full Idea: Dedekind plainly had fusions, not collections, in mind when he avoided the empty set and used the same symbol for membership and inclusion - two tell-tale signs of a mereological conception. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], 2-3) by Michael Potter - Set Theory and Its Philosophy 02.1 | |
A reaction: Potter suggests that mathematicians were torn between mereology and sets, and eventually opted whole-heartedly for sets. Maybe this is only because set theory was axiomatised by Zermelo some years before Lezniewski got to mereology. |
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? |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
Full Idea: Numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things. | |
From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
A reaction: Does this fit real numbers and complex numbers, as well as natural numbers? Frege was concerned by the lack of objectivity in this sort of view. What sort of arithmetic might the Martians have created? Numbers register sameness too. |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
Full Idea: It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
Full Idea: Dedekind and Cantor said the cardinals may be defined in terms of the ordinals: The cardinal number of a set S is the least ordinal onto whose predecessors the members of S can be mapped one-one. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 5 |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
Full Idea: Dedekind said that the notion of order, rather than that of quantity, is the central notion in the definition of number. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.4 | |
A reaction: Compare Aristotle's nice question in Idea 646. My intuition is that quantity comes first, because I'm not sure HOW you could count, if you didn't think you were changing the quantity each time. Why does counting go in THAT particular order? Cf. Idea 8661. |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
Full Idea: Dedekind's ordinals are not essentially either ordinals or cardinals, but the members of any progression whatever. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §243 | |
A reaction: This is part of Russell's objection to Dedekind's structuralism. The question is always why these beautiful structures should actually be considered as numbers. I say, unlike Russell, that the connection to counting is crucial. |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
Full Idea: It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. | |
From: Richard Dedekind (Continuity and Irrational Numbers [1872], Intro) | |
A reaction: [He seeks the origin of the theorem that differential calculus deals with continuous magnitude, and he wants an arithmetical rather than geometrical demonstration; the result is his famous 'cut']. |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
Full Idea: Whenever we have to do a cut produced by no rational number, we create a new, an irrational number, which we regard as completely defined by this cut. | |
From: Richard Dedekind (Continuity and Irrational Numbers [1872], §4) | |
A reaction: Fine quotes this to show that the Dedekind Cut creates the irrational numbers, rather than hitting them. A consequence is that the irrational numbers depend on the rational numbers, and so can never be identical with any of them. See Idea 10573. |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
Full Idea: Dedekind set up the axiom that the gap in his 'cut' must always be filled …The method of 'postulating' what we want has many advantages; they are the same as the advantages of theft over honest toil. Let us leave them to others. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - Introduction to Mathematical Philosophy VII | |
A reaction: This remark of Russell's is famous, and much quoted in other contexts, but I have seen the modern comment that it is grossly unfair to Dedekind. |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
Full Idea: One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 | |
A reaction: Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'. |
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
Full Idea: Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power. | |
From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
A reaction: Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects. |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
Full Idea: If we scrutinize closely what is done in counting an aggregate of things, we see the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, without which no thinking is possible. | |
From: Richard Dedekind (Nature and Meaning of Numbers [1888], Pref) | |
A reaction: I don't suppose it occurred to Dedekind that he was reasserting Hume's observation about the fundamental psychology of thought. Is the origin of our numerical ability of philosophical interest? |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
Full Idea: I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself is nothing else than the successive creation of the infinite series of positive integers. | |
From: Richard Dedekind (Continuity and Irrational Numbers [1872], §1) | |
A reaction: Thus counting roots arithmetic in the world, the successor operation is the essence of counting, and the Dedekind-Peano axioms are built around successors, and give the essence of arithmetic. Unfashionable now, but I love it. Intransitive counting? |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
Full Idea: A system S is said to be infinite when it is similar to a proper part of itself. | |
From: Richard Dedekind (Nature and Meaning of Numbers [1888], V.64) |
18087 | If x changes by less and less, it must approach a limit [Dedekind] |
Full Idea: If in the variation of a magnitude x we can for every positive magnitude δ assign a corresponding position from and after which x changes by less than δ then x approaches a limiting value. | |
From: Richard Dedekind (Continuity and Irrational Numbers [1872], p.27), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.7 | |
A reaction: [Kitcher says he 'showed' this, rather than just stating it] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
Full Idea: Dedekind's natural numbers: an object is in a set (0 is a number), a function sends the set one-one into itself (numbers have unique successors), the object isn't a value of the function (it isn't a successor), plus induction. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William D. Hart - The Evolution of Logic 5 | |
A reaction: Hart notes that since this refers to sets of individuals, it is a second-order account of numbers, what we now call 'Second-Order Peano Arithmetic'. |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
Full Idea: Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4 |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
Full Idea: It is Dedekind's categoricity result that convinces most of us that he has articulated our implicit conception of the natural numbers, since it entitles us to speak of 'the' domain (in the singular, up to isomorphism) of natural numbers. | |
From: comment on Richard Dedekind (Nature and Meaning of Numbers [1888]) by Ian Rumfitt - The Boundary Stones of Thought 9.1 | |
A reaction: The main rival is set theory, but that has an endlessly expanding domain. He points out that Dedekind needs second-order logic to achieve categoricity. Rumfitt says one could also add to the 1st-order version that successor is an ancestral relation. |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
Full Idea: Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241 |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
Full Idea: Dedekind is the philosopher-mathematician with whom the structuralist conception originates. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888], §3 n13) by Fraser MacBride - Structuralism Reconsidered | |
A reaction: Hellman says the idea grew naturally out of modern mathematics, and cites Hilbert's belief that furniture would do as mathematical objects. |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
Full Idea: Dedekindian abstraction says mathematical objects are 'positions' in a model, while Cantorian abstraction says they are the result of abstracting on structurally similar objects. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §6 | |
A reaction: The key debate among structuralists seems to be whether or not they are committed to 'objects'. Fine rejects the 'austere' version, which says that objects have no properties. Either version of structuralism can have abstraction as its basis. |
6984 | Smooth reductions preserve high-level laws in the lower level [Jackson] |
Full Idea: In a 'smooth' reduction the laws of the reduced theory (thermodynamics of gases) are pretty much preserved in (and isomorphic with) the corresponding laws in the reducing theory (molecular or kinetic theory of gases). | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
A reaction: Are the 'laws' of weather (e.g. linking humidity, temperature and pressure to rainfall) preserved at the level of physics? One might say that they are not preserved, but they are not lost either (they just fade away). Contradictions would be worrying. |
6978 | Baldness is just hair distribution, but the former is indeterminate, unlike the latter [Jackson] |
Full Idea: Baldness is a much more indeterminate matter than is hair distribution, nevetheless baldness is nothing over and above hair distribution. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], p.22) | |
A reaction: This seems to support Williamson's view that there is no vagueness in nature, and that 'vague' is an entirely epistemological concept. |
6993 | Redness is a property, but only as a presentation to normal humans [Jackson] |
Full Idea: We typically count things as red just if they have a property that interacts with normal human beings to make the object look red in such a way that their so looking counts as a presentation of the property to normal humans. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.4) | |
A reaction: This is Jackson's careful statement of the 'Australian' primary property view of colours. He is trying to make red a real property of objects, but personally I take the mention of 'normal' humans as a huge danger sign. Nice try, but no. See Idea 5456. |
8499 | Nominalists cannot translate 'red resembles pink more than blue' into particulars [Jackson] |
Full Idea: It is not always possible for nominalists to translate all statements putatively about universals as statements about particulars. It is not possible for 'red is a colour' and 'red resembles pink more than blue' | |
From: Frank Jackson (Statements about Universals [1977], p.89) | |
A reaction: His second example strikes me as the biggest challenge facing nominalism. I wish they wouldn't use secondary qualities as examples. I am unconvinced that the existence of universals will improve the explanation. It's a mystery. |
8500 | Colour resemblance isn't just resemblance between things; 'colour' must be mentioned [Jackson] |
Full Idea: Some red things resemble some blue things more than some pink things because of factors other than colour. Nominalists must offer 'anything red colour-resembles anything pink', but that may contain a universal in disguise. | |
From: Frank Jackson (Statements about Universals [1977], p.90) | |
A reaction: Hume and Quine are probably right that we spot resemblances instantly, and only articulate the respect of the resemblance at a later stage. |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
Full Idea: A thing (an object of our thought) is completely determined by all that can be affirmed or thought concerning it. | |
From: Richard Dedekind (Nature and Meaning of Numbers [1888], I.1) | |
A reaction: How could you justify this as an observation? Why can't there be unthinkable things (even by God)? Presumably Dedekind is offering a stipulative definition, but we may then be confusing epistemology with ontology. |
14633 | How do we tell a table's being contingently plastic from its being essentially plastic? [Jackson] |
Full Idea: On a friendly reading of Quine, there is nothing to make the difference between a table's being contingently plastic and its being essentially plastic. | |
From: Frank Jackson (Possible Worlds and Necessary A Posteriori [2010], 5) | |
A reaction: This is, of course, the dreaded modern usage of 'essential' to just mean 'necessary' and nothing more. In my view, there may be a big problem with knowing whether a problem is necessary, but knowing whether it is essential is much easier. |
14635 | An x is essentially F if it is F in every possible world in which it appears [Jackson] |
Full Idea: On the possible world's account, x's being essentially F is nothing more nor less than x's being F in every world in which it appears. | |
From: Frank Jackson (Possible Worlds and Necessary A Posteriori [2010], 6) | |
A reaction: There you go - 'true in every possible world' is the definition of metaphysical necessity, not the definition of essence. Either get back to Aristotle, or stop (forever!) talking about 'essence'! |
14632 | Quine may have conflated de re and de dicto essentialism, but there is a real epistemological problem [Jackson] |
Full Idea: The unfriendly response to Quine's objection to essentialism is that it conflates the de re and the de dicto. The friendly response is that behind that conflation is a real epistemological problem for essentialism. | |
From: Frank Jackson (Possible Worlds and Necessary A Posteriori [2010], 1) | |
A reaction: He cites Richard Cartwright 1968 for the friendly response. The epistemological question is how we can know the essentialness of an essence. |
6987 | We should not multiply senses of necessity beyond necessity [Jackson] |
Full Idea: We should not multiply senses of necessity beyond necessity. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
A reaction: It would be nice if there was just one sense of necessity, with the multiplication arising from the different ways in which necessities arise. In chess, checkmate is a necessity which rests on contingencies. Absolute necessities seem different. |
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! |
14288 | 'If A,B' affirms that A⊃B, and also that this wouldn't change if A were certain [Jackson, by Edgington] |
Full Idea: According to Jackson, in asserting 'If A,B' the speaker expresses his belief that A⊃B, and also indicates that this belief is 'robust' with respect to the antecedent A - the speaker would not abandon A⊃B if he were to learn that A. | |
From: report of Frank Jackson (On Assertion and Indicative Conditionals [1979]) by Dorothy Edgington - Conditionals (Stanf) 4.2 | |
A reaction: The point is that you must not believe A⊃B solely on the dubious grounds of ¬A. This is 'to ensure an assertable conditional is fit for modus ponens' - that is, that you really will affirm B when you learn that A is true. Nice idea. |
13769 | Conditionals are truth-functional, but should only be asserted when they are confident [Jackson, by Edgington] |
Full Idea: Jackson holds that conditionals are truth-functional, but are governed by rules of assertability, rather like 'but' compared to 'and'. The belief must be 'robust' - the speaker would not abandon his belief that A⊃B if he were to learn that A. | |
From: report of Frank Jackson (On Assertion and Indicative Conditionals [1979]) by Dorothy Edgington - Conditionals 17.3.2 | |
A reaction: This seems to spell out more precisely the pragmatic approach to conditionals pioneered by Grice, in Idea 13767. The idea is make conditionals 'fit for modus ponens'. They mustn't just be based on a belief that ¬A. |
13858 | The truth-functional account of conditionals is right, if the antecedent is really acceptable [Jackson, by Edgington] |
Full Idea: Jackson defends the truth-functional account by saying that for a conditional to be assertable, it must not only be believed that its truth-conditions are satisfied, but the belief must be robust or resilient with respect to the antecedent. | |
From: report of Frank Jackson (Conditionals and Possibilia [1981]) by Dorothy Edgington - Do Conditionals Have Truth Conditions? 4 | |
A reaction: ..That is, one would not abandon the conditional if one believed the antecedent to be true. |
14289 | There are some assertable conditionals one would reject if one learned the antecedent [Jackson, by Edgington] |
Full Idea: Jackson came to realise that there are assertable conditionals which one would not continue to believe if one learned the antecedent, such as Lewis's "If Reagan worked for the KGB, I'll never find out". | |
From: report of Frank Jackson (Conditionals [1987]) by Dorothy Edgington - Conditionals (Stanf) 4.2 | |
A reaction: That pesky David Lewis made trouble for everybody. Edgington agrees that his earlier formulation (Idea 14288) holds good for nearly all cases. There is a self-referential element in Lewis's example. |
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. |
14631 | How can you show the necessity of an a posteriori necessity, if it might turn out to be false? [Jackson] |
Full Idea: If something is offered as a candidate necessary a posteriori truth, how could we show that it is necessary, in the face of the fact that it takes investigation to show that it is true, and so, in some sense, it might have turned out to be false? | |
From: Frank Jackson (Possible Worlds and Necessary A Posteriori [2010], 1) | |
A reaction: This is the topic of his paper, which he compares with how we can know that essences are essential. |
6988 | Mathematical sentences are a problem in a possible-worlds framework [Jackson] |
Full Idea: There is notoriously a problem about what to say concerning mathematical sentences within the possible-worlds framework. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3 n25) | |
A reaction: Presumably this concerns possible axioms and their combinations. |
6975 | Possible worlds could be concrete, abstract, universals, sentences, or properties [Jackson] |
Full Idea: Possible worlds might be concrete (Lewis), or abstract (Stalnaker), or structured universals (Forrest), or collections of sentences (Jeffrey), or mere combinations of properties and relations (Armstrong). | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
A reaction: A helpful summary. I don't like concrete, or collections of sentences. Whatever they are, they had better be 'possible', so not any old collection or idea will do. |
6982 | Long arithmetic calculations show the a priori can be fallible [Jackson] |
Full Idea: We know that being fallible and being a priori can co-exist - the results of long numerical additions are well-known examples. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.2) | |
A reaction: I see this realisation as a good example of progress in philosophy. Russell, who says self-evidence comes in degrees, deserves major credit. It is the key idea that once again makes rationalism respectable. |
6991 | We examine objects to determine colour; we do not introspect [Jackson] |
Full Idea: We examine objects to determine their colour; we do not introspect. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
A reaction: Interesting, but the theory of secondary qualities did not arise from experience, but from a theory about what is actually going on. Compare pain appearing to be in your foot. |
4894 | I say Mary does not have new knowledge, but knows an old fact in a new way [Perry on Jackson] |
Full Idea: I say Mary knows an old fact in a new way, but I do not find a new bit of knowledge and a new fact. | |
From: comment on Frank Jackson (What Mary Didn't Know [1986]) by John Perry - Knowledge, Possibility and Consciousness §7.3 | |
A reaction: This seems roughly the right way to attack Jackson's 'knowledge argument', by asking exactly what he means by 'knowledge'. It is hard to see how 'qualia' can be both the means of acquiring knowledge, and the thing itself. |
4895 | Is it unfair that physicalist knowledge can be written down, but dualist knowledge can't be [Perry on Jackson] |
Full Idea: Jackson seems to imply that it isn't fair that all physicalist knowledge can be written down, but not all dualist knowledge can be. | |
From: comment on Frank Jackson (What Mary Didn't Know [1986]) by John Perry - Knowledge, Possibility and Consciousness §7.5 | |
A reaction: This pinpoints a problem for the 'Mary' example - that Mary's new sight of colour is claimed as 'knowledge', and yet the whole point is that it cannot be expressed in propositions (which seems to leave it as 'procedural' or 'acquaintance' knowledge). |
4886 | Mary knows all the physical facts of seeing red, but experiencing it is new knowledge [Jackson] |
Full Idea: Mary knows all the physical facts. ..It seems, however, that Mary does not know all there is to know. For when she is let out of the black and white room .. she will learn what it is like to see something red. | |
From: Frank Jackson (What Mary Didn't Know [1986], §1.4) | |
A reaction: Jackson is begging the question. A new physical event occurs when the red wavelength stimulates Mary's visual cortex for the first time. For an empiricist raw experience creates knowledge, so it can't BE knowledge. Does Mary acquire a new concept? |
6976 | In physicalism, the psychological depends on the physical, not the other way around [Jackson] |
Full Idea: Physicalism is associated with various asymmetry doctrines, most famously with the idea that the psychological depends in some sense on the physical, and not the other way around. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
A reaction: Sounds okay to me. Shadows depend on objects, and not the other way round. It might suggest properties depending on substances (or bare particulars), but I prefer the dependence of processes on mechanisms (waterfalls on liquid water). |
6986 | Is the dependence of the psychological on the physical a priori or a posteriori? [Jackson] |
Full Idea: Should the necessary passage from the physical account of the world to the psychological one that physicalists are committed to, be placed in the a posteriori or the a priori basket? | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
A reaction: That is, is 'the physical entails the mental' empirical or a priori? See Idea 3989. If we can at least dream of substance dualism, it is hard to see how it could be fully a priori. I think I prefer to see it as an inductive explanation. |
6992 | If different states can fulfil the same role, the converse must also be possible [Jackson] |
Full Idea: It would be strange if having learnt the lesson of multiple realisability that the same role may be filled by different states, we turned around and insisted that the converse - different roles filled by the same state - is impossible. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.4 n3) | |
A reaction: Good. The world is full of creatures who seem to enjoy the smell of decay etc. Some people (not me) like horror films. The separation of qualia and role leaves type-type physicalism as a possibility. Survival needs similar roles, not similar qualia. |
7880 | If a blind persons suddenly sees a kestrel, that doesn't make visual and theoretical kestrels different [Papineau on Jackson] |
Full Idea: An ornithological Mary might know everything theoretical about kestrels, but be blind from birth, then have her sight restored. She now knows "That bird eats mice", so visual kestrels must be ontologically distinct from theoretical ones. | |
From: comment on Frank Jackson (Epiphenomenal Qualia [1982]) by David Papineau - Thinking about Consciousness 6.3 | |
A reaction: A nice reductio, and I think this pinpoints best what is wrong with the knowledge argument. Knowledge, and the means of acquiring it, are two distinct things. When I see x, I don't acquire knowledge of x, AND knowledge of my seeing x. |
7378 | No one bothers to imagine what it would really be like to have ALL the physical information [Dennett on Jackson] |
Full Idea: That Mary "has all the physical information" is not readily imaginable, so no one bothers. They just imagine she knows lots and lots - perhaps everything known today - but that is just a drop in the bucket. | |
From: comment on Frank Jackson (Epiphenomenal Qualia [1982]) by Daniel C. Dennett - Consciousness Explained 12.5 | |
A reaction: I certainly don't see how we can rule out a priori the possibility that someone who really had all the physical knowledge might be able to infer the phenomenal properties of colour. |
7377 | Mary learns when she sees colour, so her complete physical information had missed something [Jackson] |
Full Idea: It seems obvious that Mary will learn something about the world when she is released from her black-and-white room; but then it is inescapable that her previous knowledge was incomplete; she had all the physical information, so there is more to have. | |
From: Frank Jackson (Epiphenomenal Qualia [1982], §1) | |
A reaction: This is Jackson's famous 'knowledge argument', which seems to me misconceived. Since I don't think phenomenal colours are properties of objects (Idea 5456), Mary learns more about herself, and about her means of acquiring knowledge. |
6996 | Folk psychology covers input, internal role, and output [Jackson] |
Full Idea: Folk psychology has a tripartite nature, with input clauses, internal role clauses, and output clauses. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
A reaction: Interesting, particularly that folk psychology refers to internal roles, or attempts to explain what is going on inside the 'black box'. The folk have collectively worked out a standard flow diagram for human thought. |
6977 | Egocentric or de se content seems to be irreducibly so [Jackson] |
Full Idea: I have been convinced by arguments (e.g. of Perry, Castañeda and Lewis) that egocentric or de se content is irreducibly so. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
A reaction: This is associated with the use of indexicals (like 'I' and 'now') in language. Quine disagrees, and should not be written off. Any theory of content, concepts, meaning etc. must clearly taken account of such subjective language. |
6990 | Keep distinct the essential properties of water, and application conditions for the word 'water' [Jackson] |
Full Idea: My guess is that objectors to the deflationary account of the Twin Earth parable are confusing the essential properties of water with the question of what is essential for being water. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
A reaction: That is, we must distinguish between the actual ontology of water's properties and the conditions under which we (in our society) apply the word 'water'. Interesting. The latter issue, though, might push us back towards internalism... |
6985 | Analysis is finding necessary and sufficient conditions by studying possible cases [Jackson] |
Full Idea: Conceptual analysis is sometimes understood as the business of finding necessary and sufficient conditions by the method of possible cases. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
A reaction: Some (e.g. Stich) reject this, but it seems to me undeniable that the procedure can be very illuminating, even if it is never totally successful. Jackson prefers to see analysis as the study of entailments between stories about the world. |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
Full Idea: By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics | |
A reaction: Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven? |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
Full Idea: If in an infinite system, set in order, we neglect the special character of the elements, simply retaining their distinguishability and their order-relations to one another, then the elements are the natural numbers, created by the human mind. | |
From: Richard Dedekind (Nature and Meaning of Numbers [1888], VI.73) | |
A reaction: [compressed] This is the classic abstractionist view of the origin of number, but with the added feature that the order is first imposed, so that ordinals remain after the abstraction. This, of course, sounds a bit circular, as well as subjective. |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
Full Idea: Dedekind's conception is psychologistic only if that is the only way to understand the abstraction that is involved, which it is not. | |
From: report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by William W. Tait - Frege versus Cantor and Dedekind IV | |
A reaction: This is a very important suggestion, implying that we can retain some notion of abstractionism, while jettisoning the hated subjective character of private psychologism, which seems to undermine truth and logic. |
6995 | Successful predication supervenes on nature [Jackson] |
Full Idea: Successful predication supervenes on nature. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
A reaction: A nice slogan, but it is in danger of being a tautology. If I say x and y 'are my favourites/are interesting', is that 'successful' predication? Is 'Juliet is the sun' unsuccessful? |
6989 | I can understand "He has a beard", without identifying 'he', and hence the truth conditions [Jackson] |
Full Idea: If I hear someone say "He has a beard", and I don't know whether it is Jackson, Jones, or someone else, I don't know which proposition is being expressed in the sense of not knowing the conditions under which what is said is true. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
A reaction: This is the neatest and simplest problem I have encountered for Davidson's truth-conditions account of meaning. However, we probably just say that we understand the sense but not the reference. The strict-and-literal but not contextual meaning. |
6998 | Folk morality does not clearly distinguish between doing and allowing [Jackson] |
Full Idea: We have, it seems to me, currently no clear sense of the place and rationale of the distinction between doing and allowing in folk morality. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
A reaction: Does this mean that philosophers should endeavour to appear on television in order to improve folk morality, so that Jackson, back at the ranch, can then infer the meanings of moral terms from the new improved version? |
6997 | Moral functionalism says moral terms get their meaning from their role in folk morality [Jackson] |
Full Idea: Moral functionalism is the view that the meanings of moral terms are given by their place in the network of input, internal clauses, and output that makes up folk psychology. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
A reaction: Jackson considers this enough to support a cognitivist view of morality. In assuming that there is something stable called 'folk morality' he seems to be ignoring questions about cultural relativism. |
7000 | Which are prior - thin concepts like right, good, ought; or thick concepts like kindness, equity etc.? [Jackson] |
Full Idea: 'Centralists' (e.g. Bernard Williams) say thin ethical concepts (right, good, ought) are conceptually fundamental; 'non-centralists' (e.g. Susan Hurley) say that such concepts are not conceptually prior to kindness, equity and the like. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
A reaction: My immediate intuition is to side with Susan Hurley, since morality grows out of immediate relationships, not out of intellectual principles and theoretical generalisations. This would go with particularist views of virtue theory. |
20579 | Modern totalitarianism results from lack of social ties or shared goals [Arendt, by Oksala] |
Full Idea: Arendt claims that modern totalitarianism's primary condition is an atomised mass society: isolated individuals who have no strong ties to communities and who are indifferent to shared political goals. | |
From: report of Hannah Arendt (The Origins of Totalitarianism [1968]) by Johanna Oksala - Political Philosophy: all that matters Ch.9 | |
A reaction: I think the lack of ties simply describes large modern cities. Not sure about the lack of shared goals. Hitler and Stalin rode on the back of apparent shared goals. Working classes strike me as sharing more goals than middle classes. |
20580 | The ideal subject for dictators is not a fanatic, but someone who can't distinguish true from false [Arendt, by Oksala] |
Full Idea: The ideal subject of totalitarianism is not the convinced Nazi or the convinced communist, but anyone who has lost the ability to make distinctions between fact and fiction and between true and false. | |
From: report of Hannah Arendt (The Origins of Totalitarianism [1968]) by Johanna Oksala - Political Philosophy: all that matters Ch.9 | |
A reaction: We are currently living with an apparent attempt by Donald Trump to become a totalitarian President of the U.S.A., by constantly disseminating lies, and labelling all of his critics as 'fake news'. |
6999 | It is hard to justify the huge difference in our judgements of abortion and infanticide [Jackson] |
Full Idea: We allow that abortion is permissible in many circumstances, but infanticide is hardly ever permissible, and yet it is hard to justify this disparity in moral judgement in the sense of finding the relevant difference. | |
From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
A reaction: The implications of this are tough to face. A foetus is (maybe) just not as important as a new-born babe - and so a new-born babe is of less importance than a five-year old. Birth is (or was) a hugely dangerous hurdle to be cleared. |