An adequate semantics for generic sentences must stake out positions across a range of contested territory in philosophy and linguistics. For this reason the study of generic sentences is a venue for investigating different frameworks for understanding human rationality as manifested in linguistic phenomena such as quantification, classification of individuals under kinds, defeasible reasoning, and intensionality. Despite the wide variety of semantic theories developed for generic sentences, to date these theories have been almost universally model-theoretic and representational. This essay outlines a range of proof-theoretic analyses for characterizing generics. Particular attention is given to an expressivist proof-theory that can be traced to 1) work on logical syntax that Carnap undertook prior to his turn toward truth-conditional model theory in the late 1930s, and 2) research on sequent calculi and natural deduction systems that originate in work from Gentzen and Prawitz.1
We study the problem of approximating the commuting-operator value of a two-player non-local game. It is well-known that it is $\mathrm{NP}$-complete to decide whether the classical value of a non-local game is 1 or $1- Δ$. Furthermore, as long as $Δ$ is small enough, this result does not depend on the gap $Δ$. In contrast, a recent result of Fitzsimons, Ji, Vidick, and Yuen shows that the complexity of computing the quantum value grows without bound as the gap $Δ$ decreases. In this paper, we show that this also holds for the commuting-operator value of a game. Specifically, in the language of multi-prover interactive proofs, we show that the power of $\mathrm{MIP}^{co}(2,1,1,s)$ (proofs with two provers, one round, completeness probability $1$, soundness probability $s$, and commuting-operator strategies) can increase without bound as the gap $1-s$ gets arbitrarily small. Our results also extend naturally in two ways, to perfect zero-knowledge protocols, and to lower bounds on the complexity of computing the approximately-commuting value of a game. Thus we get lower bounds on the complexity class $\mathrm{PZK}$-$\mathrm{MIP}^{co}_Ύ(2,1,1,s)$ of perfect zero-knowledge multi-prover proofs with approximately-commuting operator strategies, as the gap $1-s$ gets arbitrarily small. While we do not know any computable time upper bound on the class $\mathrm{MIP}^{co}$, a result of the first author and Vidick shows that for $s = 1-1/\text{poly}(f(n))$ and $Ύ= 1/\text{poly}(f(n))$, the class $\mathrm{MIP}^{co}_Ύ(2,1,1,s)$, with constant communication from the provers, is contained in $\mathrm{TIME}(\exp(\text{poly}(f(n))))$. We give a lower bound of $\mathrm{coNTIME}(f(n))$ (ignoring constants inside the function) for this class, which is tight up to polynomial factors assuming the exponential time hypothesis.
Starting with a trustworthy theory T, Galvan (1992) suggests to read off, from the usual hierarchy of theories determined by consistency strength, a finer-grained hierarchy in which theories higher up are capable of âexplainingâ, though not fully justifying, our commitment to theories lower down. One way to ascend Galvanâs âhierarchy of explanationâ is to formalize soundness proofs: to this extent it often suffices to assume a full theory of truth for the theory T whose soundness is at stake. In this paper, we investigate the possibility of an extension of this method. Our ultimate goal will be to extend T not only with truth axioms, but with a combination of axioms for predicates for truth and necessity.We first consider two alternative strategies for providing possibleworlds semantics for necessity as a predicate, one based on classical logic, the other on a supervaluationist interpretation of necessity. We will then formulate a deductive system of truth and necessity in classical logic that is sound with respect to the given (nonclassical) semantics.
Kant, Calculus, Consciousness, and the Mathematical Infinite in Us John H. Smith Der Begriff des Unendlichkleinen, darauf die Mathematik so öfters hinauskommt, wird mit einer angemaĂten Dreistigkeit so geradezu als erdichtet verworfen, anstatt daĂ man eher vermuten sollte, daĂ man noch nicht genug davon verstĂ€nde, um ein Urteil darĂŒber zu fĂ€llen. Die Natur selbst scheint gleichwohl nicht undeutliche BeweistĂŒmer an die Hand zu geben, daĂ dieser Begriff sehr wahr sei. Denn wenn es KrĂ€fte gibt, welche eine Zeit hindurch kontinuierlich wirken, um Bewegungen hervorzubringen, wie allem Ansehen nach die Schwere ist, so muĂ die Kraft, die sie im Anfangsaugenblicke oder in Ruhe ausĂŒbt, gegen die, welche sie in einer Zeit mitteilt, unendlich klein sein. Es ist schwer, ich gestehe es, in die Natur dieser Begriffe hineinzudringen; aber diese Schwierigkeit kann allenfalls nur die Behutsamkeit unsicherer Vermutungen, aber nicht entscheidende AussprĂŒche der Unmöglichkeit rechtfertigen.1 [The concept of the infinitely small, which comes up so often in mathematics, is rejected straight out with presumptuous audacity as a fiction, instead of assuming that it is not well enough understood to form a judgment about it. Nature itself seems, however, to provide clear proofs that there is truth to this concept. For if there are forces that work continuously through time in order to produce movements, as it would appear is the case with gravity, then the force that effects this movement in an initial instant (or rest) must be infinitely small as opposed to the one that imparts movement in time. It is difficult, I confess, to penetrate into the nature of these concepts; but this difficulty can at most justify cautiously avoiding unfounded suppositions and not claiming decisively that it is impossible.] The question that I address in this essay is simple: what is the mathematical infinite doing at crucial moments in Kantâs philosophy? By doing I mean the way that specific notions of the infinitely smallâthe infinitesimal, the differential, infinite approximation, continuityâserve as metaphors in a strong Aristotelian sense; that is, they attempt to âbring before the eyesâ something abstract and thereby contribute a kind of intuition to the unintuitable.2 And yet, there is something doubly ironic going on in this effort. On the one hand, although mathematics and the mathematization of nature have been criticized by Husserl for abstracting modern thought from the concrete life-world of experience, I will look to places where there is a turn to the mathematical infinite in order to be concrete.3 On the other hand, the clear [End Page 95] intuitions associated with the mathematical infinite can easily get caught up in contradictions that undermine the initial clarity.4 By exploring these moments of metaphoric and paradoxical representation, we can see how major thinkers grappled with a notion of the âimmanence of the infiniteâ that characterizes the epochal turn of modernity.5 First, let me give a general sense of what is at stake in the notion of the mathematical infinite and the issues of representation associated with infinitesimal calculus, which was up through the nineteenth century arguably the most powerful tool for understanding the physical world. Although Kant rarely addresses calculus as such, this tool has particular relevance for him given the fundamental role that both its inventors, Leibniz and Newton, play in the development of his critical project. Consider the problem of a line tangent to a curveâthat is, a straight line that touches any curved line at precisely one point. As I hope and expect has just occurred in the mind of any reader at this point, a somewhat-clear image has taken shape. This image can be rendered mathematically precise thanks to the technique of calculus; indeed, calculus was developed in large part to address this problem. The reason is that such a tangent can be considered the rate of change of the curve at any instant, which can be calculated given the curveâs function. Thus, say, a soaring baseball defines a parabolic arc at a changing rate of speed (fast at first, slowing at the peak, then ever faster as it returns to the ground). The tangents at any point indicate...
The argument of this paper may be summarized as follows. Causal propositions (propositions of the type âx causes yâ) are ambiguous. Such a proposition may have any one of three meanings (possibly more; but three is enough for this paper). The ambiguity, however, is of a rather odd kind. Sense I, which is historically the original sense, is pre-supposed by the others, and remains strictly speaking the one and only âproperâ sense. When we assert propositions containing the word cause in senses II and III, we are âsayingâ one thing and âmeaningâ another; we are describing certain things as if they were things of a kind which we do not actually believe them to be. This always has an element of danger in it: the danger of inadvertently beginning to âmeanâ what one had only intended to âsayâ, i.e., of thinking that things are what we describe them as if they were. This danger is much worse when our âmetaphorsâ get âmixedâ. This is what has happened with the so-called âidea of causationâ from the time of Kant onwards. It is a confusion of certain characteristics belonging to sense II with certain others belonging to sense III. Nothing can be done, therefore, towards clearing up our minds about causation, by merely analysing the idea as it stands and detailing the various elements it contains; for these elements are mutually contradictory. We must carry the process further, by segregating the elements under different heads, and distinguishing these as different âsensesâ of the word. But even this is not enough. A further step in the process is needed: namely a critical discussion of each âsenseâ taken singly. When this is done it will be found that the best way of avoiding confusion will be to restrict our use of the word cause to occasions on which it is used in its âproperâ sense, No. I; that on the occasions on which we use it in sense II we should be wise to use instead the terminology of means and ends; and that when we use it in sense III we should do better to speak of âlawsâ and their âinstancesâ. In the sense of the word that which is is the and of a and and to do it means a for we may to in the kind of in This is the time a and sense of the word with its and in and of the in of in and in A in a in causes of This not that the to the that with and it that on the up to In the sense we that a causes a to a that causes to from an It is not only a sense, it is of In is the word for as when the the of with the and the of have it that this is a use of the word and from what sense III, i.e., the sense in which one thing in is to be the cause of This is not the sense is the of the as can for will the in the and the in and and the cause in the II and III have of it by a process which in the A cause in this sense of a cause and a The is a of things the is a of things to be of these be a cause if the were A to a certain may be to by a about the of that but this not cause to to in the of an a to a not cause to in a certain if in that The is not a of things as it is a of things by the in to a a certain of the cause of is not this as it is this as to the in by The is not a as it is an A is to in a certain way not by to in that way it is to to but by to in that may be to the of but is not of this kind may the of a and in as the that a certain of things as when a of a certain the to a certain This is to the to do a certain to do The however, is an it not be done not be the it of A causes to do an is and not is a in and is for is a which A to by certain certain is the is the proposition that the by and the proposition that a in of and is for the the proposition the in this A is to the for the This not that a is a which be an which do when they speak of It means that is for the A is for the of certain to certain to the When a of a on its do is not is as an This is what when of the and A is to when about the is not on from and are In this in which a is to is not It has a and a But has done for the of the and the which in the is to cause has done for can be to cause as as to do in that the of be an which to an of on the of and has as only will not what they by the word In sense in sense I, the word cause an idea to but the in this is an intended to not but things in In this sense, the of an in is the to by which we can we to to a and it we can certain of our we about for its The is the cause of an means in this can we This sense of the word may be as follows. A cause is an of things which it is in our to and by which we can that cause it is to be. When speak of to occasions as when one a and the of things by the proposition is the with the to the This is an sense in The cause of a is the which a on the cause of is the of a the cause of a is the cause of is their in a the cause of a is that has taken the cause of a in the is that the the cause of is that and The for causes in sense II is in that sense of the in which is what a not for its and but for its for the which it is and is by The of a is the in terminology of The for is but it of i.e., by that to it to the that things are is to that we can and A of is A of time and is on is the cause of we the cause of we should be to that is the of this But should it be that the cause of to to have the cause of but that not in be of any use the cause had not a thing that be Such a be and one that had done what to It be that not what the word cause the of be it in a a proposition of the âx causes the proposition âx is that can be as of the of This sense of the word is not It can be of to the the in the of the these the A in sense II means which is by to the When in this sense we that causes we are about by We are always about in with things which we do not these will not cause to are The the cause and these as has for by the cause of an as its to sense III, not to sense the should the cause and certain are and the in that the should is of sense II and not of sense the cause is not what we have the cause but this the that the cause is the of a of and that what the cause is one of by a of with a that only to the have that this is by means It is to a on a and what the cause not by a that the of a is further from the its and that is to a to the this is what the has is one of the the of and as has one of these and it the has done what we always But an the up a and on three is the cause of the It is the it has not it has as the thing that can which the will had a by on the have to to the as the cause of the not the is a but can it The cause is not it is to a which is in the of the cause in sense It is for that the has a of things from which But this not In the the of any are in that one them for even if In the one to them should that can get a by certain may be that should not be it a were but as get it do not what these to a in one of them to get do not to what they only to what the one is that has this a which of that the of an three and that are three of A is to and only is to and only and is to and only if each of them the cause of each will have to a different is the for and for The may be by that for any the cause of a thing is that one of its which is to a a certain and the of the cause of the and the is that one must the of the cause a and the is that one must the of the cause and the is that one must the of one of these three the for the on one of the others, if for the is the of to of that it we that be done, by any towards that is to of their cause be a that not in But a cause in this sense of the word is by is this means that so-called is not The proposition in which it is in a cause of from of i.e., that one of its which to is which is to but the of in of in which we and they are that is but of the idea of cause as it is not to it should be. A further of the is for a is not to any of its a has cause and any about it will be a the of a that of had that the cause of This of a but one better from a with these to their In sense II of the word only a is with a certain kind of can an about its a are When to the of in time the idea of a the cause of to which in not are of propositions in sense II of the word they will of be in of the various in which the them can to their and of the means by which in each this can be propositions will be In them that their will on of will to a for any proposition is a of our to a certain of things by the use of certain and one what can can do may by and the that can do a thing that one has done in the the proposition âx causes is a of a it is that can be to in that is to the and are not but and the proposition of is a thing is means of of It be in this sense of the word to the cause of any thing as It is a of sense that proposition is a In sense I, proposition is an which be in the In sense III, propositions be the of the sense a is do describe this in do not they them they them they terminology to things is that of means and the must be that they to to things idea which is by the terminology and not by the is this The is not The terminology an idea not only of one to but of one to an idea of what as is this idea from in our in the of to from the of to do by argument the we in a in which can only carry by that and from the of to do it to this to the of in which we our by not of but of things in In to this we must that sense II of the word cause is a sense, and in with the of in the and that the and the an of of what we the as a of each with its and and and In and in the in the of the use of with is an a these are to be taken and to what they to namely that the way in which use what we as means to our is not in different from the way in which we use We use by them to be with of their and them in a way that they to do what is in with our This is them to in the and original sense of that word. is in much the way as we must use it to the and we can to this use of it the word in the sense, as are certain in which things if to is to their to in these and by the of to them not as they but as if is as to in our we do use which taken but that it is and to be taken and will that this about and that are with a in which that is is that we certain means to certain Sense III of the word cause an to it not to but to the characteristics which to this sense if the were and certain which in the to In the to which sense II a cause is in its as for its on in its as for the of its on In the to which sense III a cause is in its as it to in its as its what not are The cause to its by in the cause and is a can be of and of to of to the and of the in sense II from its in sense III by these senses and A cause thing to and to its to the a cause is one with its is of In to the of sense III, will to the the of in as a of a in and the that a cause its in that in is in sense but in sense III. to the of a and the its is a the and and a of But this is by the of the a of and this process is a of the to the is to the the of the and the of the is in the sense, not the in the proposition âx causes the we to use the word cause in the sense, must any it must the of the not its that process the for be an to be but its the is is the cause in sense III and when it is it its not but in sense III is with it is with its in The cause of the is the causes and that is in a and in a the from to is used in sense may be any as it is by a of which are of But if is used in sense III, must if it be any on the of a and be the and be a But the and causes in sense III, is a not cause in sense III. The of in the is a cause in sense III, is in the of sense III. The about sense III is to what is by that a cause its When is used of senses and II we what it in sense it means that a for in sense II that is means of But what it of it in sense are to this which may be the and The means A on this is a and its to its is the of to a When that means on this that and is the kind of which one has the of one of a the of the and the one as to the of one must that in a the of the can be it and even when it on the of a The therefore, that the cause is the not only in the sense that if the cause the actually but that if the cause is the is to to the of a thing can the by thinking the of Nothing in the of is This is in a in the sense if to a of in which the for causes means a for is to from This in what to to be a of and as is a in to the it that the is But the of causation, it may be as the of a be as an of the propositions by it were these propositions have to be as one that they can be by that by the so-called to be in the so-called it is this is that the what causes a and what a cause have to be by and the of a of the type not an of propositions of the type âx causes propositions of the type âx but the of propositions in that kind of and the use of propositions in the of and propositions not propositions be the of in these propositions This not be by that the in which propositions are Such a that the idea of is a idea which when will the different idea of This to be the of the of and if to it do not to but must that it not from the what the idea is that its had to the means of the this one be taken for will that the proposition âx means merely the have to be with and not in the will be with In the for and we from the of to the of the we from the of these propositions to the that the proposition the have to be with is not what we by âx but is only the on the of which we assert the different proposition âx if means of it must be that is that is is we assert on the of of what to that is what should to assert a we must from the of the propositions to the this is we to assert but on the occasions when we do assert them we to be namely to our has by in a of to which have to but and to for it and to is a of a that it is for of its argument This will the In as it to that in sense III a cause and But to of what to on the a proposition to be even that the in to a in if is a of and of may be an even if they are it may not be to them are the of any we that a will always be a that is in the of a the the which have for do not intended to and But if has a as when on for a paper get of it this i.e., to a paper on this is for to a the word is not a of a it to a of in sense I, and means that has to This sense of in which it to is to the sense which is not only in sense and sense II of the word cause but in sense III The that can be and of the that happened only the of on the that are from one original and that be not in the sense of of by but in the sense of a in it be on of and on to the cause of an but it to be that has a even we what its cause and if a is to the that an has it may may not be but it be a of of for it that that when we use the word in sense III we to by it different from and of in the and in the and that this and is in the of that this is We have to the which we when we found the idea in sense and we have to it in the what is this idea It to be that it is from our of occasions on which we have others to in certain by them in their to the that they are in of a kind that only by can they the we them to and occasions in which we have is an idea from our and in what is a way not only to our with things in II of the word but to the which these things have Causal propositions in sense III are of in The we are in the of these of that they are the of the that it up in with the of to which in sense II of the word but that in this the a of a can be to certain in by certain means to them and if is as of the but it will that will be as about certain things in by the of certain a step in the argument if we to it we should is a thing in by as a means of we to be a in of its but as in the of that must be. in that that which is by the word that word not be as a to and be the is for not the but the This not the in a of causes of the but a cause of a as from The a of the on this it that in certain for the of certain these a in certain to with a kind of and these the of and that of to the is and is a kind of one thing in thing in The and are used and to a sense of and for the of things is taken as the of these causes is a of and is a of This the in which our of and in which the to that were in the and when the of and by a the word cause not a it a and its in these when we to and the to we as a of a taken to in a kind of which to one to as to that a cause is of that in which its is if what is is a of a certain that but by the and of the it is that for the idea of is the idea of by thing which if not under this this different by This of one thing in by is the of is that a by and in have to be in it is to and this which is has to be by an on the of the that This the namely of its which it to the as an to not that this of to is the to is that as a which the of are It is to that in is of not only not assert that must have a and this in In the of a its be what as from is for means and means a from to and to the which is its from to is in sense by the of its from to for it is not is that any which to the of is an the of are in the of that is a thing as as may be any the therefore, it were to that is that is to to the as the of that is on it that is and the be of the It have that is the and that idea of causationâ is a of a to which it is is what has the in the and it has the of cause In of that we get a and of the of the of that to that as the of has to an as to up the the of the cause in certain as is not a of their in them the word cause is not used in the sense. are and they use the word cause in sense the use of the word in that sense with it a of but this is not by the A of may its The in has a of one the with its on causes in sense the of causes sense with the of and the of the cause as an in time to its the one thing in which has found namely the that what to a not a as the a which has the that has a the cause of is a and this is to not from but a be by that has a It be if were used in sense In sense II it is in that is not if we for of not to is what Kant a have with the idea in a must be used in sense III. But what can be for can only that the of cause with of that and that a of the of The cause of an can be a III, only when cause is used in sense in the proposition âx causes means be an may have but its be The of a the a these not the only that can is an that is with is in a of is a from The of the is an by the Kant has to that in the propositions the word is used in different is therefore, to it a the to the as a of of of and a certain of the in which had by when to sense III and get to sense the of cause is not only but actually the in of a of cause as can be from with with the of cause to and on a of causes a to have that the only sense of the word cause is sense III. But when as of from to causation, for the of i.e., the of the is it for in of sense II in any on the from of as as to the sense in which the word cause is will to paper the of is that has on the the The of this paper by the of on the is to a of the of has for that the of causationâ is and and that in propositions about causes have are by propositions about to to and to that from it may be only in however, a a of the of time which cause and we the may this which the if is used in the sense, this proposition is for it means that is for a certain may be which is must be in the sense. But if is to is the in the sense, of are as a is is but that not that is in that sense, its the only to a is from one sense to the when the in and that the cause it the that causes i.e., that they are in way to is that as not that causes are in way to further and that this is of the word by But what in a is not this it is the cause and have this The has by and the confusion of sense II and sense III is of a the of a proposition of the causes is to a proposition of the the must be taken to not to a of of but to the of the of the word that the word is used in sense III, the sense. But the that it is used in sense for only in that sense is it that in a proposition of the type causes and are is with a idea of in which one element is from the characteristics of sense II and from of sense III. It is not therefore, that even to any proposition must be a for a proposition of the as must be in and is that a proposition which is in is is a of which that is thing as from of a that they in but and of a of this has a on The of and its The which is the of this is the of that the that is by what has This is and the for means the belonging to an to a of have a that therefore, a this as belonging to the of The is for the a namely of of that must have a cause and that this cause must be a but that our of this is have only to what by a in to that this is the that Kant on to will not that we a on as an as a which we will is that will of and to the that one is that is of to the that which is to which it to as it to with happened that but them that we of that is a that it be is not do not that things are as they are they were as they were. But do The are one in an of which to be of them has to any Kant the propositions of which this is are that as to we a of it The have in a to which have to by the word in This is that a it and have it the The word to a of the It is not used by a is thinking is to the is this of which are and what are its have the of it when in they are of their but when they to be to the to of it as have the use of is an will are It have any of the have to that the is is the âidea of causationâ which for is the which this our to not only their but their
Quine (1966) offered his classic characterization of the notion of paradox, a taxonomy for paradoxical arguments and some vocabulary for discussing them. In this article, I shall generalize Quineâs taxonomy and defend a simpler characterization. The simpler characterization will have the virtue or the flaw (as might be) of making paradox a matter of degree. For Quine, a paradox is an apparently successful argument having as its conclusion a statement or proposition that seems obviously false or absurd. That conclusion he calls âthe proposition ofâ the paradox in question. What is paradoxical is of course that, if the argument is indeed successful as it seems to be, its conclusion must be true. On this view, to resolve the paradox is (i) to show either that (and why) despite appearances the conclusion is true after all, or that the argument is fallacious, and (ii) if the former, to explain away the deceptive appearances. Quine divides paradoxes into three groups. A âveridicalâ paradox is one whose âpropositionâ or conclusion is in fact true despite its air of absurdity. We decide that a paradox is veridical when we look carefully at the argument and it convinces us, i.e. it manages to show us how it is that the conclusion is true after all and appearances to the contrary were misleading. Quineâs two main examples of this are the puzzle of Frederic in The Pirates of Penzance (who has reached the age of 21 after passing only five birthdays) and the Barber Paradox, which Quine considers simply a sound proof that there can be no such barber as is described.1 A âfalsidicalâ paradox is one whose âpropositionâ or conclusion is indeed obviously false or self-contradictory, but which contains a fallacy that is detectably responsible for delivering the absurd conclusion. We decide that a paradox is falsidical when we look carefully at the argument and spot the fallacy. Quineâs leading example here is De Morganâs trick argument for the proposition that 2 = 1.2 Oddly, Quine does not mention a third related category, the obverse of a veridical paradox: the argument in question could have an obviously false or self-contradictory conclusion, yet rest on no error of reasoning however subtle â so long as it has a premiss that looks for all the world true until we let the argument itself show us that, and how, the premiss is false after all. For example, the Barber is classified as veridical because its conclusion is the truth that there is no barber who shaves all and only those who do not shave themselves; but turn it on its head, so that its conclusion is rather the absurdity that there is a barber who both does and does not shave her-/himself. There is still no fallacy, but only the innocent-seeming premiss that there is a barber who shaves all and only those who do not shave themselves.3 We might call this sort of paradox, for want of better, âpremiss-flawed.â Finally (returning to Quine), an âantinomyâ is an intractable paradox, one that we cannot see how to resolve in either of the foregoing two ways: the argument does not succeed in convincing us that its conclusion is true-despite-appearances (often because the conclusion is overtly contradictory or otherwise incoherent, yet we can find no fallacious move in the argument; nor is there a premiss that is shown false-despite-appearances. Antinomies, Quine says, âbring on the crises in thoughtâ (5); they show the need of drastic revision in our customary ways of looking at things. My main problem with Quineâs taxonomy is its heavy dependence on the current state of oneâs knowledge and on oneâs ability to figure things out. Let me explain. All a valid deductive argument shows, just in virtue of its validity, is that a certain set of propositions is internally inconsistent. If all we know about an argument is that it is valid, we do not thereby have even the slightest reason to believe that the conclusion C is true, even though doubtless the person who constructed the argument was reasoning, from P1, P2, ⊠taken as premisses, to C. For unless we are independently moved to accept those premisses, their jointly implying C is of little interest; and even if we do already accept them, seeing that they imply C may make us reconsider one or more of them, rather than inclining us any the more strongly to endorse C as well.4 In this sense, an argument has no intrinsic direction; its direction has been imparted to it rhetorically by a speaker who has recruited it for a particular dialectical purpose. Intrinsically, the argument is just the inconsistent set {P1, P2, âŠ, âŒC}. The relevance of that (I hope uncontroversial) point for Quine is that, faced with an apparently inconsistent set of plausible statements, anyone may choose which of the statementsâ denials to single out as âthe propositionâ or âconclusionâ of the corresponding paradoxical argument, either arbitrarily or on a ground of some sort. (Remember that a paradox in Quineâs sense has an already appalling conclusion, so there is not initially any epistemic reason, as opposed to expository reasons, why the conclusion appears as such rather than being negated and taken as a premiss.) And given a paradoxical argument, two theorists might well disagree on whether the paradox is veridical, because they may disagree as to which component propositions are more plausible than which; in particular, one theorist may find the argument veridical while the other finds the âconclusionââs denial more plausible than one of the âpremissesâ. In Quineâs examples of veridical and falsidical arguments, the comparison of plausibility is sufficiently obvious and uncontroversial that in fact no one would dispute his judgements about them. But we should bear in mind that that is because we all think roughly alike on issues of Leap Year and birthdays and barbers and arithmetic; a person who for whatever reason had different background beliefs and very different interests might resist Quineâs judgements. In short, to classify a paradox as veridical is to assume that oneâs own preferred way of resolving the paradox is the correct way. More generally, then, a Paradox (I mark my own proposed usage with the capital letter) is an inconsistent set of propositions, each of which is very plausible.5 And to resolve a Paradox is to decide on some principled grounds which of the propositions to abandon. One might then think of saying that when that decision is comparatively easy, we could call the Paradox either veridical or falsidical, depending on which of the component propositions have been designated as âpremissesâ and which has been denied by way of âconclusionâ, though when the choice of culprit is difficult or controversial, we call the Paradox an antinomy, as Quine does. But that translation of Quineâs terminology into mine would not be accurate, for in regard to my notion of Paradox, Quineâs âveridicalâ and âfalsidicalâ are not natural opposites. A Paradox would count as veridical in the proposed new sense just in case (a) one of its members turns out to be clearly less plausible than the others, and (b) the Paradox is already (for whatever reason) cast in the form of a deductive argument having the culpritâs denial as its conclusion. But there would be no such thing as a falsidical Paradox, for a falsidical argument in Quineâs sense is fallacious, and the apparent inconsistency corresponding to it is not real. In my terms, then, a falsidical paradox in Quineâs sense is only an apparent Paradox.6 But on my view the âveridicalâ/âfalsidicalâ distinction really loses its point. Rather, there are inconsistent sets containing identifiable culprits â call those âtractableâ Paradoxes â and there are the antinomies. It is better just to drop Quineâs terms. There is a further complication. I have defined âParadoxâ in terms of actual inconsistency, namely, as a set of propositions that is in fact inconsistent. But (a) a set can be inconsistent without anyoneâs knowing that it is or even being able to know that it is; and more importantly, (b) we may have reason to think that a set is inconsistent when actually it is not. Case (b), Quineâs falsidical again, is not uncommon; we have some plausible premisses and we use what seems to be a sound principle of reasoning to deduce our absurdity, but in fact the absurdity does not follow and the fault is in the principle of reasoning rather than in any of the premisses. (De Morgan divides through by a number that is covertly equal to 0; elsewhere (Lycan 1993, 2001) I have argued that when one is reasoning in English rather than in a truth-functional calculus, reliance on the rule Modus Ponens can lead from perfectly acceptable premisses to contradictory conclusions and so must be rejected.) Now, to circumvent this complication and keep the terminology neat, let us dispense with every even faintly dubious principle of reasoning. That is, let us require that for a Paradox to be worthy of its capital âPâ, it must be formulated truth-functionally, with every initially non-truth-functional principle of reasoning replaced by that principleâs corresponding material conditional inserted as a member of the inconsistent set that constitutes the Paradox in question; thus we shall make every possibly controversial inference principle explicit. And, owing to the semantical completeness of the propositional calculus, any Paradox is provably as well as model-theoretically inconsistent.7 It must be conceded that, in at least three ways, even the propositional calculus is âcontroversialâ. First, there is the question of relevant implication. Relevance logicians8 brand the truth-functional calculus as libertine, charging that some of the inferences it sanctions (notably Disjunctive Syllogism) introduce informational irrelevancies and are therefore not ones that English speakers would or should make. But however we feel about this as a complaint against the analysis of English or any other natural language in truth-functional terms, it does not apply to my idea of reconstructing paradoxes into Paradoxes; I am here using the propositional calculus and its libertine notion of validity only as a tool for strict truth-preservation in inferential moves between propositions that are already formulated in the truth-functional idiom. Disjunctive Syllogism may not be a valid principle in the logic of English (any more than are Antecedent-Strengthening and Modus Ponens), but it is valid trivially and by definition for the tilde and the vel. Second, paraconsistent systems have been offered as rivals to standard contradiction-shunning logic,9 and in particular dialetheists led by Graham Priest (1987, 1995) have maintained that there are actually true contradictions. Indeed, Priest cites some familiar paradoxes as examples; there is nothing to âresolve,â because the contradictions simply are true. But this view is no opponent of my characterization of a Paradox. It merely takes a refreshing attitude toward Paradoxes once they are identified. Third, Quine, Putnam and others have suggested that even elementary logic may be brought into question by exotic scientific developments such as in quantum mechanics. Once again we must distinguish between logical laws intended as representing the logic of English and the theorems of a formal system whose truth-theoretic semantics has been officially and stipulatively assigned. My notion of Paradox is tied to the latter, and has no implications regarding the former. But if(!) I understand quantum logicians correctly, they mean to impugn even standard propositional logic understood as formulated in terms of the traditional truth-defined connectives. Depending on oneâs view of analyticity,10 and once we have distinguished the matter of epistemic revisability from the metaphysical issue of truth by virtue of stipulated meaning, this may not make sense. But even if it does and we are thereby forced to admit a notion of falsidical Paradox after all, at least my format will make the point of contention as explicit as anything could. Two objections have been made to me; oddly (but fortunately) they oppose each other. The first11 is that most or at least many people think of paradoxes as arguments, hence, contrary to my conception, as being intrinsically directional, from premisses to conclusion. It may be that many people do so; and that way of thinking is well represented by Quineâs model. But I have pointed out that arguments themselves are not intrinsically directional, save by prior commitments of their proponents. To repeat, the speaker who has deployed the argument has chosen to present one or more propositions as its premisses and infer another proposition as its conclusion, but that is rhetoric; we can equally argue from the âconclusionâsâ negation to that of one of the âpremissesâ, and nothing about the argument itself tells us which should be preferred. The second objection is that paradigmatic paradoxes are single sentences or statements such as the Liar, hence not inconsistent sets of propositions (and, n.b., not arguments either).12 Whether or not the Liar is paradigmatic, it is a single sentence rather than an inconsistent set, and it does suggest mild readjustment of our formula. I said that a Paradox is an inconsistent set of propositions âeach of which is very plausible,â but on its face the Liar cannot be so described. It can be expressed as an inconsistent set, {â(L) is true,â â(L) is false,â â(L) is either true or false but not bothâ}, but none of those three propositions has great intuitive appeal. What is true is at best that each of the propositions has a strong argument in its defence.13 Those three arguments have premisses, such as âWhat (L) says is that (L) is falseâ and âIf S says that P then S is true iff P,â so a Paradox as I originally defined it would feature those undefended premisses, not the lemmas as above. So, either we can say that the Paradox is that more complicated set, which is not very natural (also, we would get different versions depending on exactly how the ultimate premisses were formulated), or we can liberalize the definition by replacing âeach of which is very plausibleâ by âeach of which either is very plausible in its own right or has a seemingly conclusive argument for itâ. If we stick by my notion of Paradox, we will regard the distinction between âtractableâ Paradoxes and antinomies as theory-infected and somewhat presumptuous, but above all a distinction of degree. There are actually two matters of degree involved: the disparity in plausibility between a putative culprit proposition and the other, more plausible propositions in the set, and the average degree of plausibility all around. The higher both of these degrees go, the more readily we will see a Paradox as intractable; we get a real antinomy when the first is near zero and the second is still high. If the second is low, we have only a mild Paradox, and I am loath to call it antinomic, but only an array of competing theories.14
In two important recent books, John Hawthorne and Jason Stanley each argue that non-evidential factors, such as the cost of being wrong and salience of possible error, have a place in epistemological theorizing. This point is familiar from the work of epistemological contextualists, who emphasize non-evidential speaker factors: factors which, when present in a speaker's conversational context, affect the semantic content of her knowledge attributions. According to Hawthorne and Stanley, the appropriate focus is on the subject, rather than the speaker: when the relevant non-evidential factors are present in a subject they can affect whether the subject knows. This suggests a reorientation for epistemology, away from the standard âintellectualistâ (Stanley's term) model, endorsed even by contextualists, according to which only evidential or more broadly truth-related factors (evidence, safety, sensitivity, reliability, etc.) bear on whether a subject knows. If Hawthorne and Stanley are right, then the contextualist program should give way to a program of anti-intellectualist invariantism, or to use a more common label, subject-sensitive invariantism (SSI).1 The books explore in insightful and original fashion a range of important issues in epistemology, all focused on the concept of knowledge: the lottery puzzle, skepticism, the knowledge rule of assertion, the relation of knowledge to objective chance, epistemic closure, etc. Here, we limit ourselves to the relative merits of SSI. Stanley claims that the only plausible argument for contextualism is based on intuitions about certain stakes-shifting cases (like Keith DeRose's bank cases and Stewart Cohen's airport case). (84) This is because he takes the contextualist about knowledge attributions to be positing a sort of context-sensitivity which departs significantly from the familiar sorts. He painstakingly backs up this claim in chapters 2 and 3. In chapter 2, âknowâ is shown not to be a gradable expression (it doesn't admit modifiers and has no associated comparative), and so the assumption that gradable expressions are context-sensitive is no evidence that âknowâ is. Chapter 3 argues for two general points: first, our use of propositional anaphora (âwhat I saidâ) and speech reports (âI said that I knewâ) doesn't follow the pattern displayed by familiar context-sensitive expressions (like modals, demonstratives, quantifiers, gradable expressions); second, we do not find the sorts of intra-discourse context-shifts that we find with the uncontroversial examples and which we would expect to find given the plausible assumption that context-sensitivity has its source in particular occurrences of elements in logical form.2 Stanley's conclusion is that if the intuitions in the stakes-shifting cases can be explained away adequately without resorting to contextualism, we would have little reason to accept contextualism.3 If Stanley is right about the dialectical situation, the ramifications for epistemology are significant. Contextualists have wanted to argue that, because these cases force us to acknowledge dramatic shifts in epistemic standards across contexts of use, we have good reason to think that even more dramatic shifts could be the source of the appeal of skeptical arguments. Without an independent reason to think that dramatic shifts occur, contextualists have no good answer to the charge that their response of skepticism is ad hoc, the sort of easy response available to solve almost any philosophical puzzle. With all this in mind, here are DeRose's original (1992) bank cases: Bank Case A (Low Stakes). My wife and I are driving home on a Friday afternoon. We plan to stop at the bank on the way home to deposit our paychecks. But as we drive past the bank, we notice that the lines inside are very long, as they often are on Friday afternoons. Although we generally like to deposit our paychecks as soon as possible, it is not especially important in this case that they be deposited right away, so I suggest that we drive straight home and deposit our paychecks on Saturday morning. My wife says, âMaybe the bank won't be open tomorrow. Lots of banks are closed on Saturdays.â I reply, âNo, I know it'll be open. I was just there two weeks ago on Saturday. It's open until noon.â Bank Case B (High Stakes). My wife and I drive past the bank on a Friday afternoon, as in Case A, and notice the long lines. I again suggest that we deposit our paychecks on Saturday morning, explaining that I was at the bank on Saturday morning only two weeks ago and discovered that it was open until noon. But in this case, we have just written a very large and important check. If our paychecks are not deposited into our checking account before Monday morning, the important check we wrote will bounce, leaving us in a very bad situation. And, of course, the bank is not open on Sunday. My wife reminds me of these facts. She then says, âBanks do change their hours. Do you know the bank will be open tomorrow?â Remaining as confident as I was before that the bank will be open then, still, I reply, âWell, no. I'd better go in and make sure.â (913) How do these cases support contextualism?4 It seems (premise 1), you speak the truth in both cases. But (premise 2) you have the same evidence and generally the same truth-related factors regarding the proposition in question. Therefore, (conclusion) the sentence âI know that the bank will be open on Saturdayâ must differ in semantic content in these two contexts of use, due to a difference in content associated with âknowâ: contextualism is true.5 Stanley grants both premises but denies the conclusion. The conclusion follows only on the assumption of intellectualismâonly on the assumption that, if the content of âI know that the bank is open on Saturdayâ is the same in the two cases, a difference in the sentence's truth-value across the cases requires a difference in the evidence for the bank is open on Saturday. But perhaps intellectualism is false: even if âI know that the bank will be open on Saturdayâ has the same content across the cases, it could be true in one case but false in the other because the practical facts differ. SSI can handle the bank cases just as well as contextualism. DeRose's bank cases are cases of first-person present-tense knowledge attributions in which the attributor is aware of his practical interests. SSI delivers the same results as contextualism for these cases. The same goes for first-person versions of the lottery puzzle. The contextualist says that the sentence âI don't know my ticket is a loserâ is true in a context in which the possibility that one wins is salient, even though it wasn't true in a previous context when that possibility wasn't salient (e.g., because, as in Hawthorne's example, one is thinking about whether one will have enough money to go on Safari next year). For the contextualist, the change in truth-value is due to the association of a higher epistemic standard in the later context than in the former, and this association is made possible by the content-shifting power of salience. The SSIist, piggybacking off the contextualist, may say that salience destroys knowledge. When the possibility of your winning wasn't salient, you knew you would lose. Now that it is, you don't know. And the same case could be made for skeptical arguments. The SSIist might say that the salience of the possibility that one is a brain in a vat strips one of much of one's empirical knowledge. These anti-intellectualist manoeuvres incur an explanatory burden, for it is unclear how salience of possible error, or raised practical stakes, could destroy knowledge. But the view does at least match contextualism in its claims about the truth-values of first-person present-tense knowledge attributions and denials. Moreover, the SSIist doesn't make the vindication of our intuitions about cases dependent on delicate use/mention issues, such as the distinction between the question of whether what is said in uttering âI know that pâ is true and the question of whether the subject knows that p. It appears, then, that we have a prima facie case for thinking that either contextualism or SSI is true. But which? One consideration that might seem to favor contextualism is the fact that SSI predicts the truth of odd-sounding temporal and modal embeddings. It sounds wrong to say âI don't know that p, but, assuming p is true, I used to know that p,â or âIf I didn't have so much at stake, then if p were true, I'd know it was.â But SSIists seem committed to the potential truth of both of these utterances. Is this a reason to favor contextualism over SSI? Stanley suggests (pp. 107â13) that contextualists might find themselves committed to similarly peculiar temporal and modal embeddings, depending on how they explain the source of context-sensitivity. If so, these oddities would be no reason to favor contextualism over SSI. He considers in particular David Lewis's (1996) contextualism, according to which knowledge-ascribing sentences contain a context-sensitive quantifier under semantic analysis. Under Lewis's account, âS knows that pâ is true in a context iff âS has evidence which rules out all possibilities in which not-pâ is true in the context, with âall possibilitiesâ contextually restricted to those that are not being properly ignored in the context, where attention to a possibility is one way of not being properly ignored. Because the best semantic account of quantifiers holds that they express properties, it would seem that Lewis is committed to thinking that the relevant property is not being properly ignored by A, where A is the attributor. But then we should expect that a sentence such as âIf A were properly ignoring more possibilities than he is, S would know that p, if p were trueâ to be acceptable, which of course it isn't. We have a reservation about Stanley's argument. Consider his example of âevery bottleâ. In a context of use, this expresses a property, e.g., being a bottle on such and such shelf. Which property it expresses depends on what is salient to the attributor or conversational participants, but the property expressed itself is not about salience to a certain attributor. Thus, âJohn bought every bottle but wouldn't have if I had been thinking about a different grocery storeâ won't come out true. Similarly, it seemed to us that one could revamp Lewis's view by proposing that which property âall possibilitiesâ expresses in a context of use depends on what the attributor is properly ignoring but the property expressed isn't itself about the attributor and his ignorings. So, perhaps SSI is committed to the peculiar sounding embeddings in a way that contextualism isn't. Nonetheless, there are ways to soften the blow. As Hawthorne (177n.40) remarks, anyone who thinks barn façade cases are Gettier cases must say that in many cases in which you look at a barn it is true to say, âI know that's a barn, but if unbeknownst to me there were a lot of barn facades around then even if this one was a barn I wouldn't know it was.â The defeasibility of knowledge, too, generates odd-sounding predictions like this: âI don't know that Mary is sick, now that her boyfriend told me she was faking it, but if he is misleading me, then if he hadn't told me anything, I would know (having seen her coughing earlier today).â If we can live with these embeddings, perhaps we can live with SSI's temporal and modal embeddings as well. SSIists, however, must further part company with contextualists on third person knowledge attributions. When Mary and John, whose evidence is the same as Smith's, utter not only âWe don't knowâ but also âAnd neither does Smith,â the intellectualist contextualist will say that Mary and John speak the truth about Smith if they speak the truth about themselves. The SSIist will of course have to insist that this move is in general illicit, because, e.g., less might be at stake for Smith than for Mary and John or fewer counterpossibilities of error salient to him. Yet we seem to make this move on a regular basis. It would be very odd for Mary and John to wonder, âWe don't know whether the plane stops in Chicago, but if it does, then Smith knows it does.â The SSIist has to explain away mistakes about third-person knowledge attributions and denials. Keith DeRose (2004) has called this the problem with SSI. Hawthorne and Stanley are well aware of it, and propose their own solutions. The core idea behind both proposals, spelled out most clearly in Stanley (who is trying to improve upon Hawthorne's account (see pp. 162â66)), is that we treat others as if they were in our situation, having our stakes (or finding salient possibilities we find salient). Stanley puts it this way: our real aim is to deny that if they were in our situation they'd know. Indeed, they wouldn't. But what is strictly said, that they don't know, is false. (101â4) This proposal is committed to an error theory about some of our knowledge attributions. But, as Hawthorne and Stanley would be quick to point out, contextualism has a similar problem because as we noted above, contextualists place heavy weight on the use/mention distinction. Mary and John are happy to assert not only âSmith doesn't knowâ but âWhat Smith said is false. He doesn't know any more than we do.â Equally worrisome, Stanley notes that contextualists have to strain, more than SSIists, to accommodate intuitions about other third person casesâcases in which the attributor has lower stakes than the subject. Stanley calls such cases Low Attributor-High Stakes and claims that contextualism delivers the wrong result about them. Intuitively, Stanley claims, the speaker's attribution of knowledge to the subject is false, whereas contextualism predicts its truth. Contextualism in his view also than SSI in certain person cases, such as Stakes which a subject thinks her stakes are but they are He that the weight of the versions of the stakes-shifting SSI over contextualism. does not that contextualism is false. Therefore, there is a way to accommodate without Stanley's intuitions about all the versions of the stakes cases, by for a contextualist of it is part of the for knowledge attributions that that pâ only when the subject is to as if p in of the So, when a attributor says of a subject knows that p,â the attributor that intellectualist contextualism, it will have to to This takes of all but the subject has stakes, but we have the the attributor when she says, doesn't know that handle this case, we the contextualist when one's stakes that one a certain standard to know, in one's speech context associated with having an epistemic that at least that so that if a subject doesn't it with to p, the subject doesn't with to p in one's speech possibility for all the stakes-shifting cases is to with a view which would also have the over contextualism that it doesn't different intuitions depending on whether the say or he said is rather than doesn't The possibility of these of up the to the epistemological question of whether intellectualism is true from both the semantic question of whether knowledge-ascribing sentences in content across contexts of use and the question of whether knowledge-ascribing can only be true relative to an (e.g., a or an epistemic Stanley is right that intellectualism is a for contextualism for in the of stakes-shifting cases. As Stewart in contextualist from his case of Smith and Mary and John, what is in the is a good enough reason for Smith to know, then it is a good enough reason for John and Mary to But there is no reason an anti-intellectualist to semantic or are to accommodate intuitions such as those in the cases. the are as as we know no one is on as they do the cases. these we are with intellectualist contextualism and each of which is committed to error about our to some of the cases at has to to accommodate those It will seem to some that all this and in the is an Consider what Hawthorne calls This is intellectualist invariantism with the claim that the standards for knowledge are enough so that a many of our knowledge claims are in fact true. it is that contextualism and SSI are committed to error of their own about the versions of the bank cases, there is now no from consideration of those cases, to invariantism just because it requires its own error theory to handle we to the invariantism, is a reason to that knowledge, or even is to salience or practical in the such factors are not truth-related or the used in standard Gettier misleading into the at we little in salience of possible error as a subject seems to us to be no other than the to the cases, to a between knowledge and salience of possible The situation is more for knowledge and This is the of our Hawthorne us to the are a for a lottery ticket that cost a in a ticket lottery with a and reason as I will the If I the ticket I will If I the I will a I to the This he claims, is The is that you don't know the is true. this lottery case to Hawthorne's A or so you bought a lottery ticket in a ticket the in a at I won't have enough money to go on Safari next the less as to the This is In Hawthorne's because you know the is true. like these are used to support Hawthorne's one is to use p as a in practical if and only if one knows that Hawthorne that it is to give the the difference between the and the other the lottery is that in the case the for the subject that he will is enough so as to be to the practical issues at he can the epistemic that is This knowledge out in favor of a about you can use p in practical just in case the that p is false is just in case it can be in your practical this the If this is so we give in and accept Hawthorne's is to appeal to the according to which that p is and for having epistemic or for being or for there being no epistemic for the subject that the epistemic of is the same in both cases or If it is the then by the you don't know that you will in the you don't know, in the lottery case, that you will the But if you don't that, then by you don't know that you won't have enough money to go on But the seems to be a of knowledge. Thus, Hawthorne that if the epistemic of is the same in the two cases, then skepticism So, skepticism the for you of winning between the cases, and so by the the two cases differ with to your knowledge that your ticket will lose. It follows that practical can affect knowledge in the way We can think of two ways to to Hawthorne's argument. one might argue that you know in the case isn't to in the case you do have a lottery and might be have a reason to think you might have enough money to go on Safari next In response Hawthorne (pp. argues that lottery cases can be at will for just about any of our claims to knowledge. If so, then there is about the case, because there is about the of that is a lottery one might question the We with this are the relevant to between If your epistemic for p is then, it should follow that you would be to accept a on p at any But you wouldn't be to do this for very many doesn't think he would on the of at any Thus, the seems to One can to this as Hawthorne does, by intellectualism about epistemic and so that how a proposition is for a person can with practical This seems to us If you me a on the proposition this will come up that doesn't seem to lower its and not to the that it will come up us the Is there any other reason to knowledge into the of certain of practical are and others not just on the If you an when a for his lottery he isn't to it, he will you that he doesn't know that the ticket will lose. If you the same in the he the rather than the given that he of on he will answer that he knows he won't have enough money to go on seem to knowledge its to their As Stanley A standard use of knowledge attributions is to When I I to the on the rather than the on the right, I will by that I knew that the on the had the I but I not know whether the on the right When my wife me I rather than I that I knew that it was the to go to the If we could have a view that knowledge relevant but doesn't us to the this might seem to just the right And it such a view is We can claim that knowledge is with a epistemic of error but only an This view at least the of Hawthorne's will of course to the Stanley as having rather than semantic The idea would be that there are cases in which one knows but isn't to on it, that one knows often or at least in some way that one is to on it Stanley is well aware of this and a to come up with a We that it is not easy to give such a (see our but we that he shifts the of As we above, many in our view will insist that intellectualism is a cost than positing or intellectualism us to the claim that you can or knowledge, not by or by but by or up a large check. And that seems Is there a more argument available for a When it to would deny that when can be to other It does not follow from the fact that your is even from the fact that you that you have a reason to that your won't But you know that your is you have an reason to that your won't that your is So, when it to we do to say that, when you know that p, p can be your your for course, when you know that p, p can to be your for some for the very reason that p has to do with if you know that your is that it is is not a reason you have for that is from the than But its to be a reason you in this case, is not the result of the for you that your is not the result of any other epistemic you have with to the proposition that your is When you know that p, in the for you that doesn't in the way of p being a reason you have for We can say very similar about the very there are facts such that, when you know to be true, they can be you have to do The fact that your will be by a which is the you and in the next seems to be such a that the of this fact would not that you have any reason to your (having no idea of the situation, you would be it in on the with your would your in it if be enough if that itself were not But if you know this then you do have a reason to your This is a of the situation. As with the situation, when you know that p, p might to be a reason you have for but not because of any epistemic of with to because for example, the for you that might know that your is But this is not a reason you have to your out of the way of an its to be a reason you have is not due to any epistemic with to the proposition that your is seems little to the practical and the cases in the way by the If the that doesn't in the way of p being a reason you have for for any then the that doesn't in the way of p being a reason you have for A, for any This other of the fact that, when we that p in the course of about what to we don't then p off from our about what to When we p, we can use p. But, noted that, when you know that p, then the that doesn't in the way of p being a reason you have for in with the a general not those by and more in a by Hawthorne and Stanley If you know that p, then the that doesn't in the way of p being a reason you have for or a problem for intellectualism if there are of for the that is the but are such that the that in the way of p being a reason one has but not the Consider again the airport Smith and Mary and John are with to the that the plane stops in According to the Smith and Mary and John all know that the plane stops in the that the plane doesn't stop in doesn't in the way of it being a reason they have say, In case, at For Mary and John, there is. and the assumption that Mary and John have knowledge, Mary and John have an reason not to checking with the a of the case is so that they should check with the given all that is at So, the had better not Mary and reason to just go and to Mary and John in just and How might the that the plane stops in is a reason that Mary and John have to the that, even if they have a very good reason to in their reason is by some other reason they The A proposition about the of error with the of the relevant or to use the a proposition to the that checking further A general intellectualist then, for is to make a first, having to do with of error can with about what is in fact the case and second, when the stakes are about of error can out about what is in fact the This is For this would seem to the sort of the one the plane stops the other it might And if it doesn't it the are I'd better check further to it stops in it This is not what we do when we we we do when we is the at and which is more the one the other Which is more the good or the that both that we don't facts the that those facts don't if we were facts would the one the plane is to the other it might not Which is more the fact that it is, or the that it In the intellectualist what seems to be a about having When you have a reason to or about when you have a reason to to that reason for in whether to This is not to say that, you have a reason to you should But it is to say that, when you have that you to it into with other you have without the relative of those In this you have are might not have as that it will that you will have to for the If you do then when whether to your you might have to the that it will how long you think have to for the if you have both as then you can use both in your without their to and have to So, to if I don't the Because this off the intellectualist there is us from on the of that if knowledge is with a of error, then knowledge can come and go with in the practical If Hawthorne's is false, so is
ARE CONCLUSIVE PROOFS IRRELEVANT TO RELIGION? FOR CENTURIES the proofs for God's existence have been debated and their role in religious belieÂŁ-systems assessed. There have been those who claim that the proofs are conclusive, those who claim that they are invalid , and those who claim that they are valid but inconclusive . There have been disputes, furthermore, as to whether the logical base for religious belieÂŁ systems should be sought in proofs and evidence rather than in "self-authenticating" religious experiences and acceptance oÂŁ religious authority. But no one, until recently, ever contended that even if the proofs were conclusive it would be irrelevant to religious believers. People have thought that religion must be undergirded by proof, aan be undergirded by proof, and need not be undergirded by proof, but not that proof would be irrelevant. Now oÂŁ course there are many senses in which a proof could be relevant to religious believers. The Vatican Council affirmed that iÂŁ people denied that God could be known with certainty by the natural light of human reason they would be anathema. Thus it could have made quite serious practical differences to a believer whether he accepted the proofs or not. As philosophers we are not concerned with this sort of practical difference but with philosophical ones, and the question to be explored is: Is there something philosophically at stake for believers in this question oÂŁ the proofs for the existence oÂŁ God? I want to contend that Steven M. Cahn is utterly wrongheaded in his claim that religious believers have no real interest in philosophical proofs for the existence of God.1 I am assuming that this 1 Steven M. Cahn, " The Irrelevance to Religion of Philosophic Proofs for the Existence of God," The American Philosophical Quarterly (April, 1969), pp. 170-72. Further citations will be given by page number in the text. Cahn has 727 7~8 FRANK B. DILLEY is not a statistical claim to be settled by polls but rather a philosophical claim. Cahn makes no effort to produce questionnaire results from a proper sample of believers nor shall I. To examine this question, in the context of Cahn's contention , it is fortunately not necessary to resolve the question of the validity of the proofs. In an effort to dismiss them once for all, Cahn is willing to assume that the proofs are valid, for the sake of the argument. " Suppose we assume, contrary to what most philosophers, I among them, believe, that all of these proofs are valid. Let us grant the necessary existence (whatever that might mean) of the most perfect conceivable Being, a Being who is ali-good and is the designer and creator of the universe. What implications can be drawn from this fact which would be of relevance to human life? In other words, what difference would it make in men's lives if God existed?" (p. 170) In support of his surprising thesis that religious believers are right in ignoring the proofs, he gives two chief arguments, that religious believers make their decisions as to what beliefs to hold and what practices to follow on the basis of "self-validating " personal experiences which render the proofs unnecessary , and that the success of the proofs would not enable a newly converted unbeliever to know what beliefs and practices to choose. He therefore contends that the proofs are relevant for neither the believer nor the unbeliever. In examining his contention about the relevancy of proofs I propose to look at what religious belief systems say about this problem, an approach Cahn does not seem to care to use. In this connection it should be noted that his sources are curious, for he cites not one person who would be taken by anyone to be a normal religious believer. He cites Antony Flew, Wallace Matson, C. B. Martin, and Mordecai Kaplan, but not John reprinted this essay in his Philosophy of Religion (Harper & Row, 1970), and it can also be found in Philosophy in the Age of Crisis, ed. Eleanor Kuykendall (Harper & Row, 1970) and God, Man, and Rdigion: Readings in the Philosophy of Rdigion, ed. by Keith Yandell (McGraw-Hill, 1973). ARE CONCLUSIVE PROOFS IRRELEVANT...