Popper wanted to distinguish science from non-science-a category said to include "logic, metaphys... more Popper wanted to distinguish science from non-science-a category said to include "logic, metaphysics, and psychoanalysis." Scientific claims he thought were falsifiable, at least in principle; that's what makes them special. This is apt to seem wrong in both directions. Logical claims, e.g., ϕ is unprovable, can be falsified. And while scientific hypotheses of certain forms («All Fs are G») may be falsifiable, not so hypotheses of other forms: «Each F eventually becomes G».
Oxford Handbook of Applied Philosophy of Language, ed. Luvell Anderson and Ernie Lepore, 2022
If we want everything to stay as it is, everything has to change. Giuseppe di Lampedusa, The Leop... more If we want everything to stay as it is, everything has to change. Giuseppe di Lampedusa, The Leopard
Oxford Studies in the Philosophy of Language, 2024
Analytic semantics got its start when Frege, initially in Begriffschrift and then "Uber Sinn und ... more Analytic semantics got its start when Frege, initially in Begriffschrift and then "Uber Sinn und Bedeutung," grew puzzled about differences in cognitive content between sentences that in some good sense "say the same"-sentences attributing the same properties to the same objects, or placing those objects in the same relation. He was particularly impressed by claims like
A DISTINCTION "You talk too much" can be said in more than one way. Sometimes, as in the 1960 Joe... more A DISTINCTION "You talk too much" can be said in more than one way. Sometimes, as in the 1960 Joe Jones song of that title, talking too much is holding forth on the wrong topics, especially topics you're not well informed about: You talk about people that you don't know, You talk about people that you've never seen, etc. Run-D.M.C's 1985 version returns to this theme ("You talk about places you never go") while adding a second: Twenty-five hours, eight days a week, Thirteen months outta year, is when you speak, etc Now the problem is going on too long (putting out too much content) about topics that might in themselves be perfectly appropriate. These are distinct and independent complaints; they could in principle cut across each other. You might say too much about too little (trying to wear your interrogator down, maybe, with information they already possess). Or you might say too little while spreading your topical net too wide. This paper looks at the second combination: saying too little-less than you know-about too muchmore than you know about. 2 LESS ABOUT MORE Some preliminary definitions. Q says less than P if the P-worlds (P) form a proper subset of the Q-worlds (Q), that is, Q is properly implied by P. Q is about more than P if its subject matter (q) is not included in P 's subject matter (p). 1 This combination (saying less, about more) turns up a lot in philosophy. Q in the usual case is validly inferred from P, suggesting it ought to be in as good shape as P epistemologically. And yet Q's veering off topic suggests that it might be in worse shape. Knowing your way around p does not make you an expert on q, if q ranges more widely. "Says less" thus pulls in a different direction epistemically than "about more." This tension makes P /Q inferences (topically ampliative inferences) a breeding ground for puzzles of knowledge and justification. 1. skepticism: I have a hand (P) says more than I am not a handless brain in a vat (Q). But the latter raises new issues (envattedness, etc) that one feels less on top of. 2. gettier: Jones owns a Ford or Brown is in Barcelona (Q) says less than the premise P that Smith gets it from: Jones owns a Ford. But it's about more, by virtue of bringing in Brown and Barcelona. 3. bootstrapping: 2 These apples look red and are red (P) says more than My color vision is reliable re these apples (Q). 3 But it's about more, e.g., P is silent on the case where the apples look green.. 4. dogmatism: P makes a stronger claim than Whoever denies P, never mind why, is wrong (Q). 4 But where P is about, say, the rain, Whoever denies P... is about rain-judgments. 5. grue: These emeralds are grue (Q) says less than They're green and observed (P). But it's about more: green, observed emeralds, and emeralds that are blue and unobserved. I want now to add a sixth puzzle to the list, a confirmational analogue of the Gettier puzzle. Just as it seemed pre-Gettier that a belief constituted knowledge if it was (a) justified and (b) true, it can seem today that a belief favors (would favor) H if it was (a ′) warranted/knowledgeable, and (b ′) has as its content an E making H more probable (pr(H |E) > pr(H)). The "(a)(b)⇒knowledge" connection breaks down, Gettier showed, when the belief is justified by information about one topic (Jones's car), while being true only in what it says about another topic (Brown's location). The "(a ′)(b ′)⇒evidence" connection breaks down too, arguably, in Gettier-type scenarios. A belief does not provide me with evidence for H, if is based on information about an H-irrelevant topic. Consider Smyth. She would like to think that Brown is in Barceloneta (a beach-front Barcelona neighborhood), but has no evidence for this. It occurs to her that she can get evidence by tacking K (Brown is in Barcelona) onto whatever she learns next-J (Jones owns a Ford), as it tuns out. 5 Would J ∨K thus arrived at give her evidence that Brown is in Barceloneta? One certainly hopes not. She learns it by learning about a topic (Jones's car) that's irrelevant to Brown's location. This is the puzzle of 6. misdirection: J ∨K says less than J does. But it's about more, e.g., Brown. Smyth's cluelessness about the more prevents J ∨K from functioning (for her) as evidence that Brown is in Barceloneta. You may know misdirection as the magician's trick of getting audiences to attend to the wrong thing. Smyth's trick operates on a similar principle. She creates the illusion of evidence for K by shifting attention from j (a topic we know but don't care about) to k (a topic we care but don't know about). Misdirection lies in a certain sense halfway between Gettier and Goodman (I'll speak sometimes of the Goodier puzzle). Smith retreats for some reason from J to a weaker claim (J ∨K) about a larger subject matter. Smyth too retreats from J to a weaker claim (J ∨K) about a larger subject matter. Goodman has us retreating for some reason from They're observed and green to their being observed and green or unobserved and blue-again, a weaker claim about a larger subject matter. The retreat creates in each case a simulacrum of evidence that does not afford in the usual way a basis for higher confidence. Smyth retreats for some reason.... this suggests that something fishy is going on. Is a reason really needed? Smyth does learn that Jones owns a Ford or Brown is in Barcelona. If J ∨K nevertheless leaves something to be desired qua evidence, one would like to know why. 2 Aka, the problem of easy knowledge. 3 Q is something like the disjunction over all colors C of These apples look and are C. 4 Q is trivially true, if no one denies P. 5 H entails J ∨K and that is generally all it takes. 10 See for instance [8]. 11 Builes, [4] 12 Lewis elsewhere tries to explain aboutness in terms of confirmation: 15 This is agreed all around when the second disjunct is R orLR. But not when it's LR, L∨LR being logically equivalent to L. (pr(R|L∨R) = pr(L∨LR)> pr(R) (the tosses being independent)); pr(R|L∨LR) = pr(R|L)≯ pr(R). 16 Monotonicity comes up now and then in value theory. Castañeda: "von Wright proposed in the early 1960s that X ∨Y > Z only if X > Z and Y > Z." von Wright's proposal is too strict, according to Castañeda. It "leads to the incomparability of X ∨Y with Z, where, say, Value(X) = 1,000; Value(Y) = 20, and Value(Z) = 20. In a case like this it seems to be more satisfactory to say that the value of X ∨Y is greater than the value of Z " (Castañeda [1969], 258-9). (Similarly X is preferable to Y ∨Z when X and Y are tied and X >Z.) From this it's a short step to Castañeda's Principle: If X >Y, then X >X ∨Y >Y. It follows from Castañeda's Principle that if # is neutral, then #∨Z is good if Z is. Our argument here is similar, with good replaced by good news for H.
1 Kripke must have known of this idea. It's hinted at in Kripke [2017], written originally for Qu... more 1 Kripke must have known of this idea. It's hinted at in Kripke [2017], written originally for Quine in the 1960s. Work going back to the 1970s on Carnap's version is reported in Kripke[2024].
Are physical events subject to mental influence? Even to raise the question suggests what the ans... more Are physical events subject to mental influence? Even to raise the question suggests what the answer had better be. Deny mental causation and you are denying that anyone everdoes anything: answer a question or anything else. 2 Tongues may wag and arms may wave about, but there is no action unless these things occur at the bidding of appropriate mental states. Nor is action the only casualty if mental states are physically inert. Smirking, beaming, moping about, shivering in anticipation, raising a skeptical eyebrow, favoring a ...
A development and defense of Kripke's secret doctrine, only hinted at in his work but repeatedly ... more A development and defense of Kripke's secret doctrine, only hinted at in his work but repeatedly so, of nonexistence.
Levy and Godfrey-Smith, *The Scientific Imagination* (OUP, 2020)
The title comes from a well-known paper of Putnam’s (Putnam [1980]). The content is very differen... more The title comes from a well-known paper of Putnam’s (Putnam [1980]). The content is very different. Putnam uses model theory1 to cast doubt on our ability to engage semantically with an objective world. The role of mathematics for him is to prove this pessimistic conclusion. I on the other hand am wondering how models can help us to engage semantically with the objective world. Mathematics functions for me as an analogy. Numbers among their many other accomplishments boost the language’s expressive power; they give us access to recondite physical facts. Models, among their many other accomplishments, do the same thing; they give us access to recondite physical facts. This anyway is the analogy I will try to develop in this paper.
An undemanding claim ' sometimes implies, or seems to, a more demanding one c. Some have posited,... more An undemanding claim ' sometimes implies, or seems to, a more demanding one c. Some have posited, to explain this, a confusion between ' and ' Ã , an analogue of ' that does not imply c. If-thenists take ' Ã to be If c then '. Incrementalism is the form of if-thenism that construes If c then ' as the surplus content of ' over c ('»c). The paper argues that it is the only form of if-thenism that stands a chance of being correct.
KITBOOK, a volume for Kit Fine edited by Federico Faroldi and Frederik Van De Putte, 2020
Develops update rules for permissions and commands in the spirit of truthmaker semantics, taxonom... more Develops update rules for permissions and commands in the spirit of truthmaker semantics, taxonomizing them "prospectively" by their intended static semantical results.
I reply to comments on "If-Thenism" by Suki Finn, Katharina Felka, Amie Thomasson, Seahwa Kim, Da... more I reply to comments on "If-Thenism" by Suki Finn, Katharina Felka, Amie Thomasson, Seahwa Kim, Daniel Dohrn, Gideon Rosen, Otavio Bueno, Brad Armour-Garb, Fred Kroon, Mary Leng, Joseph Ulatowski, Mark Colyvan, and Matteo Plebani.
for a volume on Unstructured Content edited by Cameron Domenico Kirk-Giannini, Andy Egan, Peter ... more for a volume on Unstructured Content edited by Cameron Domenico Kirk-Giannini, Andy Egan, Peter van Elswyk, and Dirk Kindermann
Knowledge is closed under (known) implication, according to standard theories. Orthodoxy can allo... more Knowledge is closed under (known) implication, according to standard theories. Orthodoxy can allow, though, that *apparent* counterexamples to closure exist, much as Kripkeans recognize the existence of illusions of possibility (IPOs)which they seek to explain away. Should not everyone, orthodox or not, want tomake sense of ‘‘intimations of openness’’ (IONs)? This paper compares two stylesof explanation: (1) evidence that boosts P ’s probability need not boost that of its consequence Q; (2) evidence bearing on P’s subject matter may not bear on the subject matter of Q.
Popper wanted to distinguish science from non-science-a category said to include "logic, metaphys... more Popper wanted to distinguish science from non-science-a category said to include "logic, metaphysics, and psychoanalysis." Scientific claims he thought were falsifiable, at least in principle; that's what makes them special. This is apt to seem wrong in both directions. Logical claims, e.g., ϕ is unprovable, can be falsified. And while scientific hypotheses of certain forms («All Fs are G») may be falsifiable, not so hypotheses of other forms: «Each F eventually becomes G».
Oxford Handbook of Applied Philosophy of Language, ed. Luvell Anderson and Ernie Lepore, 2022
If we want everything to stay as it is, everything has to change. Giuseppe di Lampedusa, The Leop... more If we want everything to stay as it is, everything has to change. Giuseppe di Lampedusa, The Leopard
Oxford Studies in the Philosophy of Language, 2024
Analytic semantics got its start when Frege, initially in Begriffschrift and then "Uber Sinn und ... more Analytic semantics got its start when Frege, initially in Begriffschrift and then "Uber Sinn und Bedeutung," grew puzzled about differences in cognitive content between sentences that in some good sense "say the same"-sentences attributing the same properties to the same objects, or placing those objects in the same relation. He was particularly impressed by claims like
A DISTINCTION "You talk too much" can be said in more than one way. Sometimes, as in the 1960 Joe... more A DISTINCTION "You talk too much" can be said in more than one way. Sometimes, as in the 1960 Joe Jones song of that title, talking too much is holding forth on the wrong topics, especially topics you're not well informed about: You talk about people that you don't know, You talk about people that you've never seen, etc. Run-D.M.C's 1985 version returns to this theme ("You talk about places you never go") while adding a second: Twenty-five hours, eight days a week, Thirteen months outta year, is when you speak, etc Now the problem is going on too long (putting out too much content) about topics that might in themselves be perfectly appropriate. These are distinct and independent complaints; they could in principle cut across each other. You might say too much about too little (trying to wear your interrogator down, maybe, with information they already possess). Or you might say too little while spreading your topical net too wide. This paper looks at the second combination: saying too little-less than you know-about too muchmore than you know about. 2 LESS ABOUT MORE Some preliminary definitions. Q says less than P if the P-worlds (P) form a proper subset of the Q-worlds (Q), that is, Q is properly implied by P. Q is about more than P if its subject matter (q) is not included in P 's subject matter (p). 1 This combination (saying less, about more) turns up a lot in philosophy. Q in the usual case is validly inferred from P, suggesting it ought to be in as good shape as P epistemologically. And yet Q's veering off topic suggests that it might be in worse shape. Knowing your way around p does not make you an expert on q, if q ranges more widely. "Says less" thus pulls in a different direction epistemically than "about more." This tension makes P /Q inferences (topically ampliative inferences) a breeding ground for puzzles of knowledge and justification. 1. skepticism: I have a hand (P) says more than I am not a handless brain in a vat (Q). But the latter raises new issues (envattedness, etc) that one feels less on top of. 2. gettier: Jones owns a Ford or Brown is in Barcelona (Q) says less than the premise P that Smith gets it from: Jones owns a Ford. But it's about more, by virtue of bringing in Brown and Barcelona. 3. bootstrapping: 2 These apples look red and are red (P) says more than My color vision is reliable re these apples (Q). 3 But it's about more, e.g., P is silent on the case where the apples look green.. 4. dogmatism: P makes a stronger claim than Whoever denies P, never mind why, is wrong (Q). 4 But where P is about, say, the rain, Whoever denies P... is about rain-judgments. 5. grue: These emeralds are grue (Q) says less than They're green and observed (P). But it's about more: green, observed emeralds, and emeralds that are blue and unobserved. I want now to add a sixth puzzle to the list, a confirmational analogue of the Gettier puzzle. Just as it seemed pre-Gettier that a belief constituted knowledge if it was (a) justified and (b) true, it can seem today that a belief favors (would favor) H if it was (a ′) warranted/knowledgeable, and (b ′) has as its content an E making H more probable (pr(H |E) > pr(H)). The "(a)(b)⇒knowledge" connection breaks down, Gettier showed, when the belief is justified by information about one topic (Jones's car), while being true only in what it says about another topic (Brown's location). The "(a ′)(b ′)⇒evidence" connection breaks down too, arguably, in Gettier-type scenarios. A belief does not provide me with evidence for H, if is based on information about an H-irrelevant topic. Consider Smyth. She would like to think that Brown is in Barceloneta (a beach-front Barcelona neighborhood), but has no evidence for this. It occurs to her that she can get evidence by tacking K (Brown is in Barcelona) onto whatever she learns next-J (Jones owns a Ford), as it tuns out. 5 Would J ∨K thus arrived at give her evidence that Brown is in Barceloneta? One certainly hopes not. She learns it by learning about a topic (Jones's car) that's irrelevant to Brown's location. This is the puzzle of 6. misdirection: J ∨K says less than J does. But it's about more, e.g., Brown. Smyth's cluelessness about the more prevents J ∨K from functioning (for her) as evidence that Brown is in Barceloneta. You may know misdirection as the magician's trick of getting audiences to attend to the wrong thing. Smyth's trick operates on a similar principle. She creates the illusion of evidence for K by shifting attention from j (a topic we know but don't care about) to k (a topic we care but don't know about). Misdirection lies in a certain sense halfway between Gettier and Goodman (I'll speak sometimes of the Goodier puzzle). Smith retreats for some reason from J to a weaker claim (J ∨K) about a larger subject matter. Smyth too retreats from J to a weaker claim (J ∨K) about a larger subject matter. Goodman has us retreating for some reason from They're observed and green to their being observed and green or unobserved and blue-again, a weaker claim about a larger subject matter. The retreat creates in each case a simulacrum of evidence that does not afford in the usual way a basis for higher confidence. Smyth retreats for some reason.... this suggests that something fishy is going on. Is a reason really needed? Smyth does learn that Jones owns a Ford or Brown is in Barcelona. If J ∨K nevertheless leaves something to be desired qua evidence, one would like to know why. 2 Aka, the problem of easy knowledge. 3 Q is something like the disjunction over all colors C of These apples look and are C. 4 Q is trivially true, if no one denies P. 5 H entails J ∨K and that is generally all it takes. 10 See for instance [8]. 11 Builes, [4] 12 Lewis elsewhere tries to explain aboutness in terms of confirmation: 15 This is agreed all around when the second disjunct is R orLR. But not when it's LR, L∨LR being logically equivalent to L. (pr(R|L∨R) = pr(L∨LR)> pr(R) (the tosses being independent)); pr(R|L∨LR) = pr(R|L)≯ pr(R). 16 Monotonicity comes up now and then in value theory. Castañeda: "von Wright proposed in the early 1960s that X ∨Y > Z only if X > Z and Y > Z." von Wright's proposal is too strict, according to Castañeda. It "leads to the incomparability of X ∨Y with Z, where, say, Value(X) = 1,000; Value(Y) = 20, and Value(Z) = 20. In a case like this it seems to be more satisfactory to say that the value of X ∨Y is greater than the value of Z " (Castañeda [1969], 258-9). (Similarly X is preferable to Y ∨Z when X and Y are tied and X >Z.) From this it's a short step to Castañeda's Principle: If X >Y, then X >X ∨Y >Y. It follows from Castañeda's Principle that if # is neutral, then #∨Z is good if Z is. Our argument here is similar, with good replaced by good news for H.
1 Kripke must have known of this idea. It's hinted at in Kripke [2017], written originally for Qu... more 1 Kripke must have known of this idea. It's hinted at in Kripke [2017], written originally for Quine in the 1960s. Work going back to the 1970s on Carnap's version is reported in Kripke[2024].
Are physical events subject to mental influence? Even to raise the question suggests what the ans... more Are physical events subject to mental influence? Even to raise the question suggests what the answer had better be. Deny mental causation and you are denying that anyone everdoes anything: answer a question or anything else. 2 Tongues may wag and arms may wave about, but there is no action unless these things occur at the bidding of appropriate mental states. Nor is action the only casualty if mental states are physically inert. Smirking, beaming, moping about, shivering in anticipation, raising a skeptical eyebrow, favoring a ...
A development and defense of Kripke's secret doctrine, only hinted at in his work but repeatedly ... more A development and defense of Kripke's secret doctrine, only hinted at in his work but repeatedly so, of nonexistence.
Levy and Godfrey-Smith, *The Scientific Imagination* (OUP, 2020)
The title comes from a well-known paper of Putnam’s (Putnam [1980]). The content is very differen... more The title comes from a well-known paper of Putnam’s (Putnam [1980]). The content is very different. Putnam uses model theory1 to cast doubt on our ability to engage semantically with an objective world. The role of mathematics for him is to prove this pessimistic conclusion. I on the other hand am wondering how models can help us to engage semantically with the objective world. Mathematics functions for me as an analogy. Numbers among their many other accomplishments boost the language’s expressive power; they give us access to recondite physical facts. Models, among their many other accomplishments, do the same thing; they give us access to recondite physical facts. This anyway is the analogy I will try to develop in this paper.
An undemanding claim ' sometimes implies, or seems to, a more demanding one c. Some have posited,... more An undemanding claim ' sometimes implies, or seems to, a more demanding one c. Some have posited, to explain this, a confusion between ' and ' Ã , an analogue of ' that does not imply c. If-thenists take ' Ã to be If c then '. Incrementalism is the form of if-thenism that construes If c then ' as the surplus content of ' over c ('»c). The paper argues that it is the only form of if-thenism that stands a chance of being correct.
KITBOOK, a volume for Kit Fine edited by Federico Faroldi and Frederik Van De Putte, 2020
Develops update rules for permissions and commands in the spirit of truthmaker semantics, taxonom... more Develops update rules for permissions and commands in the spirit of truthmaker semantics, taxonomizing them "prospectively" by their intended static semantical results.
I reply to comments on "If-Thenism" by Suki Finn, Katharina Felka, Amie Thomasson, Seahwa Kim, Da... more I reply to comments on "If-Thenism" by Suki Finn, Katharina Felka, Amie Thomasson, Seahwa Kim, Daniel Dohrn, Gideon Rosen, Otavio Bueno, Brad Armour-Garb, Fred Kroon, Mary Leng, Joseph Ulatowski, Mark Colyvan, and Matteo Plebani.
for a volume on Unstructured Content edited by Cameron Domenico Kirk-Giannini, Andy Egan, Peter ... more for a volume on Unstructured Content edited by Cameron Domenico Kirk-Giannini, Andy Egan, Peter van Elswyk, and Dirk Kindermann
Knowledge is closed under (known) implication, according to standard theories. Orthodoxy can allo... more Knowledge is closed under (known) implication, according to standard theories. Orthodoxy can allow, though, that *apparent* counterexamples to closure exist, much as Kripkeans recognize the existence of illusions of possibility (IPOs)which they seek to explain away. Should not everyone, orthodox or not, want tomake sense of ‘‘intimations of openness’’ (IONs)? This paper compares two stylesof explanation: (1) evidence that boosts P ’s probability need not boost that of its consequence Q; (2) evidence bearing on P’s subject matter may not bear on the subject matter of Q.
Introduction to thing/matter issues for the Norton Introduction to Philosophy , ed., Alex Byrne, ... more Introduction to thing/matter issues for the Norton Introduction to Philosophy , ed., Alex Byrne, Joshua Cohen, Gideon Rosen, and Seana Shiffrin
Indicative conditionals appear to lie on a continuum, with the subjective and information-based o... more Indicative conditionals appear to lie on a continuum, with the subjective and information-based on one side, and the objective and fact-based on the other. Attempts to bring them all under the same theoretical umbrella usually start at the subjective end; conditionals get more objective as they come to be based in higher-quality, less parochial, information. I propose to go in the other direction, looking first for a class of "absolute" conditionals, then bringing in other conditionals by relaxing the constraints defining that class. (A plan of action is laid out at the end of section 4. The final footnote of each section sketches the contents of the next.) 1
Subtraction in arithmetic is the inverse of addition; p-q is the r such that q + r = p. Division ... more Subtraction in arithmetic is the inverse of addition; p-q is the r such that q + r = p. Division is the inverse of multiplication. And so on. What about in logic? LOGICAL SUBTRACTION To go by the arithmetic analogy, P∼Q ought to be the R such that Q&R is equivalent to P. But, there are many such Rs. In the simplest case, where P implies Q, R could be anything from Q⊃P to P itself. Q⊃P stands out as the weakest solution to Q&R ⇔ P. This is the perennial favorite; but though tempting the temptation should be resisted. Lots of reasons for this.
Carnap also proposed (tentatively) a particular way of measuring the degree to which E confirms i... more Carnap also proposed (tentatively) a particular way of measuring the degree to which E confirms i H: d(H, E
Causes are often conceived as events without which the effect would not have occurred. But could... more Causes are often conceived as events without which the effect would not have occurred. But couldn't there still be causation in worlds where every effect was metaphysically inevitable? A different picture is presented: a cause of E is an event taking us part way down the road actually leading to E.
Unpublished Appendix to *Aboutness*
Worlds are ways for things to be-possible ones in some sense... more Unpublished Appendix to *Aboutness*
Worlds are ways for things to be-possible ones in some sense of "possible" (Notation: w.) Logical space is the set of worlds. (Notation: W.) Propositions are subsets of logical space, or sets of worlds. (Notation: A, B, C,....). 1 A proposition A is true in world w i↵ w ✏ A, otherwise false. 2 Sentences are, you know. (Notation: A, B, C,....) Expression is the relation sentence X bears to proposition X when for all w, X is true in w i↵ w ✏ X.
Let's play a game. I'll describe it first at an abstract level, leaving details for later. Your j... more Let's play a game. I'll describe it first at an abstract level, leaving details for later. Your job is to choose between options A and B. The options overlap in that each way of B-ing extends to two ways ⋆ and ⋆ of A-ing, and each way of A-ing is a ⋆ or ⋆ for some way of B-ing. 1 The s win you a penny, and likewise the ⋆ s. Both are as good as worthless, and worthless is the name we will know them by. All other s-the ⋆ s-win you a million dollars. The ⋆ s are the lucrative s. This leaves a lot to the imagination, of course, but we can see already that if you were to play the A/B game, A would be a better option than B. One could assign probabilities and do expected utility calculations, but none of that is really necessary. It's enough to note that A dominates B:
In this interview, Stephen Yablo talks about his parents, a psychologist and an engineer, his bar... more In this interview, Stephen Yablo talks about his parents, a psychologist and an engineer, his bar mitzvah, ping pong, Spiderman, Atlantis, impossibility, drugs, breaking and entering, correspondence courses, working with the mentally disabled, attending university of Toronto, philosophy of dance, Protagoras, van Fraassen, Joni Mitchell, taking classes with John Slater, Bas van Fraasen, and Hans Herzberger, philosophy post-Wittgenstein, moving to India, joining the program in Logic and Methodology at UC Berkeley, working with Davidson, Myro, and Grice, getting 38 (!) job interviews, embarrassing himself in front of Sellars, landing a gig at Michigan, moving to MIT, the difference between philosophical progress and understanding, The Minority Body, Nintendo Wii, the leveraged freedom chair, The Verificationist, Synecdoche, Lupin, and his last meal…
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Worlds are ways for things to be-possible ones in some sense of "possible" (Notation: w.) Logical space is the set of worlds. (Notation: W.) Propositions are subsets of logical space, or sets of worlds. (Notation: A, B, C,....). 1 A proposition A is true in world w i↵ w ✏ A, otherwise false. 2 Sentences are, you know. (Notation: A, B, C,....) Expression is the relation sentence X bears to proposition X when for all w, X is true in w i↵ w ✏ X.