Fitch’s Paradox and Probabilistic Antirealism

Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.     

Distributed Knowability and Fitch’s Paradox

Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch’s paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show how we can combine our point of view on Fitch’s paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic.     

Factive knowability and the problem of possible omniscience

Philosophical Studies - Famously, the Church–Fitch paradox of knowability is a deductive argument from the thesis that all truths are knowable to the conclusion that all truths are known. In...     

Antirealism and universal knowability

Truth’s universal knowability entails its discovery. This threatens antirealism, which is thought to require it. Fortunately, antirealism is not committed to it. Avoiding it requires adoption (and extension) of Dag Prawitz’s position in his long-term disagreement with Michael Dummett on the notion of provability involved in intuitionism’s identification of it with truth. Antirealism (intuitionism generalized) must accommodate a notion of lost-opportunity truth (a kind of recognition-transcendent truth), and even truth consisting in the presence of unperformable verifications. Dummett’s position cannot abide this, while Prawitz’s can. Antirealism’s epistemic notion of truth derives from general features of its meaning theory, not from a universal knowability principle.     

Verificationists Versus Realists: The Battle Over Knowability

Verificationism is the doctrine stating that all truths are knowable. Fitch’s knowability paradox, however, demonstrates that the verificationist claim (all truths are knowable) leads to “epistemic collapse”, i.e., everything which is true is (actually) known. The aim of this article is to investigate whether or not verificationism can be saved from the effects of Fitch’s paradox. First, I will examine different strategies used to resolve Fitch’s paradox, such as Edgington’s and Kvanvig’s modal strategy, Dummett’s and Tennant’s restriction strategy, Beall’s paraconsistent strategy, and Williamson’s intuitionistic strategy. After considering these strategies I will propose a solution that remains within the scope of classical logic. This solution is based on the introduction of a truth operator. Though this solution avoids the shortcomings of the non-standard (intuitionistic) solution, it has its own problems. Truth, on this approach, is not closed under the rule of conjunction-introduction. I will conclude that verificationism is defensible, though only at a rather great expense.     

Truth and Nonsense: A Unified Reading of the Tractatus

Upon reading the Tractatus Logico-Philosophicus, readers might be confused about the nature of the book, since there seems to be a paradox introduced by the author’s two claims: a) the book conveys truths; b) propositions in the book are nonsense. Commentators disagree as to how best to resolve this paradox. Some hold that there are ineffable truths conveyed by nonsense propositions. Others deny this kind of truth, arguing that the book is not all nonsense, for there are some propositions in the book expressing at least the therapeutic truth that philosophical propositions are just nonsense. Recently, some interpreters have claimed that there is no truth at all. While the incoherence of the context is genuine, the purpose of the book is ethical. By diagnosing these interpretations, this paper intends to provide a new perspective toward reading the book by resolving the paradox. The truth of the Tractatus is not a propositional truth, but a specific true thought. The nonsense of the Tractatus is a transcending nonsense, rather than a pure nonsense. The book intends to attain the true thought about the mystical ethics by way of transcending nonsense. In this case, the Tractatus is not an incoherent work at all, since the paradox is not genuine. The fact that the nonsense part is a means to fulfill its ethical purpose makes the book a unified whole.     

Faint-hearted Anti-realism and Knowability

It is often claimed that anti-realists are compelled to reject the inference of the knowability paradox, that there are no unknown truths. I call those anti-realists who feel so compelled ‘faint-hearted’, and argue in turn that anti-realists should affirm this inference, if it is to be consistent. A major part of my strategy in defending anti-realism is to formulate an anti-realist definition of truth according to which a statement is true only if it is verified by someone, at some time. I also liberalize what is meant by a verification to allow for indirect forms of verification. From this vantage point, I examine a key objection to anti-realism, that it is committed to the necessary existence of minds, and reject a response to this problem set forth by Michael Hand. In turn I provide a more successful anti-realist response to the necessary minds problem that incorporates what I call an ‘agential’ view of verification. I conclude by considering what intellectual cost there is to being an anti-realist in the sense I am advocating.     

Future freedom and the fixity of truth: closing the road to limited foreknowledge open theism

Unlike versions of open theism that appeal to the alethic openness of the future, defenders of limited foreknowledge open theism (hereafter LFOT) affirm that some propositions concerning future contingents are presently true. Thus, there exist truths that are unknown to God, so God is not omniscient simpliciter. LFOT requires modal definitions of divine omniscience such that God knows all truths that are logically knowable. Defenders of LFOT have yet to provide an adequate response to Richard Purtill’s argument that fatalism logically follows from the omnitemporality of truth. Hasker believes a distinction between hard and soft facts prevents fatalism, but I argue that his defense fails in light of arguments involving divine necessity. Additionally, I point out that Hasker’s philosophy of language concerning divine names faces problems that cannot be overcome, given the versions of the dilemma of freedom and foreknowledge that motivate LFOT. Thus, contra Hasker, Swinburne, and van Inwagen, open theism necessitates the alethic openness of the future.     

Anti-realism and Epistemic Accessibility

I argue that Fitch’s ‘paradox of knowability’ presents no special problem for the epistemic anti-realist who believes that reality is epistemically accessible to us. For the claim which is the target of the argument (If p then it is possible to know p) is not a commitment of anti-realism. The epistemic anti-realist’s commitment is (or should be) to the recognizability of the states of affairs which render true propositions true, not to the knowability of the propositions themselves. A formal apparatus for discussing the recognizability of states of affairs is offered, and other prima facie similar approaches to the paradox argument are reviewed.     

Reliabilism and antirealist theories of truth

In order to shed light on the question of whether reliabilism entails or excludes certain kinds of truth theories, I examine two arguments that purport to establish that reliabilism cannot be combined with antirealist and epistemic theories of truth. I take antirealism about truth to be the denial of the recognition-transcendence of truth, and epistemic theories to be those that identify truth with some kind of positive epistemic status. According to one argument, reliabilism and antirealism are incompatible because the former takes epistemic justification to be recognition-transcendent in a certain sense that conflicts with the latter’s denial of the recognition-transcendence of truth. I show that, because the recognition-transcendence of reliabilist justification is significantly weaker than the recognition-transcendence required by a realist conception of truth, antirealist theories of truth that deny the strong transcendence of truth do not threaten the externalist character of reliabilism. According to the second argument, reliabilism cannot be combined with an epistemic truth theory because reliabilists analyze positive epistemic status in terms of truth but epistemic theorists analyze truth in terms of positive epistemic status. However, I argue that reliabilists who wish to adopt an epistemic theory of truth can avoid circularity by appealing to a multiplicity of positive epistemic statuses.     

Diamonds are a Philosopher's Best Friends

The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution offered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.     

Knowability as potential knowledge

The thesis that every truth is knowable is usually glossed by decomposing knowability into possibility and knowledge. Under elementary assumptions about possibility and knowledge, considered as modal operators, the thesis collapses the distinction between truth and knowledge (as shown by the so-called Fitch-argument). We show that there is a more plausible interpretation of knowability—one that does not decompose the notion in the usual way—to which the Fitch-argument does not apply. We call this the potential knowledge-interpretation of knowability. We compare our interpretation with the rephrasal of knowability proposed by Edgington and Rabinowicz and Segerberg, inserting an actuality-operator. This proposal shares some key features with ours but suffers from requiring specific transworld-knowledge. We observe that potential knowledge involves no transworld-knowledge. We describe the logic of potential knowledge by providing models for interpreting the new operator. Finally we show that the knowability thesis can be added to elementary conditions on potential knowledge without collapsing modal distinctions.     

A THICK REALIST CONSEQUENCE OF WRIGHT'S MINIMALISM

Abstract:   According to Wright's minimalism, a notion of truth neutral with respect to realism and antirealism can be built out of the notion of warranted assertibility and a set of a priori platitudes among which the Equivalence Schema has a prominent role. Wright believes that the debate about realism and antirealism will be properly and fruitfully developed if both parties accept the conceptual framework of minimalism. In this paper, I show that this conceptual framework commits the minimalist to the realist thesis that there are mind-independent propositions; with the consequence that minimalism is not neutral to realism and antirealism. I suggest that Wright could avert this conclusion if he rejected the customary interpretation of the Equivalence Schema according to which this Schema applies to propositions. This would however render minimalism unpalatable to philosophers who welcome the traditional reading of the Equivalence Schema and believe that propositions are bearers of truth.     

On Considering a Possible World as Actual: Robert Stalnaker

Saul Kripke made a convincing case that there are necessary truths that are knowable only a posteriori as well as contingent truths that are knowable a priori. A number of philosophers have used a two-dimensional model semantic apparatus to represent and clarify the phenomena that Kripke pointed to. According to this analysis, statements have truth-conditions in two different ways depending on whether one considers a possible world 'as actual' or 'as counterfactual' in determining the truth-value of the statement relative to that possible world. There are no necessary a posteriori or contingent a priori propositions: rather, contingent a priori and necessary a posteriori statements are statements that are necessary when evaluated one way, and contingent when evaluated the other way. This paper distinguishes two ways that the two-dimensional framework can be interpreted, and argues that one of them gives the better account of what it means to 'consider a world as actual', but that it provides no support for any notion of purely conceptual a priori truth.
'Hell is paved with primary intensions'
English proverb     

Gravitational lensing and Hacking's extragalactic irreality

In Extragalactic Reality: The Case of Gravitational Lensing Hacking resumes the discussion of scientific realism from the last chapter of Representing and Intervening. Since the criterion of manipulability cannot be applied to astronomical objects, experimental entity realism seems to be restricted to terrestrial entities. In fact, Hacking explicitly argues against astronomical realism. The case at issue is the existence of gravitational lenses. In this paper, I question Hacking's chief witness for astronomical antirealism: the gravitational lens system “0957+ 561”. It will be shown that Hacking's argumentation is misleading. Discussing astronomical realism as theory realism, Hacking focuses on the question of how to infer the existence of gravitational lenses from the truth of gravitational lens theory. But neither the reconstruction of gravitational lensing in terms of inference to the best explanation (IBE) nor the argument of underdetermination are tenable under closer inspection. My thesis is that a realist account of gravitational lensing can be given by relying on observation, causal capacities and home truths.     

Knowing linguistic conventions

A linguistic convention is a principle or norm that has been adopted by a person or linguistic community about how to use, and therefore what the meaning is of, a specific term. Examples of such norms or principles are those expressed by propositions that express the laws of logic or those that express implicit definitions. Arguments about the epistemic status of linguistic conventions, very broadly, fall into two camps: the one holds that the basis of linguistic conventions is objective and that, therefore, such conventions are genuinely truth-bearing. Knowledge of such conventions is therefore knowledge of the objective truth of such conventions. This camp might be labelled ‘realist’. The other holds that there is no known basis to linguistic conventions and that conventions are, to the best of our knowledge, not objective, but invented. Their truth is stipulated by the relevant speaker or linguistic community. Such truth is, consequently, trivial and knowledge of such conventions simply knowledge of the stipulation. This camp might be labelled ‘anti-realist’. These are three standard accounts of the epistemic status of linguistic conventions, which all play into the first camp: (1) knowledge by intuition, (2) inferential a priori knowledge and (3) a posteriori knowledge. I give reasons why these accounts should be rejected. I then argue that linguistic conventions, if conceived of as trivial truths, are knowable non-inferentially a priori. Such an epistemic account provides support for the second camp. In this regard, I marshal support from some recent work by Wright and Hale.     

From Standpoint Epistemology to Epistemic Oppression

Standpoint epistemology is committed to a cluster of views that pays special attention to the role of social identity in knowledge‐acquisition. Of particular interest here is the situated knowledge thesis. This thesis holds that for certain propositions p, whether an epistemic agent is in a position to know that p depends on some nonepistemic facts related to the epistemic agent's social identity. In this article, I examine two possible ways to interpret this thesis. My first goal here is to clarify existing interpretations of this thesis that appear in the literature but that are undeveloped and often mistakenly conflated. In so doing, I aim to make clear the different versions of standpoint epistemology that one might accept and defend. This project is of significance, I argue, because standpoint epistemology provides helpful tools for understanding a phenomenon of recent interest: epistemic oppression. My second goal is to provide an analysis that makes clear how each of the readings I put forth can be used to illuminate forms of epistemic oppression.     

Discovering knowability: a semantic analysis

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle all truths are knowable, when expressed as a bi-modal principle ${\diamondsuit}$ , yields an unacceptable omniscience property all truths are known. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of stability: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting stable knowability principle and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience.