The Knowability Paradox is a logical argument to the effect that, if there are truths not actually known, then there are unknowable truths. Recently, Alexander Paseau and Bernard Linsky have independently suggested a possible way to counter this argument by typing knowledge. In this article, we argue against their proposal that if one abstracts from other possible independent considerations supporting reasons for typing knowledge and considers the motivation for a type-theoretic approach with respect to the Knowability Paradox alone, there is (...) no substantive philosophical motivation to type knowledge, except that of solving the paradox. Every attempt to independently justify the typing of knowledge is doomed to failure. (shrink)

While defending the principle of non-contradiction in Metaphysics 4, Aristotle argues that the Measure Doctrine of Protagoras is equivalent to the claim that all contradictions are true; given all appearances are true (as the Protagorean maintains), anytime people disagree we get a true contradiction. This argument seems clearly invalid: nothing guarantees that actual disagreement occurs over every matter of fact. The argument in fact works perfectly, I propose, because the Protagorean view falls prey to a version of Fitch's “paradox” of (...) knowability. The proposed reading shows how Aristotle treats the Protagorean view at issue as an epistemic theory of truth distinct from the mere claim that all appearances are true (which other opponents put forward on different grounds) and reveals Aristotle's underlying concern with the modal collapse of possibility into actuality. The revised Protagorean view Aristotle confronts in a subsequent chapter is furthermore best understood as an attempt to avoid this Fitch-style result. (shrink)

A novel solution to the knowability paradox is proposed based on Kant’s transcendental epistemology. The ‘paradox’ refers to a simple argument from the moderate claim that all truths are knowable to the extreme claim that all truths are known. It is significant because anti-realists have wanted to maintain knowability but reject omniscience. The core of the proposed solution is to concede realism about epistemic statements while maintaining anti-realism about non-epistemic statements. Transcendental epistemology supports such a view by providing for a (...) sharp distinction between how we come to understand and apply epistemic versus non-epistemic concepts, the former through our capacity for a special kind of reflective self-knowledge Kant calls ‘transcendental apperception’. The proposal is a version of restriction strategy: it solves the paradox by restricting the anti-realist’s knowability principle. Restriction strategies have been a common response to the paradox but previous versions face serious difficulties: either they result in a knowability principle too weak to do the work anti-realists want it to, or they succumb to modified forms of the paradox, or they are ad hoc. It is argued that restricting knowability to non-epistemic statements by conceding realism about epistemic statements avoids all versions of the paradox, leaves enough for the anti-realist attack on classical logic, and, with the help of transcendental epistemology, is principled in a way that remains compatible with a thoroughly anti-realist outlook. (shrink)

Some attempts have been made to block the Knowability Paradox and other modal paradoxes by adopting a type-theoretic framework in which knowledge and necessity are regarded as typed predicates. The main problem with this approach is that when these notions are simultaneously treated as predicates, a new kind of paradox appears. I claim that avoiding this paradox either by weakening the Knowability Principle or by introducing types for both predicates is rather messy and unattractive. I also consider the prospect of (...) using the truth predicate to emulate other modal notions. It turns out that this idea works quite well. (shrink)

Some philosophers have argued that a standard of correctness is constitutive of the concept or the essence of belief. By this claim they mean, roughly, that a mental state is a belief partially in virtue of being correct if and only if its content is true. In this paper I provide a new argument in support of the constitutivity of the correctness standard for belief. I first argue that the standard expresses a conceptual necessity. Then I argue that, since conceptual (...) necessities are such in virtue of some concept, the standard must also be necessary in virtue of some concept. Finally, I provide an argument by exclusion to the effect that the standard is necessary in virtue of the concept of belief. (shrink)

Some propositions are structurally unknowable for certain agents. Let me call them ‘Moorean propositions’. The structural unknowability of Moorean propositions is normally taken to pave the way towards proving a familiar paradox from epistemic logic—the so-called ‘Knowability Paradox’, or ‘Fitch’s Paradox’—which purports to show that if all truths are knowable, then all truths are in fact known. The present paper explores how to translate Moorean statements into a probabilistic language. A successful translation should enable us to derive a version of (...) Fitch’s Paradox in a probabilistic setting. I offer a suitable schematic form for probabilistic Moorean propositions, as well as a concomitant proof of a probabilistic Knowability Paradox. Moreover, I argue that traditional candidates to play the role of probabilistic Moorean propositions will not do. In particular, we can show that violations of the so-called ‘Reflection Principle’ in probability need not yield structurally unknowable propositions. Among other things, this should lead us to question whether violating the Reflection Principle actually amounts to a clear case of epistemic irrationality, as it is often assumed. This result challenges the importance of the principle as a tool to assess both synchronic and diachronic rationality—a topic which is largely independent of Fitch’s Paradox—from a somewhat unexpected source. (shrink)

Recently, it has been observed that the usual type-theoretic restrictions are not enough to block certain paradoxes involving two or more predicates. In particular, when we have a self-referential language containing modal predicates, new paradoxes might appear even if there are type restrictions for the principles governing those predicates. In this article we consider two type-theoretic solutions to multimodal paradoxes. The first one adds types for each of the modal predicates. We argue that there are a number of problems with (...) most versions of this approach. The second one, which we favour, represents modal notions by using the truth predicate together with the corresponding modal operator. This way of doing things is not only useful because it avoids multimodal paradoxes, but also because it preserves the expressive capacity of the language. As an example of the sort of theory we have in mind, we provide a type-theoretic axiomatization that combines truth with necessity and knowledge. (shrink)

The Fitch paradox poses a serious challenge for anti-realism. This paper investigates the option for an anti-realist to answer the challenge by restricting the knowability principle. Based on a critical discussion of Dummett's and Tennant's suggestions for a restriction desiderata for a principled solution are developed. In the second part of the paper a different restriction is proposed. The proposal uses the notion of uniform formulas and diagnoses the problem arising in the case of Moore sentences in the different status (...) propositional letters receive. The new proposal is able to avoid some of the criticism on its predecessors. (shrink)

In an attempt to improve upon Alexander Pruss’s work (The principle of sufficient reason: A reassessment, pp. 240–248, 2006), I (Weaver, Synthese 184(3):299–317, 2012) have argued that if all purely contingent events could be caused and something like a Lewisian analysis of causation is true (per, Lewis’s, Causation as influence, reprinted in: Collins, Hall and paul. Causation and counterfactuals, 2004), then all purely contingent events have causes. I dubbed the derivation of the universality of causation the “Lewisian argument”. The Lewisian (...) argument assumed not a few controversial metaphysical theses, particularly essentialism, an incommunicable-property view of essences (per Plantinga’s, Actualism and possible worlds, reprinted in: Davidson (ed.) Essays in the metaphysics of modality, 2003), and the idea that counterfactual dependence is necessary for causation. There are, of course, substantial objections to such theses. While I think a fight against objections to the Lewisian argument can be won, I develop, in what follows, a much more intuitive argument for the universality of causation which takes as its inspiration a result from Frederic B. Fitch’s work (J Symb Logic 28(2):135–142, 1963) [with credit to who we now know was Alonzo church’s, Referee Reports on Fitch’s Definition of value, in: (Salerno (ed.), New essays on the knowability paradox, 2009)] that if all truths are such that they are knowable, then (counter-intuitively) all truths are known. The resulting Church–Fitch proof for the universality of causation is preferable to the Lewisian argument since it rests upon far weaker formal and metaphysical assumptions than those of the Lewisian argument. (shrink)

A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic anti-realism. Since its rediscovery by Hart and McGinn (1976), many solutions to the paradox have been offered. In this article, we (...) present a new proof to the effect that not all truths are knowable, which rests on different assumptions from those of the original argument published by Fitch. We highlight the general form of the knowability paradoxes, and argue that anti-realists who favour either an hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up anti-realism or opt for a highly controversial interpretation of the principle that every truth is knowable. (shrink)

Alonzo Church (1903–1995) was a renowned mathematical logician, philosophical logician, philosopher, teacher and editor. He was one of the founders of the discipline of mathematical logic as it developed after Cantor, Frege and Russell. He was also one of the principal founders of the Association for Symbolic Logic and the Journal of Symbolic Logic. The list of his students, mathematical and philosophical, is striking as it contains the names of renowned logicians and philosophers. In this article, we focus primarily on (...) Church’s philosophical contributions. (For an account of his life and academic history see the Introduction to The Collected Works of Alonzo Church (2019).) However, we also discuss his mathematical results when it is desirable to do so in order to pursue a philosophical issue. (shrink)

One diagnosis of Fitch’s paradox of knowability is that it hinges on the factivity of knowledge: that which is known is true. Yet the apparent role of factivity and non-factive analogues in related paradoxes of justified belief can be shown to depend on familiar consistency and positive introspection principles. Rejecting arguments that the paradox hangs on an implausible consistency principle, this paper argues instead that the Fitch phenomenon is generated both in epistemic logic and logics of justification by the interaction (...) of analogues of the knowability principle and positive introspection theses that are characteristic of, even if not entailed by, epistemic internalism. (shrink)

Donald Davidson brought to our attention deviant causal chains as a problem for causal theories of action. Consider Davidson's own example: " A climber might want to rid himself of the weight and danger of holding another man on a rope, and he might know that by loosening his hold on the rope he could rid himself of the weight and danger. This belief and want might so unnerve him as to cause him to loosen his hold, and yet it (...) might be the case that he never chose to loosen his hold, nor did he do it intentionally. " The loosening of the hold on the rope is an action, according to a simple causal theory of action earlier developed by Davidson , if we can describe it in a way that renders it intentional under that description. Is there a way of describing the climber's loosening of his hold of the rope as intentional? Did he intentionally loosen his hold? Well, his loosening his hold is both rationalized and explained causally with reference to the beliefs and desires held by the climber. But there seems to be something wrong with the causal chain.Is there a simple fix? Could we not say that even if the loosening of the hold on the rope is caused by a desire held by the climber it is not caused by any proximate desire of the climber ? Or, to give a new twist to this well-known argument, could we not say that the loosening of the hold on the rope is not caused in a way that is responsive to the desire? This latter idea has recently been suggested by Markus E. Schlosser as a simple solution to the …. (shrink)

Dispositionalist accounts of belief define beliefs in terms of specific sets of dispositions. In this article, I provide a blind-spot argument against these accounts. The core idea of the argument is that beliefs having the form [p and it is not manifestly believed that p] cannot be manifestly believed. This means that one cannot manifest such beliefs in one’s assertions, conscious thoughts, actions, behaviours, or any other type of activity. However, if beliefs are sets of dispositions, they must be manifestable (...) in some way. Therefore, according to my argument, beliefs are not sets of dispositions. The argument is defended against some possible objections. (shrink)