Most claims for the falsification of the Law of the Excluded Middle rest on confusion or can be circumvented. A few of them, however, cannot. I concentrate on two of those, cases involvin...

The question whether quantum discontinuity can or cannot provide an answer to Zeno’s Paradoxes is reopened. It is observed that what is usually understood by the term “discontinuity”, namely, Einstein’s conception of the photon as described by himself and all others, is unsuitable to the task because, essentially,it reduces to the trivial ‘discontinuity’ of objects scattered in space. By contrast, quantization of energy levels, which are not in space but can only alternate in time, provide the right sort of discontinuity (...) required. Discrete quantized orbits, corresponding to eigen-frequencies, are irreducible, and nothing is allowed to stand in-between them in satisfaction of the quantum postulate, furnishing the requisite, and so far missing, immediate nextness of a point to a certain other. In this way, Zeno’s Runner need not postpone his first step indefinitely, always waiting upon an infinity of preceding steps, before it can be taken. There is now a point that is next to a point and so a step on that point, which is the first step. It follows that, if one kind of discontinuity, Einstein’s, is incapable of offerring an answer to Zeno, while another kind can, the two are discrepant. One of them, the former, is not a kind of discontinuity properly so called at all, though evidently the consequence of one. (shrink)

The question whether quantum discontinuity can or cannot provide an answer to Zeno’s Paradoxes is reopened. It is observed that what is usually understood by the term “discontinuity”, namely, Einstein’s conception of the photon as described by himself and all others, is unsuitable to the task because, essentially,it reduces to the trivial ‘discontinuity’ of objects scattered in space. By contrast, quantization of energy levels, which are not in space but can only alternate in time, provide the right sort of discontinuity (...) required. Discrete quantized orbits, corresponding to eigen-frequencies, are irreducible, and nothing is allowed to stand in-between them in satisfaction of the quantum postulate, furnishing the requisite, and so far missing, immediate nextness of a point to a certain other. In this way, Zeno’s Runner need not postpone his first step indefinitely, always waiting upon an infinity of preceding steps, before it can be taken. There is now a point that is next to a point and so a step on that point, which is the first step. It follows that, if one kind of discontinuity, Einstein’s, is incapable of offerring an answer to Zeno, while another kind can, the two are discrepant. One of them, the former, is not a kind of discontinuity properly so called at all, though evidently the consequence of one. (shrink)

The Energy-Time Uncertainty (ETU) has always been a problem-ridden relation, its problems stemming uniquely from the perplexing question of how to understand this mysterious Δ t . On the face of it (and, indeed, far deeper than that), we always know what time it is. Few theorists were ignorant of the fact that time in quantum mechanics is exogenously defined, in no ways intrinsically related to the system. Time in quantum theory is an independent parameter, which simply means independently known (...) . In the early 1960s Aharonov (1961-64) and Bohm (1961-64) mounted a spirited attack against the ETU, which sealed its fate to the present date. By emphasising that time is always “well-defined” in quantum theory, they were led to the conclusion that no ETU should exist, a view shared by many in the 1990s, if Busch (1990) is to be believed. In a similar vein, I emphasize that (a) physical systems occupy a particular energy state at a particular instant of time, if at all; (b) even in absence of all time-measuring instruments, it is still trivially warranted that one can measure a system's energy as accurately as one pleases, and simply announce “The system's energy is exactly E NOW!”, a possibility which no quantum mechanics of any sort, or any physical theory whatsoever, can afford to tamper with or change, except circularly. One never loses one's own perception of time, when one measures the energy, a fact which no measurement conceivable can interfere with or affect. Both (a) and (b) uniquely entail that energy and time are compatible, if not indeed intimately interconnected, contrary to what the relevant uncertainty seems to affirm. In response to Aharonov's and Bohm's initial problem, I reinterpret ΔEΔt ≥ h , as directly derived from authentic quantum principles, without however having to assume a direct incompatibility between its related concepts, attributing their complementarity to conditions other than ordinarily assumed. (shrink)

The question whether quantum discontinuity can or cannot provide an answer to Zeno's Paradoxes is reopened. It is observed that what is usually understood by the term "discontinuity", namely, Einstein's conception of the photon as described by himself and all others, is unsuitable to the task because, essentially,it reduces to the trivial 'discontinuity' of objects scattered in space. By contrast, quantization of energy levels, which are not in space but can only alternate in time, provide the right sort of discontinuity (...) required. Discrete quantized orbits, corresponding to eigen-frequencies, are irreducible, and nothing is allowed to stand in-between them in satisfaction of the quantum postulate, furnishing the requisite, and so far missing, immediate nextness of a point to a certain other. In this way, Zeno's Runner need not postpone his first step indefinitely, always waiting upon an infinity of preceding steps, before it can be taken. There is now a point that is next to a point and so a step on that point, which is the first step. It follows that, if one kind of discontinuity, Einstein's, is incapable of offerring an answer to Zeno, while another kind can, the two are discrepant. One of them, the former, is not a kind of discontinuity properly so called at all, though evidently the consequence of one. (shrink)

The generalization of Complementarity has been an ambition and a challenge to many a Bohrian scholar or quantum philosopher, and to Bohr himself above all others besides. A very recent attempt by Professor Gonzalo Munevar, proposing an extension of CTY to alternative conceptual schemes, re-opens this issue and seeks to place it within the context of modern day Relativism on the grounds that conceptual schemes belonging to different cultural groups or even different biological species are neither reducible to one another, (...) nor equivalent, nor however contradictory and therefore simply "complementary." Such being the case, neither conceptual scheme can overrule its rival scheme, nor however include or assimilate it, being to all intents and purposes as valid as its rival, albeit fundamentally divergent from it. This conclusion inevitably guides the steps of knowledge along the path of Relativism and Subjectivism, a route which Prof. Munevar makes it perfectly clear that he would eagerly follow. (shrink)

The generalization of Complementarity has been an ambition and a challenge to many a Bohrian scholar or quantum philosopher, and to Bohr himself above all others besides. A very recent attempt by Professor Gonzalo Munevar, proposing an extension of CTY to alternative conceptual schemes, re-opens this issue and seeks to place it within the context of modern day Relativism on the grounds that conceptual schemes belonging to different cultural groups or even different biological species are neither reducible to one another, (...) nor equivalent, nor however contradictory and therefore simply "complementary." Such being the case, neither conceptual scheme can overrule its rival scheme, nor however include or assimilate it, being to all intents and purposes as valid as its rival, albeit fundamentally divergent from it. This conclusion inevitably guides the steps of knowledge along the path of Relativism and Subjectivism, a route which Prof. Munevar makes it perfectly clear that he would eagerly follow. (shrink)

The two Heisenberg Uncertainties (UR) entail an incompatibility between the two pairs of conjugated variables E, t and p, q. But incompatibility comes in two kinds, exclusive of one another. There is incompatibility defineable as: (p → − q) & (q→ − p) or defineable as [(p →− q) & (q →− p)] ↔ r. The former kind is unconditional, the latter conditional. The former, in accordance, is fact independent, and thus a matter of logic, the latter fact dependent, and (...) thus a matter of fact. The two types are therefore diametrically opposed. In spite of this, however, the existing derivations of the Uncertainties are shown here to entail both types of incompatibility simultaneously. Δ E Δ t ≥ h is known to derive from the quantum relation E = hν plus the Fourier relation Δ ν Δ t ≥ 1. And the Fourier relation assigns a logical incompatibility between Δ ν = 0, Δ t = 0. (Defining a repetitive phenomenon at an instant t → 0 is a self contradictory notion.) An incompatibility, therefore, which is fact independent and unconditional. How can one reconcile this with the fact that Δ EΔ t exists if and only if h > 0, which latter supposition is a factual truth, entailing that a Δ E = 0, Δ t = 0 incompatibility should itself be fact dependent? Are we to say that E and t are unconditionally incompatible (via Δ ν Δ t ≥ 1) on condition that E = hν is at all true? Hence, as presently standing, the UR express a self-contradicting type of incompatibility. To circumvent this undesirable result, I reinterpret E = hν as relating the energy with a period. Though only one such period. And not with frequency literally. (It is false that E = ν. It is true that E = ν times the quantum.) In this way, the literal concept of frequency does not enter as before, rendering Δ ν Δ t ≥ 1 inapplicable. So the above noted contradiction disappears. Nevertheless, the Uncertainties are derived. If energy is only to be defined over a period, momentum only over a distance (formerly a wavelength) resulting during such period, thus yielding quantized action of dimensions Et = pq, then energies will become indefinite at instants, momenta indefinite at points, leading, as demanded, to (symmetric!) Δ E Δ t = Δ p Δ q ≥ h’s. (shrink)

The classical response to Zeno’s paradoxes goes like this: ‘Motion cannot properly be defined within an instant. Only over a period’ (Vlastos.) I show that this ob-jection is exactly what it takes for Zeno to be right. If motion cannot be defined at an instant, even though the object is always moving at that instant, motion cannot be defined at all, for any longer period of time identical in content to that instant. The nonclassical response introduces discontinuity, to evade the (...) paradox of infinite proximity of any point of a distance with any ‘next’. But it introduces the wrong sort of discontinuity because, rather than assuming the discontinuity of motion, as Quantum Theory does, it assumes the discontinuity of space. Due then to the resulting spacetime disorder, though all else is certainly lost, the Tortoise now turns up at least as fast as Achilles and hence not even this much is rescued. Zeno rejects motion because he shows that a moving object must be where it is not. Hence motion, if to occur, must violate the Law of Contradiction (LNC). Applying the concept of quantum discontinuity, I produce an alternative. If an object is to move discontinuously between two boundary points, A and B, what actually obtains is, rather, that it is nowhere at all in-between A and B. And cannot therefore be at two places in-between A and B. And cannot therefore be where it is not. Thus, LNC is conserved. However, in these conditions, the Law of the Excluded Middle (LEM) fails. To mitigate the undesirability of this effect, I show that LEM fails because LNC holds. Thus, the resulting nonbivalent logic, which is also appropriate for quantized transitions of all kinds, will always turn up nonbivalent, because consistent. And this is not too bad, considering. (shrink)

Subjectivists, taking the “collapse” of the observation-interpretation contrast much too seriously, are led to imagine that even perceptual knowledge is active. And therefore subject dependent. Turning the tables on this popular trend, I argue that even conceptual knowledge is passive. Kant’s epistemology is conceptual. But if also active, then incoherent. If synthetic a priori truths are to follow upon our mental activity, they were neither true nor, far less, a priori before that activity. “A priori” and “active” are contradictory attributes (...) of knowledge. As, indeed, are “a priori” and “subject-dependent” to begin with. Nothing a priori can be dependent on anything except itself, and least of all on the human subject. Kant does consider the active aspect of thought. The difference is that for him the more active it becomes, the less it is to be trusted. For we are no longer in the province of the Understanding, and its necessary truths, but in the realm of Pure Reason and its dialectical antinomies. Cognition activists who take a liking to Kant have simply mistaken Reason for the Understanding. And Reason is to Kant “the seat of all transcendental illusion”. (shrink)

There are two antithetical classes of Paradoxes, The Runner and the Stadium, impregnated with infinite divisibility, which show that motion conflicts with the world, and which I call Static. And the Arrow, impregnated with nothing, which shows that motion conflicts with itself, and which I call Dynamic. The Arrow is stationary, because it cannot move at a point; or move, and be at more points than one at the same time, so being where it is not. Despite their contrast, however, (...) both groups can be evaded, if motion is conducted over discrete points: (a) If no two points touch, there will be a step ahead, for there will now be nextness. And (b) if they do not touch, “here” and “there” (=not–here) will no longer be sufficiently proximal to have the body be where it is not. They will be separate. So the body is only where it is. Hence, both groups, despite their contrast, presuppose, each in its own way, the infinite proximity of any point with anynext. But the Dynamic group cannot survive what it needs. Suppose that “here” and “not–here” (i.e., “there”), are not discrete but infinitely proximal. Then Rest also would be self-contradictory. And it gets worse. For it takes two to make a contradiction, in this case, “here,” “not–here,” and their proximity. But, with regard to conditions of infinite proximity, “in the end there can be only one” (point), and hence no contradiction in the first place. The Dynamic paradoxes rest on a premise with which they are inconsistent. They need two of this, of which, in a different but just as equally vital connection, there can be only one. On the force of this remark, the Dynamic paradoxes, initially the stronger of the lot, actually turn out to be the weaker. (shrink)

I unpack the contents of the motto that “meaning is use” in fivefold fashion and point to the elements it contains, which are open to an ideological exploitation, the main reason for its strong appeal among intellectual circles. I indicate how the sense of it, “where there is use, there is meaning”, has encouraged equalitarian accounts of meaning and truth . I then present and discuss Austin’s distinction between the Sentence and the Statement, which entails the presence of meaning preceding (...) the use, and directing it, and offer a new proof that Sentences are impossible to eliminate in any semantic scheme of things. Austin’s distinction, as explained and defended, refutes the contention that “meaning is use”. I proceed to his doctrine of Locution and Illocution, reflecting the previous, indicating by a series of examples, that illocutionary varieties, which are varieties but not variances , can never extend beyond the se-mantic scope generically contained in the original, content; that is to say, the Sentence. Those that do, and they are several, violate the rules of sense. I enumerate his vast differences with Wittgenstein, and proceed to defend Austin’s noted conservatism against the novelties endorsed by the former and his disciples. Charging Wittgenstein’s private language attack as circular, I conclude by marking their further contrast on the actual foundations of meaning and truth. (shrink)

The two Heisenberg Uncertainties (UR) entail an incompatibility between the two pairs of conjugated variables E, t and p, q. But incompatibility comes in two kinds, exclusive of one another. There is incompatibility defineable as: (p → -q) & (q → -p) or defineable as [(p → -q) & (q → -p)] ↔ r. The former kind is unconditional, the latter conditional. The former, in accordance, is fact independent, and thus a matter of logic, the latter fact dependent, and thus (...) a matter of fact. The two types are therefore diametrically opposed. In spite of this, however, the existing derivations of the Uncertainties are shown here to entail both types of incompatibility simultaneously. ΔEΔt ≥ h is known to derive from the quantum relation E = hv plus the Fourier relation ΔvΔt ≥ 1. And the Fourier relation assigns a logical incompatibility between Δv = 0, Δt = 0. (Defining a repetitive phenomenon at an instant t → 0 is a self contradictory notion.) An incompatibility, therefore, which is fact independent and unconditional. How can one reconcile this with the fact that ΔEΔt exists if and only if h > 0, which latter supposition is a factual truth, entailing that a ΔE = 0, Δt = 0 incompatibility should itself be fact dependent? Are we to say that E and t are unconditionally incompatible (via ΔvΔt ≥ 1) on condition that E = hv is at all true? Hence, as presently standing, the UR express a self-contradicting type of incompatibility. To circumvent this undesirable result, I reinterpret E = hv as relating the energy with a period. Though only one such period. And not with frequency literally. (It is false that E = v. It is true that E = v times the quantum.) In this way, the literal concept of frequency does not enter as before, rendering ΔvΔt ≥ 1 inapplicable. So the above noted contradiction disappears. Nevertheless, the Uncertainties are derived. If energy is only to be defined over a period, momentum only over a distance (formerly a wavelength) resulting during such period, thus yielding quantized action of dimensions Et = pq, then energies will become indefinite at instants, momenta indefinite at points, leading, as demanded, to (symmetric!) ΔEΔt = ΔpΔq ≥ h's. (shrink)

The classical response to Zeno’s paradoxes goes like this: ‘Motion cannot properly be defined within an instant. Only over a period’ (Vlastos.) I show that this ob-jection is exactly what it takes for Zeno to be right. If motion cannot be defined at an instant, even though the object is always moving at that instant, motion cannot be defined at all, for any longer period of time identical in content to that instant. The nonclassical response introduces discontinuity, to evade the (...) paradox of infinite proximity of any point of a distance with any ‘next’. But it introduces the wrong sort of discontinuity because, rather than assuming the discontinuity of motion, as Quantum Theory does, it assumes the discontinuity of space. Due then to the resulting spacetime disorder, though all else is certainly lost, the Tortoise now turns up at least as fast as Achilles and hence not even this much is rescued. Zeno rejects motion because he shows that a moving object must be where it is not. Hence motion, if to occur, must violate the Law of Contradiction (LNC). Applying the concept of quantum discontinuity, I produce an alternative. If an object is to move discontinuously between two boundary points, A and B, what actually obtains is, rather, that it is nowhere at all in-between A and B. And cannot therefore be at two places in-between A and B. And cannot therefore be where it is not. Thus, LNC is conserved. However, in these conditions, the Law of the Excluded Middle (LEM) fails. To mitigate the undesirability of this effect, I show that LEM fails because LNC holds. Thus, the resulting nonbivalent logic, which is also appropriate for quantized transitions of all kinds, will always turn up nonbivalent, because consistent. And this is not too bad, considering. (shrink)

There are two antithetical classes of Paradoxes, The Runner and the Stadium, impregnated with infinite divisibility, which show that motion conflicts with the world, and which I call Static. And the Arrow, impregnated with nothing, which shows that motion conflicts with itself, and which I call Dynamic. The Arrow is stationary, because it cannot move at a point; or move, and be at more points than one at the same time, so being where it is not. Despite their contrast, however, (...) both groups can be evaded, if motion is conducted over discrete points: (a) If no two points touch, there will be a step ahead, for there will now be nextness. And (b) if they do not touch, “here” and “there” (=not–here) will no longer be sufficiently proximal to have the body be where it is not. They will be separate. So the body is only where it is. Hence, both groups, despite their contrast, presuppose, each in its own way, the infinite proximity of any point with anynext. But the Dynamic group cannot survive what it needs. Suppose that “here” and “not–here” (i.e., “there”), are not discrete but infinitely proximal. Then Rest also would be self-contradictory. And it gets worse. For it takes two to make a contradiction, in this case, “here,” “not–here,” and their proximity. But, with regard to conditions of infinite proximity, “in the end there can be only one” (point), and hence no contradiction in the first place. The Dynamic paradoxes rest on a premise with which they are inconsistent. They need two of this, of which, in a different but just as equally vital connection, there can be only one. On the force of this remark, the Dynamic paradoxes, initially the stronger of the lot, actually turn out to be the weaker. (shrink)

Subjectivists, taking the “collapse” of the observation-interpretation contrast much too seriously, are led to imagine that even perceptual knowledge is active. And therefore subject dependent. Turning the tables on this popular trend, I argue that even conceptual knowledge is passive. Kant’s epistemology is conceptual. But if also active, then incoherent. If synthetic a priori truths are to follow upon our mental activity, they were neither true nor, far less, a priori before that activity. “A priori” and “active” are contradictory attributes (...) of knowledge. As, indeed, are “a priori” and “subject-dependent” to begin with. Nothing a priori can be dependent on anything except itself, and least of all on the human subject. Kant does consider the active aspect of thought. The difference is that for him the more active it becomes, the less it is to be trusted. For we are no longer in the province of the Understanding, and its necessary truths, but in the realm of Pure Reason and its dialectical antinomies. Cognition activists who take a liking to Kant have simply mistaken Reason for the Understanding. And Reason is to Kant “the seat of all transcendental illusion”. (shrink)

Gilles Deleuze: The Intensive Reduction brings together eighteen essays written by an internationally acclaimed team of scholars to provide a comprehensive overview of the work of Gilles Deleuze, one of the most important and influential European thinkers of the twentieth century. Each essay addresses a central issue in Deleuzeʹs philosophy (and that of his regular co-author, Félix Guattari) that remains to this day controversial and unsettled. Since Deleuzeʹs death in 1994, the technical aspects of his philosophy have been largely neglected. (...) These essays address that gap in the existing scholarship by focusing on his contribution to philosophy. Each contributor advances the discussion of a contested point in the philosophy of Deleuze to shed new light on as yet poorly-understood problems and to stimulate new and vigorous exchanges regarding his relationship to philosophy, schizoanlysis, his aesthetic, ethical and political thought. (shrink)

Due to Gӧdel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments –Warren (2020), Murzi and Topey (2021)– for the idea that the natural deduction rules for (...) the first-order universal quantifier are categorical, i.e., they uniquely determine its semantic intended meaning. Both of them make use of McGee’s open-endedness requirement and the second one uses in addition Garson’s (2013) local models for defining the validity of these rules. I argue that the success of both these arguments is relative to their semantic or infinitary assumptions, which could be easily discharged if the introduction rule for the universal quantifier is taken to be an infinitary rule, i.e. non-compact. Consequently, I reconsider the use of the ω-rule and I show that the addition of the ω-rule to the standard formalizations of first-order logic is categorical. In addition, I argue that the open-endedness requirement does not make the first-order Peano Arithmetic categorical and I advance an argument for its categoricity based on the inferential conservativity requirement. (shrink)

This paper seeks to develop a phenomenological account of the disorientation of grief, specifically the relationship between disorientation and the breakdown in practical self-understanding at the heart of grief. I argue that this breakdown cannot be sufficiently understood as a breakdown of formerly shared practices and habitual patterns of navigating lived-in space that leaves the bereaved individual at a loss as to how to go on. Examining the experience of losing a loved person and a loved person-to-be, I instead propose (...) that this breakdown should be understood primarily in relation to a distinctive kind of futurity operative in disorientation,irrespectiveof the extent to which there is a breakdown of formerly shared practices and habitual patterns of navigating lived-in space. Drawing on the resources afforded by Heidegger’s phenomenology, I argue that it is acore characteristicof the experience of disorientation in grief that the grieving person can no longer meaningfully press ahead into aspecific futural self. This view comes with certain advantages over existing accounts of the temporality of grief for making sense of the disorientated relationship to futurity, which the appeal to Heideggerian resources makes possible. (shrink)

This paper seeks to develop a phenomenological account of the disorientation of grief, specifically the relationship between disorientation and the breakdown in practical self-understanding at the heart of grief. I argue that this breakdown cannot be sufficiently understood as a breakdown of formerly shared practices and habitual patterns of navigating lived-in space that leaves the bereaved individual at a loss as to how to go on. Examining the experience of losing a loved person and a loved person-to-be, I instead propose (...) that this breakdown should be understood primarily in relation to a distinctive kind of futurity operative in disorientation, irrespective of the extent to which there is a breakdown of formerly shared practices and habitual patterns of navigating lived-in space. Drawing on the resources afforded by Heidegger’s phenomenology, I argue that it is a core characteristic of the experience of disorientation in grief that the grieving person can no longer meaningfully press ahead into a specific futural self. This view comes with certain advantages over existing accounts of the temporality of grief for making sense of the disorientated relationship to futurity, which the appeal to Heideggerian resources makes possible. (shrink)

Modern societies are characterized by a division of epistemic labor between laypeople and epistemic authorities. Authorities are often far more competent than laypeople and can thus, ideally, inform their beliefs. But how should laypeople rationally respond to an authority’s beliefs if they already have beliefs and reasons of their own concerning some subject matter? According to the standard view, the beliefs of epistemic authorities are just further, albeit weighty, pieces of evidence. In contrast, the Preemption View claims that, when one (...) discovers what an authority believes, it is not permissible to rely on any of one’s own reasons concerning the subject matter. The original version of this view, as proposed by Linda Zagzebski, has recently been severely criticized for recommending blind trust and for abandoning even minimal standards for critical thinking. In our paper, we defend a new version of the Preemption View—Defeatist Preemptionism—in a way that differs radically from Zagzebski’s. We argue that our view can be derived from certain widely accepted general epistemic principles. In particular, we claim that preemption can be identified as a special case of source sensitive defeat. Moreover, we argue that Defeatist Preemptionism does not lead to the undesirable consequences that critics ascribe to the Preemption View. The paper thus articulates the foundations and refinements of the Preemption View, such that it adequately captures the phenomenon of epistemic authority and the rational requirements related to it. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

At last available in paperback, this book anticipates and explains the post-structuralist turn to empiricism. Presenting a challenging reading of David Hume's philosophy, the work is invaluable for understanding the progress of Deleuze's thought.

In this paper, I present a solution to the problem that the need to accommodate the phenomenon of epistemic defeat poses for reliabilism. Defeaters are supposed to remove justification for previously justified beliefs. According to standard process reliabilism, the justification of a belief depends on the reliability of a process that is already completed when a defeater for that belief is obtained. It is hard to see, then, how a defeater can affect reliabilist justification, if that justification, from the perspective (...) of the defeater, lies wholly in the past. What is more, undercutting defeaters plausibly defeat by generating incompatibilities with higher-order propositions :105–118, 2014; Melis in Philos Stud 170:433–442, 2014). This is hard to integrate with reliabilism which explicitly denies higher-order conditions for justification. I argue that both of these phenomena can be accommodated by it via what I call the “Replacement Principle”: when a defeater is obtained, it generates either a logical incompatibility or a doxastic incompatibility. The resulting tension is registered and initiates a reasoning process that compares the epistemic support for the defeater with that for the defeated belief. This process may replace the original reliable formation process as a doxastic base for the defeated belief. If the defeater is not given its due weight in the reasoning process, that process was unreliable and if the defeated belief is retained as a result, it will be unjustified. This is intuitively the right result. Since reasoning is reliable, only if it is rational, the account manages to capture the intuition that disregarding a defeater would be irrational without having to make rationality a condition for justification. Replacement is not only plausible on causal pictures of doxastic basing, but also required in order to allow for the possibility of belief reevaluation in general and is therefore not an ad hoc addition to reliabilism, but rather part of its inherent explanatory resources. (shrink)

Vann McGee has recently argued that Belnap’s criteria constrain the formal rules of classical natural deduction to uniquely determine the semantic values of the propositional logical connectives and quantifiers if the rules are taken to be open-ended, i.e., if they are truth-preserving within any mathematically possible extension of the original language. The main assumption of his argument is that for any class of models there is a mathematically possible language in which there is a sentence true in just those models. (...) I show that this assumption does not hold for the class of models of classical propositional logic. In particular, I show that the existence of non-normal models for negation undermines McGee’s argument. (shrink)

An important collection of essays providing a comprehensive overview of the thought of Gilles Deleuze, one of the most influential thinkers of the twentieth century.

Is knowledge-how, or “practical” knowledge, a species of knowledge-that, or “theoretical” knowledge? There is no comfortable position to take in the debate around this question. On the one hand, there are counterexamples against the anti-intellectualist thesis that practical knowledge is best analysed as an ability. They show that having an ability to ϕ is not necessary for knowing how to ϕ. On the other hand, the intellectualist analysis of practical knowledge as a subspecies of theoretical knowledge is threatened by its (...) own set of counterexamples, which convincingly establish that practical knowledge lacks many of the typical characteristics of theoretical knowledge. Most strikingly it does not even appear to require a belief. In this paper, I develop an account of practical knowledge that avoids these counterexamples. It also manages to preserve both the status of such knowledge as a cognitive achievement and its apparently close conceptual relation to abilities. I start with the counterexamples against the necessity of abilities for practical knowledge and show that they fail because they underestimate the cognitive demands of attempts. I then make use of the logic of dispositions to bridge the gap that counterexamples against the necessity of abilities for practical knowledge open. It is argued that, instead of the ability to ϕ, it is a specific disposition to have the ability to ϕ that constitutes practical knowledge about ϕ. The resulting theory is an anti-intellectualist position that preserves essential intellectualist motivations and thus should be satisfactory for proponents of both views. (shrink)

This volume presents the concepts of schizoanalysis and ecosophy as Felix Guattari and Gilles Deleuze understood them, in interviews and analyses by their contemporaries and followers. This accessible yet authoritative introduction is written by distinguished specialists, combining testimonies from some of Guattari's colleagues at the La Borde psychiatric clinic where he practiced, with expository essays on his main ideas, schizoanalysis and ecosophy, as well as his relations with Lacan. The last section of the book deals with the subsequent creative application (...) of those ideas by his philosophical and psychoanalytic followers situated within the contemporary moment. This collection also provides the crucial historical context of France at the time Guattari was developing his concepts, including the role of the Maoists and the significance of the political situation in Algeria. (shrink)