Combining Philosophers

All the ideas for Anaxarchus, Mark Colyvan and Frank Jackson

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74 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
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.
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
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.
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....
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
3. Truth / B. Truthmakers / 4. Truthmaker Necessitarianism
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?
3. Truth / B. Truthmakers / 5. What Makes Truths / d. Being makes truths
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.
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Rejecting double negation elimination undermines reductio proofs [Colyvan]
     Full Idea: The intuitionist rejection of double negation elimination undermines the important reductio ad absurdum proof in classical mathematics.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3)
Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan]
     Full Idea: In intuitionist logic double negation elimination fails. After all, proving that there is no proof that there can't be a proof of S is not the same thing as having a proof of S.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3)
     A reaction: I do like people like Colyvan who explain things clearly. All of this difficult stuff is understandable, if only someone makes the effort to explain it properly.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
     Full Idea: The law of excluded middle (for every proposition P, either P or not-P) must be carefully distinguished from its semantic counterpart bivalence, that every proposition is either true or false.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3)
     A reaction: So excluded middle makes no reference to the actual truth or falsity of P. It merely says P excludes not-P, and vice versa.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
'¬', '&', 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?
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
     Full Idea: Löwenheim proved that if a first-order sentence has a model at all, it has a countable model. ...Skolem generalised this result to systems of first-order sentences.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2)
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
     Full Idea: A set of axioms is said to be 'categorical' if all models of the axioms in question are isomorphic.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 2.1.2)
     A reaction: The best example is the Peano Axioms, which are 'true up to isomorphism'. Set theory axioms are only 'quasi-isomorphic'.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
Ordinal numbers represent order relations [Colyvan]
     Full Idea: Ordinal numbers represent order relations.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.2.3 n17)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Intuitionists only accept a few safe infinities [Colyvan]
     Full Idea: For intuitionists, all but the smallest, most well-behaved infinities are rejected.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3)
     A reaction: The intuitionist idea is to only accept what can be clearly constructed or proved.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan]
     Full Idea: The problem with infinitesimals is that in some places they behaved like real numbers close to zero but in other places they behaved like zero.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.2)
     A reaction: Colyvan gives an example, of differentiating a polynomial.
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan]
     Full Idea: Given Dedekind's reduction of real numbers to sequences of rational numbers, and other known reductions in mathematics, it was tempting to see basic arithmetic as the foundation of mathematics.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.1)
     A reaction: The reduction is the famous Dedekind 'cut'. Nowadays theorists seem to be more abstract (Category Theory, for example) instead of reductionist.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
Transfinite induction moves from all cases, up to the limit ordinal [Colyvan]
     Full Idea: Transfinite inductions are inductive proofs that include an extra step to show that if the statement holds for all cases less than some limit ordinal, the statement also holds for the limit ordinal.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1 n11)
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Most mathematical proofs are using set theory, but without saying so [Colyvan]
     Full Idea: Most mathematical proofs, outside of set theory, do not explicitly state the set theory being employed.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.1)
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan]
     Full Idea: Structuralism is able to explain why mathematicians are typically only interested in describing the objects they study up to isomorphism - for that is all there is to describe.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2)
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan]
     Full Idea: In re structuralism does not posit anything other than the kinds of structures that are in fact found in the world. ...The problem is that the world may not provide rich enough structures for the mathematics.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 3.1.2)
     A reaction: You can perceive a repeating pattern in the world, without any interest in how far the repetitions extend.
7. Existence / C. Structure of Existence / 2. Reduction
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.
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
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.
8. Modes of Existence / B. Properties / 1. Nature of Properties
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.
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
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.
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
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.
9. Objects / D. Essence of Objects / 9. Essence and Properties
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.
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'!
9. Objects / D. Essence of Objects / 15. Against Essentialism
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.
10. Modality / A. Necessity / 3. Types of Necessity
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.
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
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!
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
'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.
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.
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.
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.
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?
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.
(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.
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
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.
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.
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.
10. Modality / B. Possibility / 8. Conditionals / f. Pragmatics of conditionals
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.
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
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.
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
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.
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
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.
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
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.
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / a. Qualities in perception
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.
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
     Full Idea: Anaxarchus said that he was not even sure that he knew nothing.
     From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1
14. Science / C. Induction / 6. Bayes's Theorem
Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
     Full Idea: Those who see probabilities as ratios of frequencies can't use Bayes's Theorem if there is no objective prior probability. Those who accept prior probabilities tend to opt for a subjectivist account, where probabilities are degrees of belief.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.8)
     A reaction: [compressed]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Mathematics can reveal structural similarities in diverse systems [Colyvan]
     Full Idea: Mathematics can demonstrate structural similarities between systems (e.g. missing population periods and the gaps in the rings of Saturn).
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2)
     A reaction: [Colyvan expounds the details of his two examples] It is these sorts of results that get people enthusiastic about the mathematics embedded in nature. A misunderstanding, I think.
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
Mathematics can show why some surprising events have to occur [Colyvan]
     Full Idea: Mathematics can show that under a broad range of conditions, something initially surprising must occur (e.g. the hexagonal structure of honeycomb).
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 6.3.2)
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
     Full Idea: Another style of proof often cited as unexplanatory are brute-force methods such as proof by cases (or proof by exhaustion).
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1)
Reductio proofs do not seem to be very explanatory [Colyvan]
     Full Idea: One kind of proof that is thought to be unexplanatory is the 'reductio' proof.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1)
     A reaction: Presumably you generate a contradiction, but are given no indication of why the contradiction has arisen? Tracking back might reveal the source of the problem? Colyvan thinks reductio can be explanatory.
If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
     Full Idea: It might be argued that any proof by induction is revealing the explanation of the theorem, namely, that it holds by virtue of the structure of the natural numbers.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.1)
     A reaction: This is because induction characterises the natural numbers, in the Peano Axioms.
Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]
     Full Idea: The proof of the four-colour theorem raises questions about whether a 'proof' that no one understands is a proof.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.6)
     A reaction: The point is that the theorem (that you can colour countries on a map with just four colours) was proved with the help of a computer.
15. Nature of Minds / B. Features of Minds / 5. Qualia / a. Nature of qualia
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.
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).
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?
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan]
     Full Idea: One type of generalisation in mathematics extends a system to go beyond what is was originally set up for; another kind involves abstracting away from some details in order to capture similarities between different systems.
     From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 5.2.2)
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
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).
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
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.
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
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.
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / c. Knowledge argument
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.
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.
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.
18. Thought / A. Modes of Thought / 4. Folk Psychology
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.
18. Thought / C. Content / 1. Content
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.
18. Thought / C. Content / 5. Twin Earth
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...
18. Thought / D. Concepts / 4. Structure of Concepts / c. Classical concepts
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.
19. Language / C. Assigning Meanings / 3. Predicates
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?
19. Language / C. Assigning Meanings / 6. Truth-Conditions Semantics
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.
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
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?
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
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.
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.
25. Social Practice / F. Life Issues / 3. Abortion
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.