Hilary Putnam first published the consistencyobjection against Ludwig Wittgenstein’s account of mathematics in 1979. In 1983, Putnam and Benacerraf raised this objection against all conventionalist accounts of mathematics. I discuss the 1979 version and the scenario argument, which supports the key premise of the objection. The wide applicability of this objection is not apparent; I thus raise it against an imaginary axiomatic theory T similar to Peano arithmetic in all relevant aspects. I argue that (...) a conventionalist can explain the consistency of T and suggest that an analogous explanation can be provided for the consistency of Peano arithmetic. (shrink)
This paper is a critical analysis of Putnam’s “consistencyobjection,” an objection made against a particular reading of Wittgenstein’s philosophy of mathematics (“up-to-us-ism”). I show that Putnam’s objection presupposes a rather unlikely version of Wittgenstein’s “up-to-us-ism” and is unable to undermine a more likely anti-Platonist version. I also show that a companion argument, (the “something more” argument) is unable to overturn this more sophisticated anti-Platonist version of Wittgenstein’s up-to-us-ism. Along the way I try to clarify Wittgenstein’s (...) anti-Plalonist account of mathematics, so that others do not repeat Putnam’s mistake. (shrink)
This paper has two main purposes: first to compare Wittgenstein's views to the more traditional views in the philosophy of mathematics; second, to provide a general outline for a Wittgensteinian reply to two objections against Wittgenstein's account of mathematics: the objectivity objection and the consistency objections, respectively. Two fundamental thesmes of Wittgenstein's account of mathematics title the first two sections: mathematical propositions are rules and not descritpions and mathematics is employed within a form of life. Under each heading, (...) I examine Wittgenstein's rejection of alternative views. My aim is to make clear the differences and to suggest some similarities. As will become clear, Wittgenstein often rejects opposing views for the same or similar reasons. This comparison will provide the necessary background for better understanding Wittgenstein's philosophy of mathematics, for appreciating its many unappreciated advantages and, finally, for defending a conventionalist account of mathematics. (shrink)
I trace the development of arguments for the consistency of non-Euclidean geometries and for the independence of the parallel postulate, showing how the arguments become more rigorous as a formal conception of geometry is introduced. I analyze the kinds of arguments offered by Jules Hoüel in 1860-1870 for the unprovability of the parallel postulate and for the existence of non-Euclidean geometries, especially his reaction to the publication of Beltrami’s seminal papers, showing that Beltrami was much more concerned with the (...) existence of non-Euclidean objects than he was with the formal consistency of non-Euclidean geometries. The final step towards rigorous consistency proofs is taken in the 1880s by Henri Poincaré. It is the formal conception of geometry, stripping the geometric primitive terms of their usual meanings, that allows the introduction of a modern fully rigorous consistency proof. (shrink)
One of the earliest discussions of the so-called 'bad company' objection to Neo-Fregeanism, I show that the consistency of an arbitrary second-order 'contextual definition' (nowadays known as an 'abstraction principle' is recursively undecidable. I go on to suggest that an acceptable such principle should satisfy a condition nowadays known as 'stablity'.
Consequentialism, many philosophers have claimed, asks too much of us to be a plausible ethical theory. Indeed, the theory's severe demandingness is often claimed to be its chief flaw. My thesis is that as we come to better understand this objection, we see that, even if it signals or tracks the existence of a real problem for Consequentialism, it cannot itself be a fundamental problem with the view. The objection cannot itself provide good reason to break with Consequentialism, (...) because it must presuppose prior and independent breaks with the view. The way the objection measures the demandingness of an ethical theory reflects rather than justifies being in the grip of key anti-Consequentialist conclusions. We should reject Consequentialism independently of the Objection or not at all. Thus, we can reduce by one the list of worrisome fundamental complaints against Consequentialism. (shrink)
In this paper I consider Saul Kripke’s famous Humphrey objection to David Lewis’s views on de re modality and argue that responses to this objection currently on the market fail to mitigate its force in any significant way.
Rationality (or something similar) is usually given as the relevant difference between all humans and animals; the reason humans do but animals do not deserve moral consideration. But according to the Argument from Marginal Cases not all humans are rational, yet if such (marginal) humans are morally considerable despite lacking rationality it would be arbitrary to deny animals with similar capacities a similar level of moral consideration. The slippery slope objection has it that although marginal humans are not strictly (...) speaking morally considerable, we should give them moral consideration because if we do not we will slide down a slippery slope where we end up by not giving normal humans due consideration. I argue that this objection fails to show that marginal humans have the kind of direct moral status proponents of the slippery slope argument have in mind. (shrink)
Many philosophers have claimed that we might do well to adopt a hybrid theory of well-being: a theory that incorporates both an objective-value constraint and a pro-attitude constraint. Hybrid theories are attractive for two main reasons. First, unlike desire theories of well-being, hybrid theories need not worry about the problem of defective desires. This is so because, unlike desire theories, hybrid theories place an objective-value constraint on well-being. Second, unlike objectivist theories of well-being, hybrid theories need not worry about being (...) overly alienating. This is so because, unlike objectivist theories, hybrid theories place a pro-attitude constraint on well-being. However, from the point of view of objectivists, hybrid theories are not objectivist enough, and this can be seen clearly in missing-desires cases. For instance, hybrid theories entail that, if someone lacks the desire for health, then health is not a component of her well-being. This, objectivists say, is implausible. It is obvious, objectivists say, that someone’s life goes better for herself inasmuch as she is healthy, and hence that health is a component of her welfare. This paper focuses on the missing-desires objection (as leveled by objectivists) to hybrid theories of well-being. My argument is that the missing-desires objection can be answered in a way that is generally convincing and, in particular, in a way that pays a good deal of respect to objectivist intuitions about well-being. My hope, then, is that this paper will help to persuade objectivists about well-being to become hybrid theorists. (shrink)
This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for (...) Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical objection” to his view that machines can think. Logico-mathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human mathematicians presumably do. (shrink)
Machine generated contents note: Preface; 1. Introduction; 2. Three approaches to conscientious objection in health care: conscience absolutism, the incompatibility thesis, and compromise; 3. Ethical limitations on the exercise of conscience; 4. Pharmacies, health care institutions, and conscientious objection; 5. Students, residents, and conscience-based exemptions; 6. Conscience clauses: too little and too much protection; References.
G. Priest's anti-consistency argument (Priest 1979, 1984, 1987) and J. R. Lucas's anti-mechanist argument (Lucas 1961, 1968, 1970, 1984) both appeal to Gödel incompleteness. By way of refuting them, this paper defends the thesis of quartet compatibility, viz., that the logic of the mind can simultaneously be Gödel incomplete, consistent, mechanical, and recursion complete (capable of all means of recursion). A representational approach is pursued, which owes its origin to works by, among others, J. Myhill (1964), P. Benacerraf (1967), (...) J. Webb (1980, 1983) and M. Arbib (1987). It is shown that the fallacy shared by the two arguments under discussion lies in misidentifying two systems, the one for which the Gödel sentence is constructable and to be proved, and the other in which the Gödel sentence in question is indeed provable. It follows that the logic of the mind can surpass its own Gödelian limitation not by being inconsistent or non-mechanistic, but by being capable of representing stronger systems in itself; and so can a proper machine. The concepts of representational provability, representational maximality, formal system capacity, etc., are discussed. (shrink)
What should individuals do when their firmly held moral beliefs are prima facie inconsistent with their religious beliefs? In this article we outline several ways of posing such consistency challenges and offer a detailed taxonomy of the various responses available to someone facing a consistency challenge of this sort. Throughout the paper, our concerns are primarily pedagogical: how best to pose consistency challenges in the classroom, how to stimulate discussion of the various responses to them, and how (...) to relate such consistency challenges to larger issues, such as whether Scripture is, in general, a reliable guide to truth. (shrink)
Model RB is a model of random constraint satisfaction problems, which exhibits exact satisfiability phase transition and many hard instances, both experimentally and theoretically. Benchmarks based on Model RB have been successfully used by various international algorithm competitions and many research papers. In a previous work, Xu and Li defined two notions called i-constraint assignment tuple and flawed i-constraint assignment tuple to show an exponential resolution complexity of Model RB. These two notions are similar to some kind of consistency (...) in constraint satisfaction problems, but seem different from all kinds of consistency so far known in literatures. In this paper, we explicitly define this kind of consistency, called variable-centered consistency, and show an upper bound on a parameter in Model RB, such that up to this bound the typical instances of Model RB are variable-centered consistent. (shrink)
In this paper, I argue that van Fraassen’s “bad lot objection” against Inference to the Best Explanation [IBE] severely misses its mark. First, I show that the objection holds no special relevance to IBE; if the bad lot objection poses a serious problem for IBE, then it poses a serious problem for any inference form whatever. Second, I argue that, thankfully, it does not pose a serious threat to any inference form. Rather, the objection misguidedly blames (...) a form of inference for not achieving what it never set out to achieve in the first place. (shrink)
We give a simple and direct proof that super-consistency implies the cut-elimination property in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut-free calculus. As an application, we compare our work with the cut-elimination theorems in higher-order logic that involve V-complexes.
The Many Gods Objection (MGO) is widely viewed as a decisive criticism of Pascal’s Wager. By introducing a plurality of hypotheses with infinite expected utility into the decision matrix, the wagerer is left without adequate grounds to decide between them. However, some have attempted to rebut this objection by employing various criteria drawn from the theological tradition. Unfortunately, such defenses do little good for an argument that is supposed to be an apologetic aimed at atheists and agnostics. The (...) purpose of this paper is to offer a defensive strategy of a different sort, one more suited to the Wager’s apologetic aim and status as a decision under ignorance. Instead of turning to criteria independent of the Wager, it will be shown that there are characteristics already built into its decision theoretic structure that can be used to block many categories of theological hypotheses including MGO’s more outrageous “cooked-up” hypotheses and “philosophers’ fictions”. (shrink)
Defenders of medical professionals’ rights to conscientious objection (CO) regarding emergency contraception (EC) draw an analogy to CO in the military. Such professionals object to EC since it has the possibility of harming zygotic life, yet if we accept this analogy and utilize jurisprudence to frame the associated public policy, those who refuse to dispense EC would not have their objection honored. Legal precedent holds that one must consistently object to all forms of the relevant activity. In the (...) case at hand, then, I argue that these professionals must also oppose morally innocuous practices that may prevent pregnancy after fertilization. These results reveal that such objectors cannot offer a plausible and consistent objection to harming zygotic life. Additionally, there are good reasons to reject the analogy itself. In either case, these findings call into question the case supporting refusals of EC based on scruples. (shrink)
In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and 1 1-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and (...) T prove the existence of infinitely many non-logical objects (T deriving,moreover, the nonexistence of the value-range concept). Some implications concerning the interpretation of Frege's proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Finally, I explore the relation of T toCantor's theorem which is somewhat surprising. (shrink)
In this paper I refute an apparently obvious objection to Frankfurt-type counterexamples to the Principle of Alternate Possibilities according to which if in the counterfactual scenario the agent does not act, then the agent could have avoided acting in the actual scenario. And because what happens in the counterfactual scenario cannot count as the relevant agent’s actions given the sort of external control that agent is under, then we can ground responsibility on that agent having been able to avoid (...) acting. I illustrate how this objection to Frankfurt’s famous counterexample is motivated by Frankfurt’s own ‘guidance’ view of agency. My argument consists in showing that even if we concede that the agent does not act in the counterfactual scenario, that does not show that the agent could have avoided acting in the actual scenario. This depends on the crucial distinction between ‘not φ-ing’ and ‘avoiding φ-ing’. (shrink)
According to luck egalitarianism, inequalities are justified if and only if they arise from choices for which it is reasonable to hold agents responsible. This position has been criticised for its purported harshness in responding to the plight of individuals who, through their own choices, end up destitute. This paper aims to assess the Harshness Objection. I put forward a version of the objection that has been qualified to take into account some of the more subtle elements of (...) the luck egalitarian approach. Revising the objection in this way suggests that the Harshness Objection has been overstated by its proponents: because luck egalitarians are sensitive to the influence of unequal brute luck on individuals’ choices, it is unlikely that there will be any real world cases in which the luck egalitarian would not have to provide at least partial compensation. However, the Harshness Objection still poses problems for the luck egalitarian. First, it is not clear that partial compensation will be sufficient to avoid catastrophic outcomes. Second, the Harshness Objection raises a theoretical problem in that a consistent luck egalitarian will have to regard it as unjust if any assistance is provided to the victim of pure option luck, even if such assistance could be provided at no cost. I consider three strategies the luck egalitarian could pursue to accommodate these concerns and conclude that none of these strategies can be maintained without either violating basic luck egalitarian principles or infringing upon individual liberty. (shrink)
This paper continues a debate among philosophers concerning the implications of situationist experiments in social psychology for the theory of virtue. In a previous paper (2002), I argued among other things that the sort of character trait problematized by Hartshorne and May's (1928) famous study of honesty is not the right sort to trouble the theory of virtue. Webber (2006) criticizes my argument, alleging that it founders on an ambiguity in "cross-situational consistency" and that Milgram's (1974) obedience experiment is (...) immune to the objections I levelled against Hartshorne and May. Here I respond to his criticisms. The most important error in Webber's argument is that it overlooks a distinction between "one time performance" experiments and "iterated trial" experiments. I explain why the former cannot begin to trouble the theory of virtue. CiteULike Connotea Del.icio.us What's this? (shrink)
The possibility of time travel, as permitted in General Relativity, is responsible for constraining physical fields beyond what laws of nature would otherwise require. In the special case where time travel is limited to a single object returning to the past and interacting with itself, consistency constraints can be avoided if the dynamics is continuous and the object's state space satisfies a certain topological requirement: that all null-homotopic mappings from the state-space to itself have some fixed point. Where (...) class='Hi'>consistency constraints do exist, no new physics is needed to enforce them. One needs only to accept certain global topological constraints as laws, something that is reasonable in any case. (shrink)
John Doris has recently argued that since we do not possess character traits as traditionally conceived, virtue ethics is rooted in a false empirical presupposition. Gopal Sreenivasan has claimed, in a paper in Mind, that Doris has not provided suitable evidence for his empirical claim. But the experiment Sreenivasan focuses on is not one that Doris employs, and neither is it relevantly similar in structure. The confusion arises because both authors use the phrase ‘cross-situational consistency’ to describe the aspect (...) of character traits that they are concerned with, but neither defines this phrase, and it is ambiguous: Doris uses it in one sense, Sreenivasan in another. Partly for this reason, the objections Sreenivasan raises fail to block the argument Doris provides. In particular, the most reliable data Doris employs, Milgram’s famous study of authority, is entirely immune to Sreenivasan’s objections. Sreenivasan has not shown, therefore, that Doris provides unsuitable evidence for his claim. (shrink)
The possibility of time travel, as permitted in General Relativity, is responsible for constraining physical fields beyond what the laws normally require. In the special case where time travel is limited to a single object returning to the past and interacting with itself, consistency constraints can be avoided if the dynamics is continuous and the object’s state space satisfies a certain topological requirement: that all null-homotopic mappings from the state-space to itself have some fixed point. Where consistency constraints (...) do exist, no new physics is needed to enforce them. All one needs for their accommodation is to grant a kind of law-like status to some kinds of global boundary conditions. (shrink)
Robert Talisse objects that Deweyan democrats, or those who endorse John Dewey’s philosophy of democracy, cannot consistently hold that (i) “democracy is a way of life” and (ii) democracy as a way of life is compatible with pluralism, at least as contemporary political theorists define that term. What Talisse refers to as his “pluralist objection” states that Deweyan democracy resembles a thick theory of democracy, that is, a theory establishing a set of prior restraints on the values that can (...) count as legitimate within a democratic community. In this paper, it is argued that his pluralist objection succumbs to some combination of four charges. The first two sections of the paper are devoted to presentations of Talisse’s two formulations of his pluralist objection, as they appear in his essay “Can Democracy be a Way of Life?” and his book A Pragmatist Philosophy of Democracy , respectively. The four charges against the pluralist objection receive attention in the second section. In the third section, Dewey’s pluralist procedure is articulated and illustrated using a recent Canadian public policy debate, followed by some concluding remarks on the acceptability of relying on contemporary political examples of Deweyan democracy in action. (shrink)
One objection that has been consistently raised for theorists who are committed to the idea that we have a positive duty to aid the global poor is the overdemandingness objection. This article is a critical discussion of this objection. First, the objection is laid out in some detail. A number of influential attempts to meet the overdemandingness objection are then discussed, and it is argued that they all fail in their intended purpose. The conclusion of (...) the article is not that the overdemandingness objection cannot be met. Rather, the conclusion is that the overdemandingness objection constitutes a serious challenge to anyone who accepts the objection and goes beyond the standard libertarian doctrine and commits herself to the existence of positive duties to aid the global poor. (shrink)
This note employs the recently established consistency theorem for infinite regresses of probabilistic justification (Herzberg in Stud Log 94(3):331–345, 2010) to address some of the better-known objections to epistemological infinitism. In addition, another proof for that consistency theorem is given; the new derivation no longer employs nonstandard analysis, but utilises the Daniell–Kolmogorov theorem.
For well over a hundred years, commentators have examined the importance of the famous ‘neglected alternative’ (NA) objection to transcendental idealism. By contrast, very little attention has been paid to what the NA objection means for a later philosophical system of the 19th century that was highly indebted to Kant, namely, that of Arthur Schopenhauer. I seek to redress this lacuna in Schopenhauer scholarship and argue first that Schopenhauer acknowledged NA ( avant la lettre ) and took it (...) seriously. Second, I evaluate the arguments he gave against NA and in favor of the exclusive subjectivity of space and time, and thus for the thesis that the thing in itself is aspatiotemporal. Finally, I consider the threat posed by NA for Schopenhauer's thought in general. This investigation ultimately yields a clearer understanding of the basis upon which Schopenhauer founded his metaphysics, and how he attempted to provide a more self-consistent version of transcendental idealism. These topics have not been sufficiently appreciated by commentators to date. (shrink)
As virtue ethics has developed into maturity, it has also met with a number of objections. This essay focuses on the self-centeredness objection: since virtue ethics recommends that we be concerned with our own virtues or virtuous characters, it is self-centered. In response, I first argue that, for Zhu Xi’s neo-Confucianism, the character that a virtuous person is concerned with consists largely in precisely those virtues that incline him or her to be concerned with the good of others. While (...) such an answer is also available to the Aristotelian virtue ethics, I argue that Zhu Xi’s neo-Confucianism can better respond to the objection on two deeper levels: (1) a virtuous person is not only concerned with others’ external well-being but also their virtuous characters, and (2) a virtuous person’s concern with others’ wellbeing, both internal and external, is neither self-indulgent nor self-effacing. (shrink)
In his book Moralna spoznaja Baccarini argues that, with respect to the individual reasoning about morality, the method of reflective equilibrium is the appropriate method of moral reasoning. The starting point of my argument is Baccarini’s refutation of Hare’s view. As I see it, one of Baccarini’s central arguments against Hare consists in claiming that Hare’s approach to the amoralist objection weakens the deductive model of moral reasoning. I argue that the amoralist objection also posses a threat to (...) the method of reflective equilibrium. At the end of the paper, I consider another view of moral reasoning which, in my view, is better suited to deal with the amoralist objection. (shrink)
On the one hand, first-order theories are able to assert the existence of objects. For instance, ZF set theory asserts the existence of objects called the power set, while Peano Arithmetic asserts the existence of zero. On the other hand, a first-order theory may or not be consistent: it is if and only if no contradiction is a theorem. Let us ask, What is the connection between consistency and existence?
In a series of closely connected papers, Rosenthal has defended what has come to be known as “the higher-order thought theory of state-consciousness.” According to this theory, a mental state which one instantiates is conscious if and only if one is conscious of being in it in some relevant way, and one’s being conscious of being in the state which is conscious consists in one’s having a contemporaneous thought to the effect that one is in that state. The main aim (...) of this paper is to disarm a Searle-style objection to Rosenthal’s account of state-consciousness, one that takes mentality, in particular intentionality, to presuppose state-consciousness. It is argued that the Searlean attempt to convict Rosenthal’s hypothesis of circularity fails, because the postulation of what Searle called “subjective ontology,” as well as the requirement that there be an uncancelable connection between mode of representation and state-consciousness, is unreasonable. While defending Rosenthal against Searle, this paper also aims to develop a fresh objection to the higher-order thought conception of state-consciousness. (shrink)
The main aim is to extend the range of logics which solve the set-theoretic paradoxes, over and above what was achieved by earlier work in the area. In doing this, the paper also provides a link between metacomplete logics and those that solve the paradoxes, by finally establishing that all M1-metacomplete logics can be used as a basis for naive set theory. In doing so, we manage to reach logics that are very close in their axiomatization to that of the (...) logic R of relevant implication. A further aim is the use of metavaluations in a new context, expanding the range of application of this novel technique, already used in the context of negation and arithmetic, thus providing an alternative to traditional model theoretic approaches. (shrink)
Branching theories are popular frameworks for modeling objective indeterminism in the form of a future of open possibilities. In such theories, the notion of a history plays a crucial role: it is both a basic ingredient in the axiomatic definition of the framework, and it is used as a parameter of truth in semantics for languages with a future tense. Furthermore, histories—complete possible courses of events—ground the notion of modal consistency: a set of events is modally consistent iff there (...) is a history containing that set. We will explain these roles of histories and highlight some critical aspects having to do with the fact that histories are global and, in a relevant sense, “big” objects. The notion of modal consistency, on the other hand, has both local and global aspects. We ask in how far a local notion of modal consistency can serve as an alternative to the common uses of histories, and work out two recent approaches to alternatives to histories. Combining these approaches, we develop a novel semantics for branching time. (shrink)
Legal positivism’s multi-faceted insistence on the separability of law and morality includes an insistence on the thoroughly conventional status of legal norms as legal norms. Yet the positivist affirmation of the conventionality of law may initially seem at odds with the mind-independence of the existence and contents and implications of legal norms. Mind-independence, a central aspect of legal objectivity, has been seen by some theorists as incompatible with the mind-dependence of conventions. Such a perception of incompatibility has led some anti-positivist (...) theorists to reject the notion of law’s conventionality, and has led some positivist theorists to query law’s mind-independence. What will be contended here is that both camps are mistaken. (shrink)
“Evidence” in the form of data collected and analysis thereof is fundamental to medicine, health and science. In this paper, we discuss the “evidence-based” aspect of evidence-based medicine in terms of statistical inference, acknowledging that this latter field of statistical inference often also goes by various near-synonymous names—such as inductive inference (amongst philosophers), econometrics (amongst economists), machine learning (amongst computer scientists) and, in more recent times, data mining (in some circles). Three central issues to this discussion of “evidence-based” are (i) (...) whether or not the statistical analysis can and/or should be objective and/or whether or not (subjective) prior knowledge can and/or should be incorporated, (ii) whether or not the analysis should be invariant to the framing of the problem (e.g. does it matter whether we analyse the ratio of proportions of morbidity to non-morbidity rather than simply the proportion of morbidity?), and (iii) whether or not, as we get more and more data, our analysis should be able to converge arbitrarily closely to the process which is generating our observed data. For many problems of data analysis, it would appear that desiderata (ii) and (iii) above require us to invoke at least some form of subjective (Bayesian) prior knowledge. This sits uncomfortably with the understandable but perhaps impossible desire of many medical publications that at least all the statistical hypothesis testing has to be classical non-Bayesian—i.e. it is not permitted to use any (subjective) prior knowledge. (shrink)
The first premise of the Kalam cosmological argument has come under fire in the last few years. The premise states that the universe had a beginning, and one of two prominent arguments for it turns on the claim that an actual infinite collection of entities cannot exist. After stating the Kalam cosmological argument and the two approaches to defending its first premise, I respond to two objections against the notion that an actual infinite collection is impossible: a Platonistic objection (...) from abstract objects and a set-theoretic objection from an ambiguity in the definition of ‘=’ and ‘. (shrink)
In the first part of this paper I will characterize the specific nature of rational intuition. It will be claimed that rational intuition is an evidential state with modal content that has an a priori source. This claim will be defended against several objections. The second part of the paper deals with the so-called explanationist objection against rational intuition as a justifying source. According to the best reading of this objection, intuition cannot justify any judgment since there is (...) no metaphysical explanation of its reliability. It will be argued that in the case of intuition the very demand of such an explanation is based on a category mistake. (shrink)
Pascal's Wager is finding ever more defenders who aim to undermine the old Many Gods Objection. It is my thesis that they are mistaken. After describing the Wager and the objection, I report on Jeff Jordan's repeated attempt to limit legitimate religious hypotheses to those that are traditional. In separate sections I criticize Jordan, first coming from epistemology and second from anthropology. Then I describe George Schlesinger's repeated appeal to the ‘simplest’ religious hypothesis, and argue that it fails (...) for similar reasons. Finally, I summarize and reject miscellaneous defences of Pascal by Robert Anderson, Bradley Armour-Garb, James Franklin, Joshua Golding, and Nicholas Rescher. (shrink)
Utilitarians are attracted to the idea that an act is morally right iff it leads to the best outcome. But critics have pointed out that in many cases we cannot determine which of our alternatives in fact would lead to the best outcome. So we can’t use the classic principle to determine what we should do. It’s not “practical”; it’s not “action-guiding”. Some take this to be a serious objection to utilitarianism, since they think a moral theory ought to (...) be practical and action-guiding. In response, some utilitarians propose to modify utilitarianism by replacing talk of actual utility with talk of expected utility. Others propose to leave the original utilitarian principle in place, but to combine it with a decision procedure involving expected utility. What all these philosophers have in common is this: they move toward expected utility in order to defend utilitarianism against the impracticality objection. My aim in this paper is to cast doubt on this way of replying to the objection. My central claim is that if utilitarians are worried about the impracticality objection, they should not turn to expected utility utilitarianism. That theory does not provide the basis for a cogent reply to the objection. (shrink)
In this paper, we show that presentism?the view that the way things are is the way things presently are?is not undermined by the objection from being-supervenience. This objection claims, roughly, that presentism has trouble accounting for the truth-value of past-tense claims. Our demonstration amounts to the articulation and defence of a novel version of presentism. This is brute past presentism, according to which the truth-value of past-tense claims is determined by the past understood as a fundamental aspect of (...) reality different from things and how things are. (shrink)
This article argues that practitioners have a professional ethical obligation to dispense emergency contraception, even given conscientious objection to this treatment. This recent controversy affects all medical professionals, including physicians as well as pharmacists. This article begins by analyzing the option of referring the patient to another willing provider. Objecting professionals may conscientiously refuse because they consider emergency contraception to be equivalent to abortion or because they believe contraception itself is immoral. This article critically evaluates these reasons and concludes (...) that they do not successfully support conscientious objection in this context. Contrary to the views of other thinkers, it is not possible to easily strike a respectful balance between the interests of objecting providers and patients in this case. As medical professionals, providers have an ethical duty to inform women of this option and provide emergency contraception when this treatment is requested. (shrink)
Managers often encounter situations that require them to make decisions with ethical implications that affect the organization as well as the managers themselves. The issue we address in this study concerns whether the ethical consistency of managerial decisions is situation dependent. That is, are the decisions managers make ethically consistent when they are faced with different ethical situations? We hypothesize that managerial decisions will vary depending on the type of ethical situation they encounter. We also hypothesize that gender plays (...) a role in determining the ethical consistency of managerial decisions. Results of statistical analyses support our hypotheses. (shrink)
What is the relation between a clay statue andthe lump of clay from which it is made? According to the defender of the standardaccount, the statue and the lump are distinct,enduring objects that share the same spatiallocation whenever they both exist. Suchobjects also seem to share the samemicrophysical structure whenever they bothexist. This leads to the standard objection tothe standard account: if the statue and thelump of clay have the same microphysicalstructure whenever they both exist, how canthey differ in (...) their de re temporalproperties, de re modal properties and soon? In this paper I develop amereological answer to this question – thestatue and the lump differ with respect totheir parts and this explains theirdifference with respect to de re temporalproperties, de re modal properties andthe like. (shrink)
When it is suggested that the fine-tuning of the universe for life provides evidence for a cosmic designer, the multiple-universe hypothesis is often presented as an alternative. Some philosophers object that the multiple-universe hypothesis fails to explain why ’this’ universe is fine-tuned for life. We suggest the "this universe" objection is no better than the "this planet" objection. We also fault proponents of the "this universe" objection for presupposing that we could not have existed in any other (...) universe and that the values of the free parameters of the universe could have been different. Lastly, we reflect on why fine-tuning for life needs explaining. (shrink)
According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, (...) within the constraints of a non-reductive physicalism and a holism concerning the concepts of truth, reference and meaning, conceding Field’s physicalistic inadequacy conclusion while rejecting his conceptual deficiency conclusion is a promising reply to the incompleteness objection. (shrink)
A common objection raised against naturalism is that anaturalized epistemology cannot account for the essential normative character of epistemology. Following an analysis of different ways in which this charge could be understood, it will be argued that either epistemology is not normative in the relevant sense, or if it is, then in a way which a naturalized epistemology can account for with an instrumental and hypothetical model of normativity. Naturalism is here captured by the two doctrines of empiricism and (...) gradualism. Epistemology is a descriptive discipline about what knowledge is and under what conditions a knowledge-claim is justified. However, we can choose to adopt a standard of justification and by doing so be evaluated by it. In this sense our epistemic practices have a normative character, but this is a form of normativity a naturalized epistemology can make room for. The normativity objection thus fails. However, in the course of this discussion, as yet another attempt to clarify the normativity objection, such a naturalistic model will be contrasted with Donald Davidson's theory of interpretation. Even though this comparison will not improve upon the negative verdict upon the original objection, it will be argued that naturalism cannot accept Davidson's theory since it contains at least one constitutive principle – the principle of charity – whose epistemic status is incompatible with the naturalistic doctrine of gradualism. So, if this principle has this role, then epistemology cannot be naturalized. (shrink)
The paper presents a proof of the consistency of Peano Arithmetic (PA) that does not lie in deducing its consistency as a theorem in an axiomatic system. PA’s consistency cannot be proved in PA, and to deduce its consistency in some stronger system PA+ is self-defeating, since the stronger system may itself be inconsistent. Instead, a semantic proof is constructed which demonstrates consistency not relative to the consistency of some other system but in an (...) absolute sense. (shrink)
The Molinist doctrine that God has middle knowledge requires that God knows the truth-values of counterfactuals of freedom, propositions about what free agents would do in hypothetical circumstances. A well-known objection to middle knowledge, the grounding objection, contends that counterfactuals of freedom have no truth-value because there is no fact to the matter as to what an agent with libertarian freedom would do in counterfactual circumstances. Molinists, however, have offered responses to the grounding objection that they believe (...) are adequate for maintaining the coherence of middle knowledge. I argue that these responses to the grounding objection are not adequate, and that what I call the ‘generic grounding objection’ still poses a serious challenge to middle knowledge. (shrink)
Medieval theologians discussed the logical structure of reduplicative propositions in the midst of their discussions of the Incarnation and the Trinity. Aquinas has the usual medieval analyzes of reduplicative propositions: the specificative and the strictly reduplicative. But neither analysis resolves successfully the problems of the consistency of the statements about God while avoiding making the Trinity or the Incarnation a merely accidental feature of Him. However, Scotus introduces another analysis: abstractive. I shall conclude that Scotus’s view of reduplication, one, (...) if not invented by him, as least stressed and developed by him, offers a better solution of the consistency of the Incarnation and the Trinity than that of Aquinas. (shrink)
Gottlob Frege famously rejects the methodology for consistency and independence proofs offered by David Hilbert in the latter's Foundations of Geometry. The present essay defends against recent criticism the view that this rejection turns on Frege's understanding of logical entailment, on which the entailment relation is sensitive to the contents of non-logical terminology. The goals are (a) to clarify further Frege's understanding of logic and of the role of conceptual analysis in logical investigation, and (b) to point out the (...) extent to which his understanding of logic differs importantly from that of the model-theoretic tradition that grows out of Hilbert's work. (shrink)
It is often thought that Blackburn and Boghossian have provided an effective reply to the finiteness objection to dispositional theories of meaning, presented by Kripke's Wittgenstein. In this paper I distinguish two possible readings of the sceptical demand for meaning-constitutive facts. The demand can be formulated in one of two ways: an A-question or a B-question. Any theory of meaning will give one of these explanatory priority over the other. I will then argue that the standard reply only works (...) if B-questions are seen as prior, while the dominant dispositionalist theories of meaning see A-questions as prior. (shrink)
Preference utilitarianism is widely considered a significant advance on classical utilitarianism when it comes to explaining why it is wrong to kill people. This paper focuses attention on the nature of the preference utilitarian 'direct' objection to killing a person and on the related claim that a person's preferences are non-replaceable. I argue that the preference utilitarian case against killing people is overstated and overrated. My concluding remarks indicate the relevance of this discussion to deeper issues in normative moral (...) theory. (shrink)
Using an axiomatization of second-order arithmetic (essentially second-order Peano Arithmetic without the Successor Axiom), arithmetic's basic operations are defined and its fundamental laws, up to unique prime factorization, are proven. Two manners of expressing a system's consistency are presented - the "Godel" consistency, where a wff is represented by a natural number, and the "real" consistency, where a wff is represented as a second-order sequence, which is a stronger notion. It is shown that the system can prove (...) at least its Godel consistency and that closely allied systems can prove their real consistency. (shrink)
In the worlds of philosophy, linguistics, and communications theory, a view has developed which understands conscious experience as experience which is 'reflected' back upon itself through language. This indicates that the consciousness we experience is possible only because we have culturally invented language and subsequently evolved to accommodate it. This accords with the conclusions of Daniel Dennett (1991), but the 'hermeneutic objection' would go further and deny that the objective sciences themselves have escaped the hermeneutic circle. -/- The consciousness (...) we humans experience is developed only within the context of crossing the 'symbolic threshold' (Percy 1975; Deacon 1997) and one of the earliest and most important symbols we acquire is that of the self, or 'the subject of experience'. It is only when we achieve self-awareness that the world, as such, comes to exist for us as an object (which contains categories and sub-categories of objects). Any consciousness imputed to prelinguistic stages of development is based on projection and guesswork, since we can know nothing directly of it. It can be said that any experience which does not separate an inner subject from an outer world is probably a continuum of sensation in which environmental stimulus and instinctive response are experienced as a unity; it may be 'lived experience' but it is experience 'lived' non-consciously. -/- Speech requires assertion and by learning to speak we find ourselves asserting, in essence, our selves into the world. The narrative form of language allows us to develop life stories, self-knowledge, and, most important, narrative memory coincident with narrative time. All this is made possible with the intersubjective 'net' of language which allows us to know ourselves by first identifying with the viewpoint of others; and, later, such allows us to identify with other minds as we anticipate their reception our communication. These three, assertion, narrative, and intersubjectivity are the essence of what language is and are the keystones that make culture possible outside of nature. (shrink)
It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive (...) diagnoses of the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible. (shrink)
Many people believe that there is a Dutch Book argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book argument for it, because countable additivity conflicted with intuitive principles about the scope of authentic consistency constraints. These he often claimed were logical in nature, but he never attempted to relate this (...) idea to deductive logic and its own concept of consistency. This I do, showing that at one level the definitions of deductive and probabilistic consistency are identical, differing only in the nature of the constraints imposed. In the probabilistic case I believe that R.T. Cox's scale-free axioms for subjective probability are the most suitable candidates. 1 Introduction 2 Coherence and Consistency 3 The Infinite Fair Lottery 4 The Puzzle Resolved—But Replaced by Another 5 Countable Additivity, Conglomerability and Dutch Books 6 The Probability Axioms and Cox's Theorem 7 Truth and Probability 8 Conclusion: Logical Omniscience CiteULike Connotea Del.icio.us What's this? (shrink)
The author argues in this article that it is possible to have a consistent and coherent version of the doctrine of divine timelessness. Towards the objection that a timeless God cannot act it is defended that a timeless God can certainly act in the world and can love human people. In spite of the consistency and coherence of the doctrine of divine timelessness, however, the author has serious problems with the fruitfulness of this doctrine when it comes to (...) essential practices of the Christian faith, such like seeking help from God, loving God, and prayer. (shrink)
The ‘Responsibility Objection’ to Judith Thomson's famous argument for the permissibility of abortion challenges the relevance of her ‘Violinist Analogy’ to certain types of voluntary unwanted pregnancy, on the grounds that those pregnancies, even though they may be unwanted, are pregnancies for which the woman can be plausibly held responsible. This article considers the force of a number of recent objections to the Responsibility Objection, advanced by Harry Silverstein, David Boonin, and Jeff McMahan, and judges them to be (...) unpersuasive. It is concluded that, in the absence of further considerations, the Responsibility Objection carries force. (shrink)
The worst possible way to resolve this issue is to leave it up to individual choice. There is no known social good coming from the conquest of death (Bailey, 1999). - Daniel Callahan Dramatically extending the human lifespan seems increasingly possible. Many bioethicists object that life-extension will have Malthusian consequences as new Methuselahs accumulate, generation by generation. I argue for a Life-Years Response to the Malthusian Objection. If even a minority of each generation chooses life-extension, denying it to them (...) deprives them of many years of extra life, and their total extra life-years are likely to exceed the total life-years of a majority who do not want life-extension. This is a greater harm to those who want extended life than the Malthusian harms to those who refuse extended life, both because losing an extra year of life is worse than enduring a year of Malthusian conditions, and because the would-be Methuselahs have more life-years at stake. Therefore, even if life-extension seems likely to cause severe overcrowding and resource shortages, that threat is not sufficient to justify society in restricting the development or availability of life-extension. (shrink)
Relatively little attention has been paid to Socrates' argument against akrasia in Plato's "Protagoras" as an example of Socratic method. Yet seen from this perspective the argument has some rather unusual features: in particular, the presence of an impersonal interlocutor ("the many") and the absence of the crisp and explicit argumentation that is typical of Socratic elenchus. I want to suggest that these features are problematic, considerably more so than has sometimes been supposed, and to offer a reading of the (...) argument that accounts for them. My reading revolves around the connections between Socratic method, consistency and akrasia. I argue that Socrates' discussion of akrasia aims at exposing the interlocutor's inconsistency, and to this extent is typical of Socratic inquiry; but it is also untypical, insofar as Socrates' chief concern here is with the inconsistency between an interlocutor's statements and his actions (what I call "word-deed inconsistency") rather than, as more usually, inconsistency among an interlocutor's various statements ("word-word inconsistency"). I use this reading to show how the akrasia argument, despite its untypical features, is not just a variant, but in an important way a paradigm, of Socratic method. (shrink)
David Lewis has long defended an analysis of counterfactuals in terms of comparative similarity of possible worlds. The purpose of this paper is to reevaluate Lewis’s response to one of the oldest and most familiar objections to this proposal, the future similarity objection.
One of the central problems afflicting reductionism in the epistemology of testimony is the apparent fact that infants and small children are not cognitively capable of having the inductively based positive reasons required by this view. Since non-reductionism does not impose a requirement of this sort, it is thought to avoid this problem and is therefore taken to have a significant advantage over reductionism. In this paper, however, I argue that if this objection undermines reductionism, then a variant of (...) it similarly undermines non-reductionism. Thus, considerations about the cognitive capacities of infants and small children do not effectively discriminate between these two competing theories of testimonial justification. (shrink)
In this paper I examine the most common objection to strict product liability: that it is unfair to manufacturers. Critics have maintained that it is unfair because it allows manufacturers to be held liable even when they have not been negligent, and are not morally blameworthy or at fault. In response to this objection, I argue 1) that there are in fact cases in which it is at least somewhat unfair to manufacturers to impose compensation requirements upon them (...) in accordance with the strict product liability doctrine, but 2) that there is also a class of cases in which it is fair to manufacturers to hold them responsible for compensating injured product users, as strict product liability requires, even though they have not been negligent and are not morally blameworthy or at fault. My analysis of the fairness issue provides a basis for some concluding remarks about the defensibility of the strict product liability doctrine. (shrink)
Reductionism is a central issue in the philosophy of biology. One common objection to reduction is that molecular explanation requires reference to higher-level properties, which I refer to as the context objection. I respond to this objection by arguing that a well-articulated notion of a mechanism and what I term mechanism extension enables one to accommodate the context-dependence of biological processes within a reductive explanation. The existence of emergent features in the context could be raised as (...) an objection to the possibility of reduction via this strategy. I argue that this objection can be overcome by showing that there is no tenable argument for the existence of emergent properties that are not susceptible to a reductive explanation. (shrink)
Whether refusal is an act of civil disobedience meant to challenge the state politically as a form of protest, or an action which reflects a deep moral objection to the policies of the state, selective conscientious objection presents the state and its citizens with a number of difficult legal and moral challenges. Appeals to authority outside of the state, whether religious or secular, influence both citizenship and the behavior of the government itself. As Israel raises funds to defend (...) IDF officers from charges of human rights violations in the United Kingdom, it may find itself in need of a better defense against those citizens hesitant to be placed in harm's way, militarily and legally. At some point in the future it may find itself unable to field soldiers for whom service in the Occupied Territories is prohibited by inviolable secular or religious law. And for those who will continue to argue that they cannot abide service in an army of occupation, an expression sounded in 1968 by Yeshayahu Leibowitz, the moral crisis of an individual conscience rent between obligations to the state and obligations to self, will linger along with the pain of a conscience nurtured and then rejected by this democratic society. (shrink)
Scientific realists often appeal to some version of the conjunction objection to argue that scientific instrumentalism fails to do justice to the full empirical import of scientific theories. Whereas the conjunction objection provides a powerful critique of scientific instrumentalism, I will show that mathematical instrumentalism escapes the conjunction objection unscathed.
In his 'The Disorder of Things' John Dupré presents an objection to reductionism which I call the 'anti-essentialist objection': it is that reductionism requires essentialism, and essentialism is false. I unpack the objection and assess its cogency. Once the objection is clearly in view, it is likely to appeal to those who think conceptual analysis a bankrupt project. I offer on behalf of the reductionist two strategies for responding, one which seeks to rehabilitate conceptual analysis and (...) one (more concessive) which avoids commitment to any such analysis. (shrink)
After a brief flirtation with logicism around 1917, David Hilbertproposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays andWilhelm Ackermann, throughout the 1920s. The two technical pillars of the project were the development of axiomatic systems for everstronger and more comprehensive areas of mathematics, and finitisticproofs of consistency of these systems. Early advances in these areaswere made by Hilbert (and Bernays) in a series of lecture courses (...) atthe University of Göttingen between 1917 and 1923, and notably in Ackermann's dissertation of 1924. The main innovation was theinvention of the -calculus, on which Hilbert's axiom systemswere based, and the development of the -substitution methodas a basis for consistency proofs. The paper traces the developmentof the ``simultaneous development of logic and mathematics'' throughthe -notation and provides an analysis of Ackermann'sconsistency proofs for primitive recursive arithmetic and for thefirst comprehensive mathematical system, the latter using thesubstitution method. It is striking that these proofs use transfiniteinduction not dissimilar to that used in Gentzen's later consistencyproof as well as non-primitive recursive definitions, and that thesemethods were accepted as finitistic at the time. (shrink)
The last section of “Lecture at Zilsel’s” [9, §4] contains an interesting but quite condensed discussion of Gentzen’s first version of his consistency proof for P A [8], reformulating it as what has come to be called the no-counterexample interpretation. I will describe Gentzen’s result (in game-theoretic terms), fill in the details (with some corrections) of Godel's reformulation, and discuss the relation between the two proofs.
The Doctrine of Temporal Parts (sometimes abbreviated herein as 'DTP') asserts that, for each portion (including infinitely small portions) of the smallest period of time during which a material object exists, there is an object-a temporal part of the material object in question-which exists at that and at no other time. In "Things Change," Mark Heller offers an argument for DTP, and responds to a objection, the "No-Change" objection, to that doctrine.2 My goal in this paper is to (...) undermine both Heller's argument in favor of DTP and his response to that criticism. (shrink)
Eliminative materialism is the position that common?sense psychology is false and that beliefs and desires, like witches and demons, do not exist. One of the most popular criticisms of this view is that it is self?refuting or, in some sense, incoherent. Hence, it is often claimed that eliminativism is not only implausible, but necessarily false. Below, I assess the merits of this objection and find it seriously wanting. I argue that the self?refutation objection is (at best) a misleading (...) reformulation of much more mundane objections to eliminativism and that, contrary to its advocates? endorsements, it adds nothing of genuine interest to the debate over the existence of prepositional attitudes. (shrink)
A certain objection to belief in God is based on the intrinsic incoherence of the concept of Divine Being or God. In particular, it questions the major traditional characteristic, notably omniscience, and its relation to omnipotence, moral unassailability, and absence of embodiment on the part of the Divine Being. In this paper, an attempt is made to counter this objection by an appeal, not to natural theology, but rather to physicalism in its application to human beings, and by (...) extension to the possible consistency of God’s omniscience with the other divine attributes, which philosophers such as Michael Martin have found to be mutually inconsistent and therefore wanting. (shrink)
The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.
: This article draws upon the Roman Catholic distinction between "ordinary" and "extraordinary" means of medical treatment to analyze the case of "Jodie" and "Mary," the Maltese conjoined twins whose surgical separation was ordered by the English courts over the objection of their Roman Catholic parents and Cormac Murphy-O'Connor, the Roman Catholic Cardinal Archbishop of Westminster. It attempts to shed light on the use of that distinction by surrogate decision makers with respect to incompetent patients. In addition, it critically (...) analyzes various components of the distinction by comparing the reasoning used by Catholic moralists in this case with the reasoning used in other cases that raise similar issues, including women facing crisis pregnancies who prefer abortion to adoption and the Indiana "Baby Doe" case. (shrink)
From time to time, the idea that enduring things can change has been challenged. The latest challenge has come in the form of what David Lewis has called a “decisive objection”, which claims to deduce a contradiction from the idea that enduring things change with respect to their temporary intrinsics, when that idea is combined with eternalism. It is my aim in this paper to explain why I think that no argument has yet appeared that deduces a contradiction from (...) a combination of eternalism and the idea that enduring things change with respect to their temporary intrinsics, except ones that do so by committing scope fallacies. (shrink)
The theory that ``consistency implies existence'' was put forward by Hilbert on various occasions around the start of the last century, and it was strongly and explicitly emphasized in his correspondence with Frege. Since (Gödel's) completeness theorem, abstractly speaking, forms the basis of this theory, it has become common practice to assume that Hilbert took for granted the semantic completeness of second order logic. In this paper I maintain that this widely held view is untrue to the facts, and (...) that the clue to explain what Hilbert meant by linking together consistency and existence is to be found in the role played by the completeness axiom within both geometrical and arithmetical axiom systems. (shrink)
The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical inference that agree with (...) certain compelling consistency requirements. This paper reviews these consistency arguments and the surrounding controversy. It is shown that the uniqueness proofs are flawed, or rest on unreasonably strong assumptions. A more general class of inference rules, maximizing the so-called Re[acute ]nyi entropies, is exhibited which also fulfill the reasonable part of the consistency assumptions. (shrink)
This paper investigates consistency in applied moral philosophy with regard to the recent controversy over Makah whaling in the state of Washington. The first part presents both sides of the controversy. The second part examines the meaning of 'tradition' and distinguishes between 'new' and 'old' traditions. The third part explores what might constitute moral consistency for the Makah and what might constitute moral consistency for the larger community.
This book shows that civil disobedience is generally more defensible than private conscientious objection. -/- Part I explores the morality of conviction and conscience. Each of these concepts informs a distinct argument for civil disobedience. The conviction argument begins with the communicative principle of conscientiousness. According to this principle, having a conscientious moral conviction means not just acting consistently with our beliefs and judging ourselves and others by a common moral standard. It also means not seeking to evade the (...) consequences of our beliefs and being willing to communicate to them to others. The conviction argument shows that, as a constrained, communicative practice, civil disobedience has a better claim than private objection does to the protections that liberal societies give to conscientious dissent. This view reverses the standard liberal picture which sees private 'conscientious' objection as a modest act of personal belief and civil disobedience as a strategic, undemocratic act whose costs are only sometimes worth bearing. -/- The conscience argument is narrower and shows that genuinely morally responsive civil disobedience honours the best of our moral responsibilities and is protected by a duty-based moral right of conscience. -/- Part II translates the conviction argument and conscience argument into two legal defences. The first is a demands-of-conviction defence. The second is a necessity defence. Both of these defences apply more readily to civil disobedience than to private disobedience. Part II also examines lawful punishment, showing that, even when punishment is justifiable, civil disobedients have a moral right not to be punished. (shrink)
We give a consistency proof within a weak fragment of arithmetic of elementary algebra and geometry. For this purpose, we use EFA (exponential function arithmetic), and various first order theories of algebraically closed fields and real closed fields.
It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing (...) 1 1-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case. (shrink)
The business practices of multinational corporations raise many provocative moral issues and offer a touchstone for some fundamental ethical concepts. This essay identifies a wide range of problems but centers on the matter of consistency in corporate policy between foreign and domestic practices and the kind of generality of standards that is required to achieve consistency. Two considerations are singled out for illustrative discussion: wage scales and bribes. Proposals are offered for achieving consistency and generality in each (...) case, the principle of contextual generality for the first and the notion of structural universals for the second. (shrink)
This paper develops the theory that a set of rules is consistent if it is not possible that (1) the conditions of the rules in the set are all satisfied, (2) there is no exception to either one of the rules, and (3) the consequences of the rules are incompatible. To this purpose the notion of consistency is generalised to make it cover rules and is relativised to some background of constraints.This theory is formalised by means of Rule Logic, (...) in which rules are treated as constraints on the possible worlds in which they exist. Rule Logic itself is introduced by giving a model-theory for it. It is characterised by means of constraints on worlds that are possible according to Rule Logic. (shrink)
I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he concedes a contradictory (...) set of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (shrink)
The claim that nature is self-consistent has recently been contested by a number of paraconsistent logicians. In this paper I will survey the arguments which paraconsistent logicians have presented for the thesis that nature is actually inconsistent. My conclusion is that these arguments all fail.The paraconsistency programme has to date been concerned primarily with outlining the philosophical inadequacy of classical logic, and detailed discussions of issues bearing upon the philosophical adequacy of the paraconsistency position itself are not to be found (...) as yet in the literature. This inadequacy will be illustrated here with respect to the question of the self-consistency of nature. (shrink)
A paraconsistent logic is a logic which allows non-trivial inconsistent theories. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa’s approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved. da Costa’s approach has led to the family of Logics of Formal (In)consistency (LFIs). In this paper we provide non-deterministic semantics for a very large (...) family of first-order LFIs (which includes da Costa’s original system.. (shrink)
In this paper we study the consistency strength of the theory $\mathbf\mathrm{ZFC} + (\exists\kappa \text{strong limit})(\forall\mu , and we prove the consistency of this theory relative to the consistency of the existence of a supercompact cardinal and an inaccessible above it.
In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.
It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.
One common objection to fetal tissue transplantation (FTT) is that, if it were to become a standard form of treatment, it would encourage or entrench the practice of abortion. This claim is at least factually plausible, although it cannot be definitively established. However, even if true, it does not constitute a compelling ethical argument against FTT. The harm allegedly brought about by FTT, when assessed by widely accepted non-consequentialist criteria, has limited moral significance. Even if FTT would cause more (...) abortions to be performed, and abortion is taken to be a serious moral wrong, this is not sufficient in itself to make FTT wrong. (shrink)
Many philosophers, both past and present, object to materialism not from any romantic anti-scientific bent, but from sheer inability to understand the thesis. It seems utterly inconceivable to some that qualia should exist in a world which is entirely material. This paper investigates the grain objection, a much neglected argument which purports to prove that sensations could not be brain events. Three versions are examined in great detail. The plausibility of the first version is shown to depend crucially on (...) whether one holds a direct or non-direct theory of perception. Only on the latter is this version plausible. An analysis of the second "semantic" version concludes that a materialist description and explanation of the world should not be expected to transparently convey all that would be of interest or importance to human beings. The final version explicitly makes use of Grover Maxwell's non-direct perceptual theory of structural realism. Although a confusion is charged to Maxwell between phenomenal and objective properties, the critical difficulty for the grain objection is its failure to characterize "structure" from a non-percipient point of view. As the grain objection is ultimately found wanting, the real difficulty for materialism crystallizes as its irreconciliability with the mere existence of sentience, which seems to force some sort of emergence upon us. (shrink)
The semantic blindness objection to contextualism challenges the view that there is no incompatibility between (i) denials of external-world knowledge in contexts where radical-deception scenarios are salient, and (ii) affirmations of external-world knowledge in contexts where such scenarios are not salient. Contextualism allegedly attributes a gross and implausible form of semantic incompetence in the use of the concept of knowledge to people who are otherwise quite competent in its use; this blindness supposedly consists in wrongly judging that there is (...) genuine conflict between claims of type (i) and type (ii). We distinguish two broad versions of contextualism: relativistic-content contextualism and categorical-content contextualism. We argue that although the semantic blindness objection evidently is applicable to the former, it does not apply to the latter. We describe a subtle form of conflict between claims of types (i) and (ii), which we call différance-based affirmatory conflict. We argue that people confronted with radical-deception scenarios are prone to experience a form of semantic myopia (as we call it): a failure to distinguish between différance-based affirmatory conflict and outright inconsistency. Attributing such semantic myopia to people who are otherwise competent with the concept of knowledge explains the bafflement about knowledge-claims that so often arises when radical-deception scenarios are made salient. Such myopia is not some crude form of semantic blindness at all; rather, it is an understandable mistake grounded in semantic competence itself: what we call a competence-based performance error. (shrink)
Dunn and Hellman's objection to Popper and Miller's alleged disproof of inductive probability is considered and rejected. Dunn and Hellman base their objection on a decomposition of the incremental support P(h/e)-P(h) of h by e dual to that of Popper and Miller, and argue, dually to Popper and Miller, to a conclusion contrary to the latters' that all support is deductive in character. I contend that Dunn and Hellman's dualizing argument fails because the elements of their decomposition are (...) not supports of parts of h. I conclude by reinforcing a different line of criticism of Popper and Miller due to Redhead. (shrink)
The main questions considered in this paper are the consistency of a variant of a set theory with intuitionistic logic, with Brouwer's principle and the investigation of the comparative power of the Church's Thesis' variants at the set theory level.
