Francesco Praolini has recently put pressure on the view that justified believability is closed under conjunction introduction. Based on what he calls ‘the hybrid paradox,’ he argues that accepting the principle of conjunction closure for justified believability, quite surprisingly, entails that one must also accept the principle of factivity for justified believability, i.e. that there are no propositions that are justifiably believable and false at the same time. But proponents of conjunction closure can do without factivity, (...) as I argue in this short note. A less demanding principle is available. (shrink)

The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that (...) stands between knowing the truth of the premises of a valid inference and knowledge of its conclusion is inferring it from the premises, the evidence for each of the premises may jointly count against the conclusion. The intuitive view regarding inferred knowledge says one thing, the evidence says another. One epistemological framework that seems to have the resources to resolve this tension endorses the view that knowledge always requires conclusive evidence. A second framework resolves the tension by limiting the scope of the closure principle. Only inferences drawn directly from propositions contained in the scope of a single knowledge operator are considered closed. The aim of the present essay is to revive the unpopular third option, the idea that knowledge is open. The essay proceeds by arguing that in different ways the two former frameworks only succeed in relocating the problem, not in resolving it. The first framework, the infallibilist view, relocates the problem to a sharp separation between knowledge of the occurrences of events from knowledge of their chance of occurring, a separation leading to several significant additional problems. The fallibilist view, the second framework, in endorsing closure neglects to take into full account the ways in which evidence fails to be transitive. For instance, evidence can count in favor of a conjunction while counting against each of its conjuncts. This fact, which is argued for in the essay on probabilistic as well as non-probabilistic grounds, is used as the foundation of an argument against closed knowledge that can be used as a way to understand several of the most fundamental challenges of epistemology. Not only can an open knowledge view that is based on open evidence resolve all these problems in a simple and natural way, it can also respond to formidable challenges that significantly hinder other open knowledge views. There are good reasons, then, to view both knowledge and evidence as open. (shrink)

It is well-known that versions of the lottery paradox and of the preface paradox show that the following three principles are jointly inconsistent: (Sufficiency) very probable propositions are justifiably believable; (Conjunction Closure) justified believability is closed under conjunction introduction; (No Contradictions) propositions known to be contradictory are not justifiably believable. This paper shows that there is a hybrid of the lottery and preface paradoxes that does not require Sufficiency to arise, but only Conjunction Closure and No Contradictions; and (...) it argues that, given any plausible solution to this paradox, if one is not ready to deny Conjunction Closure (and analogous consistency principles), then one must endorse the thesis that justified believability is factive. (shrink)

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, (...) 2019). This paradox synthesises elements of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some (...) formal characterisations of the surprise notion, crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes. (shrink)

In this essay I defend a solution to a skeptical paradox. The paradox I focus on concerns epistemic justification (rather than knowledge), and skeptical scenarios that entail that most of our ordinary beliefs about the external world are false. This familiar skeptical paradox hinges on a “closure” principle. The solution is to restrict closure, despite its first appearing as a fully general principle, so that it can no longer give rise to the paradox. This has some (...) extra advantages. First, it suggests a general strategy that provides solutions to other versions of the paradox, not just those that depend on closure. Second, it clarifies the relation between the paradox and other kinds of skeptical problem. (shrink)

Stephenson (2022) has argued that Kant’s thesis that all transcendental truths are transcendentally a priori knowable leads to omniscience of all transcendental truths. His arguments depend on luminosity principles and closure principles for transcendental knowability. We will argue that one pair of a luminosity and a closure principle should not be used, because the closure principle is too strong, while the other pair of a luminosity and a closure principle should not be used, (...) because the luminosity principle is too strong. Stephenson’s argument also depends on a factivity principle for transcendental knowability, which we will argue to be false. (shrink)

On Fred Dretske’s account of knowledge, the Epistemic Closure Principle for knowledge is not valid. Dretske takes this to be a virtue since the account is thus able to saves ordinary knowledge from skepticism. On it, you may know that you have hands, although you do not know that you are not a handless brain in a vat. As a correlate, the account also has to countenance the existence of what has come to be known as ‘abominable conjunctions’ (...) – conjunctions of the form ‘I know I have hands but I do not know that I am not a handless brain in a vat’. These conjunctions are abominable in that they look false or in some way incoherent. Dretske suggests that the abomination is merely pragmatic and can be explain in terms of conversational features, more precisely, in terms of the Gricean Conversation Principles and its associated Maxims of Conversation. I argue that no such Gricean explanation is forthcoming, and that the abomination cannot be thought of as a merely pragmatic or conversational phenomenon. As I show, the abomination goes deeper, into the semantics. (shrink)

Bradwardine’s solution to the the logical paradoxes depends on the idea that every sentence signifies many things, and its truth depends on things’ being wholly as it signifies. This idea is underpinned by his claim that a sentence signifies everything that follows from what it signifies. But the idea that signification is closed under entailment appears too strong, just as logical omniscience is unacceptable in the logic of knowledge. What is needed is a more restricted closure principle. A (...) clue can be found in speech act pluralism, whereby indirect speech reports are closed under intersubstitutivity of co-referential terms. The conclusion is that solving the semantic paradoxes does not require revision of logic, thus saving logic from paradox. (shrink)

Skeptical puzzles and arguments often employ knowledge-closure principles . Epistemologists widely believe that an adequate reply to the skeptic should explain why her reasoning is appealing albeit misleading; but it’s unclear what would explain the appeal of the skeptic’s closure principle, if not for its truth. In this paper, I aim to challenge the widespread commitment to knowledge-closure. But I proceed by first examining a new puzzle about failing to know—what I call the New Ignorance Puzzle (...) . This puzzle resembles to the Old Ignorance Puzzle , although it does not involve a closure principle. It instead centers on the standard view of ignorance, a highly intuitive principle stating that ignorance is merely a failure to know. In Sects. 2 and 3, I argue that the best way to solve the New Ignorance Puzzle is to reject the standard view of ignorance and to explain away its appeal via conversational implicature. I then use this solution to the New Ignorance Puzzle as a way of explaining why knowledge-closure principles would seem true, and why abominable conjunctions would seem abominable, even if such principles were false . The upshot is a new way of explaining why the skeptic’s reasoning is appealing albeit misleading. (shrink)

This article shows that there is a liar-like paradox that arises for rational credence that relies only on very weak logical and credal principles. The paradox depends on a weak rational reflection principle, logical principles governing conjunction, and principles governing the relationship between rational credence and proof. To respond to this paradox, we must either reject even very weak rational reflection principles or reject some highly plausible logical or credal principle.

The question whether epistemological concepts are closed under deduction is an important one since many skeptical arguments depend on closure. Such skepticism can be avoided if closure is not true of knowledge (or justification). This response to skepticism is rejected by Peter Klein and others. Klein argues that closure is true, and that far from providing the skeptic with a powerful weapon for undermining our knowledge, it provides a tool for attacking the skeptic directly. This paper examines (...) various arguments in favor of closure and Klein's attempted use of closure to refute skepticism. Such a refutation of skepticism is mistaken. But the closure principle is in any case false, so the skepticism that depends on it is undermined. The appeal of the closure principle derives from a failure to recognize an important feature of our epistemological concepts, namely, their context relativity. (shrink)

We study closure properties of measurable ultrapowers with respect to Hamkin's notion of freshness and show that the extent of these properties highly depends on the combinatorial properties of the underlying model of set theory. In one direction, a result of Sakai shows that, by collapsing a strongly compact cardinal to become the double successor of a measurable cardinal, it is possible to obtain a model of set theory in which such ultrapowers possess the strongest possible closure properties. (...) In the other direction, we use various square principles to show that measurable ultrapowers of canonical inner models only possess the minimal amount of closure properties. In addition, the techniques developed in the proofs of these results also allow us to derive statements about the consistency strength of the existence of measurable ultrapowers with non-minimal closure properties. (shrink)

Scientific realists contend that theory-conjunction presents a problem for empiricist conceptions of scientific knowledge and practice. Van Fraassen (1980) has offered a competing account of theory-conjunction which I argue fails to capture the mercenary character of epistemic dependence in science. Representative cases of theory-conjunction developed in the present paper show that mercenary reliance implies a "principle of epistemic symmetry" which only a realist can consistently accommodate. Finally, because the practice in question involves the conjunction of theories, a version of (...) realism more robust than the "entity realism" of Cartwright (1983, 1989) and Hacking (1983) is required to explain the success of theory-conjunction. (shrink)

Consider the following causal exclusion principle: For all distinct properties F and F* such that F* supervenes on F, F and F* do not both cause a property G. Peter Menzies and Christian List have proven that it follows from a natural conception of causation as difference-making that this exclusion principle is not generally true. Rather, it turns out that whether the principle is true is a contingent matter. In addition, they have shown that in a wide (...) range of empirically ordinary cases, it follows that F* causes G and F does not. These cases plausibly include instances where F* is a mental property and F and G are physical properties. If this is the right conception of causation, it therefore turns out that the physical world is not causally closed. In this paper I show that there is an alternative conception of causation as difference-making that does not have the same consequences. Whether the physical world is causally closed therefore turns out to depend, inter alia, on which conception of difference-making is correct. I give a number of arguments for the alternative conception of difference-making. (shrink)

The present paper argues that substantialist metaphysics are in tension with the physicalist idea that the universe is causally closed. The argument is a rather specific one and proceeds through three steps. The first step consists in arguing that monistic substance metaphysics allow for the existence of entities that cannot belong to the intended first order domain. This result sensitively depends on the nature of substances as invariant entities. The second step concludes that, if further domains are to be admitted, (...) then they are inhabited by “higher” or (systematically) “non-standard” entities and that, in both cases if not made somehow innocuous, such entities may take part on the metaphysical construction of the world through their own distinctive properties and causal powers. However, this latter claim is in contradiction with causal closure. But closure is the principle that mainly characterizes physicalist approaches in metaphysics and as such physicalist metaphysics cannot get rid of it. Who attempted making exotic properties and causal powers innocuous usually appealed to the Supervenience Argument. Unfortunately, as the third step proves, this argument is invalid. Finally, the paper looks forward and toward alternative models for physicalist metaphysics, like process-based models. (shrink)

The goal of synthetic biology is to create artificial organisms. To achieve this it is essential to understand what life is. Metabolism-replacement systems, or (M, R)-systems, constitute a theory of life developed by Robert Rosen, characterized in the statement that organisms are closed to efficient causation, which means that they must themselves produce all the catalysts they need. This theory overlaps in part with other current theories, including autopoiesis, the chemoton, and autocatalytic sets, all of them invoking some idea of (...) closure. A simple model of an (M, R)-system has been implemented in the computer, and behaves in ways that may shed light on the requirements for a prebiotic self-organizing system. In addition to a trivial steady state in which nothing happens, it can establish a non-trivial steady state in which all intermediates have finite concentrations, with their rates of degradation balanced by their rates of synthesis. The system can be regenerated from the set of food components plus a single intermediate, and maintain itself in that state indefinitely, despite continuous degradation. At the very low compartment volumes that may have existed in prebiotic conditions, for example in cavities in minerals, or in micelles formed by simple amphiphiles, statistical fluctuations in the numbers of molecules need to be taken into account. With the stochastic approach there is no non-trivial steady state in strict mathematical terms, because the system will always collapse to the trivial state after sufficient time. However, the average time before collapse is so long for volumes greater than $10^{-19}\;{\textsc{l}}$ (much smaller than the volume of the order of $10^{-15}\;{\textsc{l}}$ for a typical bacterial cell) that for practical purposes the self-maintaining state of non-null concentrations becomes significant, recalling the situation of bistability that is observed in deterministic analysis. In turn, there exists a minimum size below which the self-organizing system cannot maintain itself on chemically relevant time scales. The value of the critical volume depends on the particular concentrations and rate constants assumed, but the principle could apply generally. (shrink)

In the contemporary expanding literature on transmission failure and its connections with issues such as the Closure principle, the nature of perceptual warrant, Moore’s proof of an external world and the effectiveness of Humean scepticism, it has often been assumed that there is just one kind of it: the one made familiar by the writings of Crispin Wright and Martin Davies. Although it might be thought that one kind of failure is more than enough, Davies has recently challenged (...) this view: apparently, there are more ways in heaven and earth that warrant can fail to transmit across valid inference from one (set of) belief(s) to another, than have been dreamt of in philosophy so far. More specifically, Davies thinks that a second kind of transmission failure has to be countenanced. He connects each kind of failure of transmission of warrant with two different kinds of epistemic project, respectively, and with the exploration of whether the current dispute between conservatives such as Wright, and liberals such as Jim Pryor, on the nature of perceptual warrant, would have a bearing on them. I point out why Davies’s second kind of transmission failure is indeed no such thing. I then move on to canvass another kind of transmission failure, different from the one studied by both Wright and Davies, and dependent on an alternative conception of the structure of empirical warrants, which I dub “moderatism”. I then consider how this alternative notion of transmission failure fares with respect to Moore’s proof, its relationship with Wright’s kind of transmission failure and with the Closure principle. In closing, I defend it from criticisms that can be elicited from Pryor’s recent work. (shrink)

Take the following principle (or schema) as the focus of the ensuing discussion (“P” and “Q” are placeholders for propositions): 1 (Closure) If one knows P and competently deduces Q from P, thereby coming to believe Q, while retaining one's knowledge that P, one comes to know that Q. My strategy in outline: first, I want to set out Fred Dretske's classic challenge to (Closure) – a challenge which began in 1970–1971. Then I want to consider a (...) specific, recent counter‐challenge to Dretske's challenge to (Closure) mounted by John Hawthorne, and to defend Dretske's challenge from Hawthorne's counter‐challenge. Doing this is not to invalidate (Closure). In this regard my conclusions are modest: Dretske's challenge to (Closure) is – or, better: can be made – sophisticated and, so far, unmet. (shrink)

The present paper argues that substantialist metaphysics are in tension with the physicalist idea that the universe is causally closed. The argument is a rather specific one and proceeds through three steps. The first step consists in arguing that monistic substance metaphysics allow for the existence of entities that cannot belong to the intended first order domain. This result sensitively depends on the nature of substances as invariant entities. The second step concludes that, if further domains are to be admitted, (...) then they are inhabited by “higher” or (systematically) “nonstandard” entities and that, in both cases if not made somehow innocuous, such entities may take part on the metaphysical construction of the world through their own distinctive properties and causal powers. However, this latter claim is in contradiction with causal closure. But closure is the principle that mainly characterizes physicalist approaches in metaphysics and as such physicalist metaphysics cannot get rid of it. Who attempted making exotic properties and causal powers innocuous usually appealed to the Supervenience Argument. Unfortunately, as the third step proves, this argument is invalid. Finally, the paper looks forward and toward alternative models for physicalist metaphysics, like processbased models. Keywords: Metaphysics of Quantities, Abstraction Principles, Locationism. (shrink)

Unlike inert objects, organisms and their cells have the ability to initiate activity by themselves and thus change their properties or states even in the absence of an external cause. This crucial difference led us to search for principles suitable for the study organisms. We propose that cells follow the default state of proliferation with variation and motility, a principle of biological inertia. This means that in the presence of sufficient nutrients, cells will express their default state. We also (...) propose a principle of variation that addresses two central features of organisms, variation and historicity. To address interdependence between parts, we use a third principle, the principle of organization, more specifically, the notion of the closure of constraints. Within this theoretical framework, constraints are specific theoretical entities defined by their relative stability with respect to the processes they constrain. Constraints are mutually dependent in an organized system and act on the default state.Here we discuss the application and articulation of these principles for mathematical modeling of morphogenesis in a specific case, that of mammary ductal morphogenesis, with an emphasis on the default state. Our model has both a biological component, the cells, and a physical component, the matrix that contains collagen fibers. Cells are agents that move and proliferate unless constrained; they exert mechanical forces that act (i) on collagen fibers and (ii) on other cells. As fibers are organized, they constrain the cells’ ability to move and to proliferate. This model exhibits a circularity that can be interpreted in terms of the closure of constraints. Implementing our mathematical model shows that constraints to the default state are sufficient to explain the formation of mammary epithelial structures. Finally, the success of this modeling effort suggests a stepwise approach whereby additional constraints imposed by the tissue and the organism can be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. (shrink)

The Principle of Dependent Choice is shown to be equivalent to: the Baire Category Theorem for Čech-complete spaces (or for complete metric spaces); the existence theorem for generic sets of forcing conditions; and a proof-theoretic principle that abstracts the "Henkin method" of proving deductive completeness of logical systems. The Rasiowa-Sikorski Lemma is shown to be equivalent to the conjunction of the Ultrafilter Theorem and the Baire Category Theorem for compact Hausdorff spaces.

In this paper I outline an account of the structure of perceptual justification that develops Wittgenstein’s thought that the possibility of acquiring any degree of justification for our beliefs depends on placing certain propositions outside the route of empirical inquiry, turning them into the ‘hinges’ of our rational evaluations. The proposal is akin to ‘moderate’ accounts of the structure of perceptual justification, but it conjoins Wittgenstein’s insight with explanationist and contrastivist ideas, and so differs in important respects both from such (...) accounts and from other versions of hinge epistemology. I maintain that the basic presuppositions of the epistemic practice of taking experience at face value are not totally refractory to evidential assessment, arguing that they can receive some degree of second-order empirical justification via inference to the best explanation. And I address the worry that the account may face the problem of ‘easy knowledge’ by helping myself to the contrastivist view that empirical knowledge is best understood as a three-place, contrastive relation between an agent, a proposition (or fact) and a contrast. This leads me to replace the usual closure principles for epistemic justification and knowledge with corresponding contrastive principles, filling in the final details of contrastive hinge epistemology. (shrink)

This paper explores some consequences of Lewis’s (Australas J Philos 74(4):549–567, 1996) understanding of how knowledge is compartmentalized. It argues, first, that he underestimates how badly it impacts his view. When knowledge is compartmentalized, it lacks at least one of two essential features of Lewis’s account: (a) Elusiveness—familiar skeptical possibilities, when relevant, are incompatible with everyday knowledge. (b) Knowledge is a modality—when a thinker knows that p, there is no relevant possibility where p is false. Lewis proposes compartmentalized knowledge to (...) keep treating knowledge as a modality while mitigating one of its unrealistic epistemological implications: In normal modal epistemic logic (and standard possible world semantics), a thinker always counts as knowing the strongest proposition that follows from the set of all the individual propositions that this thinker knows. Lewis’s compartmentalization proposal is that thinkers merely know the conjunctions of propositions that are known in each of, but not across, their compartments. The irony is that in avoiding overblown knowledge the view now allows for thinkers to attend to skeptical error possibilities and yet knowledge is present. The account avoids inflation of knowledge in one sense only to acquire another type of knowledge the view denies subjects can have. This problem motivates an inspection of knowledge accounts whose intra-compartment closure principles are weaker than those that are valid in normal modal-logic. The conclusion is that some formulations of closure can avoid the challenge Lewis’s view faces. Nevertheless, even these closure principles pose a barrier—perhaps an implausible barrier—for knowledge of ignorance. Even when the reasoning supporting the lack of knowledge is sound, a subject cannot always know she doesn’t know. Interestingly, this obstacle is one that knowledge of knowledge doesn’t seem to face. (shrink)

The safety conception of knowledge holds that a belief constitutes knowledge iff relevantly similar beliefs—its epistemic counterparts—are true. It promises an instructive account of why certain general principles of knowledge hold. We focus on two such principles that anyone should endorse: the closure principle that knowledge is downward closed under competent conjunction elimination, and the counter-closure principle that knowledge is upward closed under competent conjunction introduction. We argue that anyone endorsing the former must also endorse the (...) latter on pains of an unacceptable form of bootstrapping. We devise new formal models to identify necessary and sufficient conditions for these principles to hold on conceptions that construe knowledge in terms of true counterparts. These conditions state that counterparts of premise and conclusion beliefs are coordinated in certain ways whenever these beliefs stand in the relevant inferential relations. We show that the safety conception faces insuperable problems vindicating these coordination principles, because its epistemic counterpart relation is symmetric. We conclude that it thus proves unable to account for minimal closure properties of knowledge. More generally, our formal results establish parameters within which any conception must operate that construes knowledge in terms of true counterparts. (shrink)

I argue that there are living and everyday case in which rationality requires you, as a non-idealized human thinker, to have inconsistent beliefs while recognizing the inconsistency. I defend my argument against classical and insightful objections by Doris Olin, as well as others. I consider three versions of the preface paradox as candidate cases, including Makinson’s original version. None is free from objection. However, there is a fourth version, Modesty, that supposes that you believe that at least one of your (...) beliefs is false. I argue that this version escapes all the objections that could trouble the other versions, including the objection that given certain closure principles for justified belief, justified inconsistent beliefs saddle you with a pair of justified beliefs that are in explicit contradiction. I also argue more tentatively for the same verdict for Modesty*, a version that supposes that you believe that at least one of your beliefs is false. In that case, your belief guarantees that its content is true, in which case your beliefs are inconsistent, because at least one of them must be false. Once you think you’re wrong, you must be right! Crucial to my argument is a distinction between explicitly contradictory beliefs and three forms of inconsistency in belief. In the first of these, you believe contingent propositions each of which is logically independent of the others, yet you also believe the syntactic negation of their conjunction. In the second, your beliefs are inconsistent because of the rigid designation of demonstratives such as ‘this’ embedded in their contents. In the third, as in Modesty and Modesty* your beliefs are inconsistent because of self-reference. (shrink)

The safety conception of knowledge holds that a belief constitutes knowledge iff relevantly similar beliefs—its epistemic counterparts—are true. It promises an instructive account of why certain general principles of knowledge hold. We focus on two such principles that anyone should endorse: the closure principle that knowledge is downward closed under competent conjunction elimination, and the counter-closure principle that knowledge is upward closed under competent conjunction introduction. We argue that anyone endorsing the former must also endorse the (...) latter on pains of an unacceptable form of bootstrapping. We devise new formal models to identify necessary and sufficient conditions for these principles to hold on conceptions that construe knowledge in terms of true counterparts. These conditions state that counterparts of premise and conclusion beliefs are coordinated in certain ways whenever these beliefs stand in the relevant inferential relations. We show that the safety conception faces insuperable problems vindicating these coordination principles, because its epistemic counterpart relation is symmetric. We conclude that it thus proves unable to account for minimal closure properties of knowledge. More generally, our formal results establish parameters within which any conception must operate that construes knowledge in terms of true counterparts. (shrink)

Objections to reliabilist theories of knowledge and justification have looked insuperable. Reliability is a property of the process of belief formation. But the generality problem apparently makes the specification of any such process ambiguous. The externalism of reliability theories clashes with strongly internalist intuitions. The reliability property does not appear closed under truth-preserving inference, whereas closure principles have strong intuitive appeal. And epistemic paradoxes, like the preface and the lottery, seem unavoidable if knowledge or justification depends on the frequency (...) with which a process generates true beliefs. The present theory has the conceptual resources to meet these challenges. It requires that a justificatory belief-formation process be intentionally applied. It distinguishes the justification of beliefs from that of the believer. And it avoids a frequency interpretation of reliability by introducing a notion of the normalcy of conditions under which processes are intentionally used. (shrink)

In 1957, Gödel proved that completeness for intuitionistic predicate logic HPL implies forms of Markov's Principle, MP. The result first appeared, with Kreisel's refinements and elaborations, in Kreisel. Featuring large in the Gödel-Kreisel proofs are applications of the axiom of dependent choice, DC. Also in play is a form of Herbrand's Theorem, one allowing a reduction of HPL derivations for negated prenex formulae to derivations of negations of conjunctions of suitable instances. First, we here show how to deduce (...) Gödel's results by alternative means, ones arguably more elementary than those of Kreisel. We avoid DC and Herbrand's Theorem by marshalling simple facts about negative translations and Markov's Rule. Second, the theorems of Gödel and Kreisel are commonly interpreted as demonstrating the unprovability of completeness for HPL, if means of proof are confined within strictly intuitionistic metamathematics. In the closing section, we assay some doubts about such interpretations. (shrink)

The concept of being in a position to know is an increasingly popular member of the epistemologist’s toolkit. Some have used it as a basis for an account of propositional justification. Others, following Timothy Williamson, have used it as a vehicle for articulating interesting luminosity and anti-luminosity theses. It is tempting to think that while knowledge itself does not obey any closure principles, being in a position to know does. For example, if one knows both p and ‘If p (...) then q’, but one dies or gets distracted before being able to perform a modus ponens on these items of knowledge and for that reason one does not know q, one is still plausibly in a position to know q. It is also tempting to suppose that, while one does not know all logical truths, one is nevertheless in a position to know every logical truth. Putting these temptations together, we get the view that being in a position to know has a normal modal logic. A recent literature has begun to investigate whether it is a good idea to give in to these twin temptations—in particular the first one. That literature assumes very naturally that one is in a position to know everything one knows and that one is not in a position to know things that one cannot know. It has succeeded in showing that, given the modest closure condition that knowledge is closed under conjunction elimination, being a position to know cannot satisfy the so-called K axiom of normal modal logics. In this paper, we explore the question of the normality of the logic of being in a position to know in a more far-reaching and systematic way. Assuming that being in a position to know entails the possibility of knowing and that knowing entails being in a position to know, we can demonstrate radical failures of normality without assuming any closure principles at all for knowledge. Moreover, the failure of normality cannot be laid at the door of the K axiom for knowledge, since the standard principle NEC of necessitation also fails for being in a position to know. After laying out and explaining our results, we briefly survey the coherent options that remain. (shrink)

We present a theory of cooperative-competitive intelligence (CCI), its measures, research program, and applications that stem from it. Within the framework of this theory, satisficing sub-optimal behavior is any behavior that does not promote a decrease in the prospective control of the functional action diversity/unpredictability (D/U) potential of the agent or team. This potential is defined as the entropy measure in multiple, context-dependent dimensions. We define the satisficing interval of behaviors as CCI. In order to manifest itself at individual (...) or team level, this capacity harnesses properties such as degeneracy, pleiotropy (pluri-potentiality), synergies, and metastability. Intelligence is embodied because intelligent behavior is deeply dependent on body functionalities, defined as entropy measures. We base our theory on three principles: (a) relativity of functional entropy/ information in agent (team)-environment systems, (b) tendency toward the satisficing level of D/U potential, and (c) tendency toward the non-decreasing D/U potential. The conjunction of these three principles provides existence of sub-optimal behaviors associated with CCI. First, we deal with the problem of how to reduce multidimensional behavior to a concept that accounts for the vast set of scenarios in which CCI is manifested. Secondly, we define and discuss the three interacting principles that underpin CCI behavior as well as providing an outline for a future CCI research program supported by agent￾based modeling and empirical research. Finally, we provide some preliminary practical issues that stem from the theory. (shrink)

The paper critically discusses two prominent arguments against closure principles for knowledge. The first one is the “argument from aggregation”, claiming that closure under conjunction has the consequence that, if one individually knows i premises, one also knows their i-fold conjunction—yet, every one of the premises might exhibit interesting positive epistemic properties while the i-fold conjunction might fail to do so. The second one is the “argument from concatenation”, claiming that closure under entailment has the consequence that, (...) if one knows a premise, one also knows each of its remote consequences one arrives at—yet, again, the premise might exhibit interesting positive epistemic properties while some of its remote consequences might fail to do so. The paper firstly observes that the ways in which these two arguments try to establish that the relevant closure principle has the relevant problematic consequence are strikingly similar. They both crucially involve showing that, given the features of the case, the relevant closure principle acts in effect as a soritical principle, which is in turn assumed to lead validly to the relevant problematic consequence. There are however nontransitive logics of vagueness where soritical principles do not have any problematic consequence. Assuming that one of these logics is the correct logic of vagueness, the paper secondly observes that both arguments describe situations where knowledge is arguably vague in the relevant respects, so that a tolerant logic should be used in reasoning about it, with the effect that the relevant soritical principle no longer validly leads to the relevant problematic consequence. This shows an interesting respect in which the gap between validity and good inference that arguably arises in a transitive framework can be bridged in a tolerant one, thereby approximating better certain features of our epistemic lives as finite subjects. Moreover, even for those who do not subscribe to tolerant logics, the paper’s two observations jointly indicate that, for all the arguments from aggregation and concatenation show, the status of the relevant closure principles should be no worse than that assigned by one’s favoured theory of vagueness to soritical principles, which only rarely is plain falsity and can indeed get arbitrarily close to full truth. (shrink)

A recent approach to the problem of logical omniscience holds that belief is question-sensitive: what an agent believes depends on what question they try to answer (Pérez Carballo, 2016; Yalcin, 2018; Hoek, 2022). While the question-sensitive approach can avoid some logical omniscience problems, we argue that it suffers from nearby problems. First, these accounts all validate closure principles that are just as implausible as the ones it was designed to avoid. Second, question-sensitivity by itself isn’t suitable for explaining many (...) kinds of failures of logical omniscience. Recognizing the flaws of this approach, however, naturally leads to a more promising solution. Our account generalizes the question-sensitive approach by appealing to (1) the defeasible nature of dispositions toward action associated with belief and (2) the algorithms an agent uses to make decisions. On our view, then, believing that φ means being disposed to employ an algorithm which outputs acting on the information that φ in normal circumstances associated with φ. We argue that this account naturally generalizes the question-sensitive accounts while avoiding their faults. (shrink)

In simplified form, the argument that I am defending holds that the incompatibility of our freedom with determinism follows from the conjunction of (1) a plausible supervenience claim which says that whether a human agent is free depends only on what happens during the agent’s life and (2) a freedom-cancellation principle of Richard Gale which says that an agent is not free if all of her actions are intentionally brought about by another agent. Improved versions of (1) and (2) (...) are also considered. (shrink)

Epistemic justification has been widely accepted as both a gradational and relational notion. Given those properties, a natural thought is to take degrees of epistemic justification to be probabilities. In this paper, we present a simple Bayesian framework for justification. In the first part, after putting the model in an evidentialist form, we distinguish different senses of “being evidence for” and “confirming”. Next, we argue that this conception should accommodate the two relevant kinds of qualitative confirmation or evidential support. In (...) the second part of the paper, we discuss the claim that this view is unable to satisfy the modified version of the conjunction closure for beliefs in probabilistically independent propositions. We defend that the underlying assumption on which this objection depends leads to an improper reading of the concept of epistemic probability. After providing a better interpretation of it, we put forward a rationale, which is based on the notion of conditional uncertainty, in support of a more plausible and restricted version of the closure of justification under conjunction. (shrink)

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory (...) validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (shrink)

Causal closure arguments against interactionist dualism are currently popular amongst physicalists. Such an argument appeals to some principles of the causal closure of the physical, together with certain other premises, to conclude that at least some mental events are identical with physical events. However, it is crucial to the success of any such argument that the physical causal closure principle to which it appeals is neither too strong nor too weak by certain standards. In this paper, (...) it is argued that various forms of naturalistic dualism, of an emergentist character, are consistent with the strongest physical causal closure principles that can plausibly be advocated. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:184 BOOK REVIEWS knower, one may avoid undercutting the position that the cognitive powers are passive, without failing to do justice to the fact that aware· ness and discrimination are activities of the knower {pp. 71-72; 148· 49, n. 6). Second, Kai holds that the individual human being cannot really he said to have intuitive mind in himself: "Man has mind; hut only to a certain degree and without (...) mind losing its independence from the human whole.... the divine mind is present in man without los· ing its character of divine mind " (p. 75). If only God has intuitive mind {pp. 155, n. 32; 156-57, n. 13), how can the individual human being really know, even in the sense of having discursive thought? Since knowledge depends on first principles, what does not possess the intuitive mind which knows the first principles would, it seems, not properly have knowledge. The only hope for a definitive interpretation of the disconcertingly brief De Anima, 3. 5, lies in the possibility that one can establish a definite connection between this chapter and other elements in the Aris· totelian corpus, a connection that would elucidate the otherwise in· scrutable teaching on active mind. It is the great merit of Kai to have made an excellent case for a connection between De Anima, 3. 5, and two other elements in the Aristotelian corpus: nous as it functions in the logic and epistemology, and the unmoved mover of Metaphysics, Lambda. Exploring this connection in a penetrating and thorough analysis of a great body of Aristotelian and secondary te~ts, Kai has not merely taken a position on a more than two-thousand-year-old con· troversy, hut also has decisively advanced our understanding of active mind. St. John's University Jamaica, New York JAMES T. H. MARTIN Anselm Studies: An Occasional Journal. Vol. 2. Edited by JosEPH ScHNAUBELT, OSA, et al., White Plains, New York: Kraus Inter· national Publications, 1988. Pp. 634. $55.00. This volume contains the proceedings of the Fifth International Saint Anselm Conference (Villanova University, September 16-21, 1985). Held in conjunction with the Tenth International Patristic, Medieval, and Renaissance Conference, the meeting occasioned papers concen· trating on areas of "influence and juncture" in the life and thought of St. Anselm and St. Augustine. Given the dependence of much of Anselm's work on the thought of St. Augustine, the Conference took as its particular objective the understanding of the relationship between BOOK REVIEWS 185 faith and reason. While the focus of the papers in this volume includes both saints, the principal emphasis falls on Anselm as inheritor and interpretor of the methods and ideas of his intellectual ancestor. A brief introduction provides cameo presentations of Anselm's character as abbot, monk, and archbishop, together with a conspectus on Anselm's position vis-a-vis the canonical and ecclesiological issues of his day. The papers are then divided into five chapters: "Anselm's Monasticism." "The Proslogion Argument," "Truth: Anselm and Augustine," "Theological Method," and "The Anselmian Worldview." While the papers are of use to scholarly readers desiring detailed treatment of central issues in Anselm's logic and epistemology, the un· doubted strength of the collection lies in its well-calculated effort to integrate an understanding of Anselm's intellectual and spiritual out· look with the theological, spiritual, and literacy currents of his time. Especially for the historian of intellect and society, the essays in this volume provide analysis that advances our understanding of the cultural context of the 11th and 12th centuries. The contribution to our understanding of Anselm's culture is par· ticularly clear in the first and fourth divisions of the volume, the sec· tions dealing with monasticism and Anselm's worldview. In the former division, Glenn Olsen's assessment of " Anselm and Homosexuality" neatly evaluates the evidence for Anselm's sexual orientation made controversial by John Boswell's Christianity, Social Tolerance, and Homosexuality. In fact, the present article, together with its notes, provides a useful summary of the critical literature which has grown up of late around the Boswellian thesis as well as the study of literary expressions of affection in the 11th and 12th centuries. Olsen grasps the... (shrink)

En este artículo, considero algunos supuestos costos intuitivos relativos a la negación de la generalidad del Principio de Cierre para el conocimiento. Usualmente los filósofos descartan tal negación como altamente contra-intuitiva pero argumento que, por lo menos en relación a los supuestos costos aquí considerados, esto es incorrecto: dadas nuestras intuiciones folk, no hay tales costos. Por lo tanto un falibilista que busca detener el argumento escéptico basado en el principio de cierre puede restringir el principio sin sufrir esos supuestos (...) costos intuitivos. (shrink)

This paper argues that a necessary condition on inferential knowledge is that one knows all the propositions that knowledge depends on. That is, I will argue in support of a principle I call the Knowledge from Knowledge principle: (KFK) S knows that p via inference or reasoning only if S knows all the propositions on which p depends. KFK meshes well with the natural idea that (at least with respect to deductively valid or induc- tively strong arguments) the (...) epistemic status of one’s belief in the conclusion of an argument is a function of the epistemic status of the attitudes one has to the premises of that argument. One gets what one puts in: S’s belief in the conclusion C of an argument A has epistemic status E for S only if S’s belief in each of the premises C depends on also has epistemic status E.1 This is compatible, of course, with the epistemic status of S’s conclusion being greater than the epistemic status of the premises on which the conclusion of her reasoning depends. Furthermore, even though KFK applies more straightforwardly to non-suppositional inferences, we can also plausibly apply the principle to sup- positional reasoning if we treat S’s assuming for the sake of argument that p,2 as S assuming for the sake of argument that she knows that p.3 Although extremely plausible, philosophers have failed to present a concerted case in support of KFK. Most of their energy goes to articulating and/or defending some form of closure principle for knowledge.4 What is more, recently versions of this principle have been dismissed as problematic but I think without the reasons in its support been fully appreciated. This paper is an e fort to change the current state of affairs. Its focus is positive, however: my goal is to make the best case I can in support of KFK.5 To that end, the paper presents the reasons we have to accept KFK (§1), consid- ers an objection to the principle (§2), and situates the principle in the broader normative context of knowledge norms (§3). (shrink)

Some theories of rational belief assume that beliefs should be closed under conjunction. I motivate the rejection of the conjunction closure, and point out that the consequences of this rejection are not as severe as it is usually thought. An often raised objection is that without the conjunction closure people are unable to reason. I outline an approach in which we can – in usual cases – reason using conjunctions without accepting the closure in its whole generality. (...) This solution is based on the notion of confidence levels, which can be defined using probabilities. Moreover, on this approach, reasoning has a scalable computational complexity adaptable to cognitive abilities of both rationally bounded and perfectly rational agents. I perform a simulation to assess its error rate, and compare it to reasoning with conjunction closure. (shrink)

The use of predicate and sentential operators to express the practical modalities -- ability, control, openness, etc. -- has given new life to a fatalistic argument against determinist theories of responsible agency. A familiar version employs the following principle: the consequences of what is unavoidable (beyond one's control) are themselves unavoidable. Accordingly, if determinism is true, whatever happens is the consequence of events in the remote past, or, of such events together with the laws of nature. But laws and (...) the remote past are not under our control and, by the principle, neither are their consequences. Therefore, none of our choices and actions, nor anything that results from them, is under our control.1 Whether refinements of the closure principle underlying this unavoidability argument are acceptable depends upon the precise sense of 'consequence' and 'unavoidable' involved. Roughly, a proposition P is a consequence of a set of propositions M iff it is impossible that P be false when each member of M is true, or, conversely, when M necessitates P. Since P is unavoidable for S when P is true and S is (was) unable to prevent P from being true, it might seem that if P is unavoidable the same should hold of what is necessitated by P. There is, in fact, 1 an easy defense of the principle which utilizes the incompatibilist condition that S is able to do action K only if it is as yet undetermined whether or not S will K. With it, there is no question but that one is unable to accomplish what is already determined by what one was unable to prevent. Of course, this reasoning is unlikely to impress the compatibilist who rejects the condition outright and, expectedly, it is not the procedure of the proponents of the unavoidability argument. The latter might rest content with appeals to intuition, but more significant are defenses of the closure principle and independent derivations of the unavoidability argument that rely upon distinct principles concerning the logic of the practical modalities, for example, closure of ability under entailment (Cross 1986, Brown 1988) or, claims about the "fixity of the past" and the "inescapability of laws" (Ginet 1990).. (shrink)

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling epistemic problem. (...) Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

This paper evaluates a number of closure principles (for both knowledge and justification) that have appeared in the literature. Counterexamples are presented to all but one of these principles, which is conceded to be true but trivially so. It is argued that a consequence of the failure of these closure principles is that certain projects of doxastic logic are doomed, and that doxastic logic is of dubious merit for epistemologists interested in actual knowers in the actual world.

Mylan Engels paper (2004) is divided into two parts: a negative part, criticizing the costs of contextualism and a constructive part proposing a noncontextualist resolution of the skeptical problem. I will only address the constructive part here. The constructive part is composed of three elements: (i) a reconstruction or reformulation of the original skeptical argument, which draws on the notion of epistemic possibility (e-possibility), (ii) a distinction between two senses of knowledge (and two corresponding kinds of e-possibility): fallibilistic and infallibilistic, (...) and (iii) an argument which tries to hoist the skeptic by their own petard, namely the closure principle (CP). As I will argue, there are two ways to understand Engels anti-skeptical argument. Only in one interpretation does the argument depend on the proposed reconstruction of the skeptical argument in terms of e-possibility. But this version of the argument is unsound. More importantly, the skeptic has a strong prima facie objection at her disposal, which applies to both interpretations of the argument. If this objection is valid, Engels argument does not hold. But once it is invalidated, his argument is superfluous. (shrink)

In contrast to the most common view, I argue that one can consistently affirm that fundamental moral principles are objective and invariable, and yet are dependent on God. I explore and reject appealing to divine simplicity as a basis for affirming this conjunction. Rather, I develop the thesis that God is identical to the Good (the Identity View or IV) and argue that the IV does not fall to the criticisms of simplicity. I then consider a divine will theory (...) (DWT) that claims moral principles are grounded in God’s will. When the IV is conjoined with a DWT, there is reason to affirm an objective, theistically based ethics. The IV and DWT proposed here are models and while I attempt to increase their plausibility, I do not argue for their truth. The IV conjoined with a moral theory such as DWT explains the dependence of moral principles on God, while allowing for objectivity since morality is rooted in the eternal unchanging standard of the Good. (shrink)

We plead for a fluid margin, or mixed/indeterminate buffer zone, between Physical and Non-Physical Causal Closures, and for a Neutrosophic Causal Closure Principle claiming that the chances of all physical effects are determined by their prior partially physical and partially non-physical causes.

This paper assesses several prominent recent attacks on the view that epistemic justification is conceptually prior to knowledge. I argue that this view—call it the Received View (RV)—emerges from these attacks unscathed. I start with Timothy Williamson’s two strongest arguments for the claim that all evidence is knowledge (E>K), which impugns RV when combined with the claim that justification depends on evidence. One of Williamson’s arguments assumes a false epistemic closure principle; the other misses some alternative (to E>K) (...) explanations of a putative fact about the evidence a particular subject has. Next, I neutralize each of Jonathan Sutton’s three recent arguments to the conclusion that any justified belief constitutes knowledge. Finally, I consider a recent analysis of justification due to Alexander Bird, according to which justified belief is possible knowledge. I argue that Bird’s analysis delivers neither a sufficient nor (more importantly) a necessary condition for justification. [Word count: 149]. (shrink)

The conservation laws do not establish the central premise within the argument from causal overdetermination – the causal completeness of the physical domain. Contrary to David Papineau, this is true even if there is no non-physical energy. The combination of the conservation laws with the claim that there is no non-physical energy would establish the causal completeness principle only if, at the very least, two further causal claims were accepted. First, the claim that the only way that something non-physical (...) could affect a physical system is by affecting the amount of energy or momentum within it, or redistributing the energy and momentum within it. Second, the claim that redistribution of energy and momentum cannot be brought about without supplying energy or momentum. Both of these claims, however, are exceedingly difficult to defend in the context of the argument. (shrink)

A puzzle about warranted belief, often attributed to Kripke, has recently come to prominence. This puzzle claims to show that it follows from the possession of a warrant for one's belief in an empirical proposition that one is entitled to dismiss all subsequent evidence against that proposition as misleading. The two main solutions that have been offered to this puzzle in the recent literature - by James Cargile and David Lewis - argue for a revisionist epistemology which, respectively, either denies (...) the so-called 'Closure' principle that warrants transmit across known entailments, or 'contextualizes' the epistemic operator in question. In contrast, it is argued here that such revisionism is unnecessary because the puzzle in fact depends upon an ambiguity in the notion of warrant. It is claimed that once this ambiguity is made explicit then the puzzle dissipates. (shrink)