Logical abductivism is the epistemic view about logic according to which logical theories are justified by abduction (or Inference to the Best Explanation), that is on how well they explain the relevant evidence, so that the correct logical theory turns out to be the one that explains it best. Arguably, this view should be equally applied to both deductive and non-deductive logics, abduction included. But while there seems to be nothing wrong in principle in using abduction (...) to determine the correct logical theories of deduction and induction, things might be more complicated regarding logical theories of abduction. We may wonder whether allowing for an abductive justification of a theory of abduction is an epistemically legitimate move, since here circularity casts its shadow and makes the situation darker. This is the issue to which this work is devoted. I will defend that, to be effective, an abductive justification for a theory of abduction calls for a justification of abduction in advance, which we do not yet have. (shrink)

I argue against abductivism about logic, which is the view that rational theory choice in logic happens by abduction. Abduction cannot serve as a neutral arbiter in many foundational disputes in logic because, in order to use abduction, one must first identify the relevant data. Which data one deems relevant depends on what I call one's conception of logic. One's conception of logic is, however, not independent of one's views regarding many of the foundational disputes that one may hope (...) to solve by abduction. (shrink)

The notion of strength has featured prominently in recent debates about abductivism in the epistemology of logic. Following Williamson and Russell, we distinguish between logical and scientific strength and discuss the limits of the characterizations they employ. We then suggest understanding logical strength in terms of interpretability strength and scientific strength as a special case of logical strength. We present applications of the resulting notions to comparisons between logics in the traditional sense and mathematical theories.

K. R. Popper distinguished between two main uses of logic, the demonstrational one, in mathematical proofs, and the derivational one, in the empirical sciences. These two uses are governed by the following methodological constraints: in mathematical proofs one ought to use minimal logical means (logical minimalism), while in the empirical sciences one ought to use the strongest available logic (logical maximalism). In this paper I discuss whether Popper’s critical rationalism is compatible with a revision of logic in (...) the empirical sciences, given the condition of logical maximalism. Apparently, if one ought to use the strongest logic in the empirical sciences, logic would remain immune to criticism and, thus, non-revisable. I will show that critical rationalism is theoretically compatible with a revision of logic in the empirical sciences. However, a question that remains to be clarified by the critical rationalists is what kind of evidence would lead them to revise the system of logic that underlies a physical theory, such as quantum mechanics? Popper’s falsificationist methodology will be compared with the recently advocated extension of the abductive methodology from the empirical sciences to logic by T. Williamson, since both of them arrive at the same conclusion concerning the status of classical logic. (shrink)

A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest (...) in—and endorsement of—justification holism due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory. (shrink)

Anti-exceptionalism about logic is the thesis that logic is not special. In this paper, I consider, and reject, a challenge to this thesis. According to this challenge, there are basic logical principles, and part of what makes such principles basic is that they are epistemically exceptional. Thus, according to this challenge, the existence of basic logical principles provides reason to reject anti-exceptionalism about logic. I argue that this challenge fails, and that the exceptionalist positions motivated by it are (...) thus unfounded. I make this case by disambiguating two senses of ‘basic’ and showing that, once this disambiguation is taken into account, the best reason we have for thinking that there are basic principles actually implies that those principles do not require a special epistemology. Consequently, the existence of basic logical principles provides reason to accept, rather than reject, anti-exceptionalism concerning the epistemology of logic. I conclude by explaining how an abductivist, anti-exceptionalist approach to the epistemology of logic can accommodate the notion of basic logical principles. (shrink)

Logical anti-exceptionalism is the view that logic is not special among the sciences. In particular, anti-exceptionalists claim that logical theory choice is effected on the same bases as any other theory choice procedure, i.e., by abduction, by weighting pros and cons of rival views, and by judging which theory scores best on a given set of parameters. In this paper, we first present the anti-exceptionalists favourite method for logical theory choice. After spotting on important features of the (...) method, we discuss how they lead to trouble when the subject matter of choice is logic itself. The major difficulty we find concerns the role of the logic employed to evaluate theory choice, or, more specifically, the role of the metalanguage employed to run the abductive method. When rival logical theories are being evaluated and compared, we argue, it is difficult not to beg some important questions; the metalanguage introduce biases difficult to avoid. These difficulties seem to be inherent to the method described. We suggest that they put some constraints on the scope of application of the method of abductive theory choice in logic and on the kind of disputes the anti-exceptionalist may plausibly expect to solve with it. We end the paper with some suggestions for how the anti-exceptionalist may address these issues on this front. (shrink)

Drawing on the epistemology of logic literature on anti-exceptionalism about logic, we set out to investigate the following metaphilosophical questions empirically: Is philosophy special? Are its methods (dis)continuous with science? More specifically, we test the following metaphilosophical hypotheses empirically: philosophical deductivism, philosophical inductivism, and philosophical abductivism. Using indicator words to classify arguments by type (namely, deductive, inductive, and abductive arguments), we searched through a large corpus of philosophical texts mined from the JSTOR database (N = 435,703) to find patterns (...) of argumentation. The results of our quantitative, corpus-based study suggest that deductive arguments are significantly more common than abductive arguments and inductive arguments in philosophical texts overall, but they are gradually and steadily giving way to non-deductive (i.e. inductive and abductive) arguments in academic philosophy. (shrink)

We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: an intension, taking care of truth conditions; and a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the (...) logic of knowledge per se for arbitrary agents, and isolate three explanatory factors for them: the topic-sensitivity of content; the fragmentation of knowledge states; the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections. (shrink)

To reconcile the standard possible worlds model of knowledge with the intuition that ordinary agents fall far short of logical omniscience, a Stalnakerian strategy appeals to two components. The first is the idea that mathematical and logical knowledge is at bottom metalinguistic knowledge. The second is the idea that non-ideal minds are often fragmented. In this paper, we investigate this Stalnakerian reconciliation strategy and argue, ultimately, that it fails. We are not the first to complain about the Stalnakerian (...) strategy. But in contrast to existing complaints, we want to cause trouble for the strategy directly on its home turf. That is, we will advance our objection while granting both the plausibility of the fragmentation component—save for an extreme version of it—and that of the metalinguistic component. Once our central objection to the Stalnakerian strategy is in place, we will show how it negatively affects Adam Elga and Augustín Rayo’s recent attempt to apply the Stalnakerian strategy in the context of Bayesian decision theory. (shrink)

This paper examines the evolution of Husserl’s philosophy of nonintuitive intentions. The analysis has two stages. First, I expose a mistake in Husserl’s account of non-intuitive acts from his 1901 Logical Investigations. I demonstrate that Husserl employs the term “signitive” too broadly, as he concludes that all non-intuitive acts are signitive. He states that not only meaning acts, but also the contiguity intentions of perception are signitive acts. Second, I show how Husserl, in his 1913/14 Revisions to the Sixth (...) Logical Investigation, amends his 1901 theory of non-intuitive acts, which he now calls “empty” intentions. He there accurately distinguishes empty meaning acts from the empty intentions of perception. In the conclusion, I reveal how Husserl’s alterations to his theory of non-intuitive intentions can inform our understanding of a larger shift in his philosophy. (shrink)

A good metaphysical account of logical form, must make clear why logical form is logical. However, this task has proved to be very elusive. Here, I analyze different attempts to meet this challenge and defend an inferential externalism where logical form is grounded on external logical relations as our most promising option.

Let T be any logical truth. Does the subject know that T (any random subject)? It is not rational for any subject to believe that they don’t, whoever they are. Similarly, it is not rational for them to believe that their evidence doesn’t support T, and it is not even rational for them to believe that they don’t believe that T. It is not rational for anyone anywhere at any time to believe that they don’t know that T. Such (...) are the conclusions arrived at in this paper. (shrink)

The paper presents a new approach to the history of analytic philosophy. Instead of exploring different kinds of analysis (Michael Beaney), or to marry analytic philosophy to the analytic / synthetic distinction (Scott Soames), we turn attention to the fact that it was rooted in two different types of logical constructing. The discrepancy between the two concepts of logical constructing produced much unclarity in our understanding of analytic philosophy.

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give the (...) latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ‘general logic’ built in this framework. (shrink)

James Sterba uses the Pauline Principle to argue that the occurrence of significant, horrendous evils is logically incompatible with the existence of a good God. The Pauline Principle states that (as a rule) one must never do evil so that good may come from it, and according to Sterba, this principle implies that God may not permit significant evils even if that permission would be necessary to secure other, greater goods. By contrast, I argue that the occurrence of significant evils (...) is logically compatible with the existence of a good God because victims of significant evils may themselves reasonably consent to their suffering. In particular, I argue that they may be able to accept their suffering if it turns out that there was no way for God to secure relevant greater goods (or prevent other, greater evils) except by way of allowing their suffering, and God also provides them with other compensating, heavenly comforts. After using this consent-based argument to address Sterba’s logical problem from evil, I briefly consider how this argument may also help address a related evidential problem from evil, which suggests that while it is possible that victims of significant evils would consent to their suffering, it is unlikely that they would do so. While I do not provide a definitive solution to this evidential problem of evil, I highlight one important example of a trade-off that God may need to make that would—along with the provision of compensating, heavenly comforts—potentially persuade victims of significant evils to consent to their suffering. Specifically, I argue that there may be a necessary trade-off that God needs to make between permitting significant evils (on the one hand) and protecting a certain, morally significant form of free will (on the other hand). (shrink)

This paper accomplishes three goals. First, the essay demonstrates that Edmund Husserl’s theory of meaning consciousness from his 1901 Logical Investigations is internally inconsistent and falls apart upon closer inspection. I show that Husserl, in 1901, describes non-intuitive meaning consciousness as a direct parallel or as a ‘mirror’ of intuitive consciousness. He claims that non-intuitive meaning acts, like intuitions, have substance and represent their objects. I reveal that, by defining meaning acts in this way, Husserl cannot account for our (...) experiences of countersensical, absurd, or impossible meanings. Second, I examine how Husserl came to recognize this 1901 mistake in his 1913/14 Revisions to the Sixth Logical Investigation. I discuss how he accordingly reformulates his understanding of non-intuitive meaning acts from the ground up in those Revisions, where this also allows for him to properly account for the experience of impossible meanings. Instead of describing them as mirrors of intuitions, Husserl takes non-intuitive meaning acts to be modifications of intuitions, where they have no substance and do not represent their objects. Finally, in the conclusion to this essay, I demonstrate how this fundamental change to his understanding of meaning consciousness forced Husserl to revise other central tenets of his philosophy, such that the trajectory of his thought can only be properly understood in light of these revisions to his theory of non-intuitive meaning consciousness. (shrink)

In the last decade Human-Computer Interaction (HCI) has started to focus attention on forms of persuasive interaction where computer technologies have the goal of changing users behavior and attitudes according to a predefined direction. In this work, we hypothesize a strong connection between logical fallacies (forms of reasoning which are logically invalid but cognitively effective) and some common persuasion strategies adopted within web technologies. With the aim of empirically evaluating our hypothesis, we carried out a pilot study on a (...) sample of 150 e-commerce websites. (shrink)

The aim of this paper is to discuss the “Austro-American” logical empiricism proposed by physicist and philosopher Philipp Frank, particularly his interpretation of Carnap’s Aufbau, which he considered the charter of logical empiricism as a scientific world conception. According to Frank, the Aufbau was to be read as an integration of the ideas of Mach and Poincaré, leading eventually to a pragmatism quite similar to that of the American pragmatist William James. Relying on this peculiar interpretation, Frank intended (...) to bring about a rapprochement between the logical empiricism of the Vienna Circle in exile and American pragmatism. In the course of this project, in the last years of his career, Frank outlined a comprehensive, socially engaged philosophy of science that could serve as a “link between science and philosophy”. (shrink)

According to a prevalent view among philosophers formal logic is the philosopher’s main tool to assess the validity of arguments, i.e. the philosopher’s ars iudicandi. By drawing on a famous dispute between Russell and Strawson over the validity of a certain kind of argument – of arguments whose premises feature definite descriptions – this paper casts doubt on the accuracy of the ars iudicandi conception. Rather than settling the question whether the contentious arguments are valid or not, Russell and Strawson, (...) upon discussing the proper logical analysis of definite descriptions, merely contrast converse informal validity assessments rendered explicit by nonequivalent logical for-malizations. (shrink)

In the theory of meaning, it is common to contrast truth-conditional theories of meaning with theories which identify the meaning of an expression with its use. One rather exact version of the somewhat vague use-theoretic picture is the view that the standard rules of inference determine the meanings of logical constants. Often this idea also functions as a paradigm for more general use-theoretic approaches to meaning. In particular, the idea plays a key role in the anti-realist program of Dummett (...) and his followers. In the theory of truth, a key distinction now is made between substantial theories and minimalist or deflationist views. According to the former, truth is a genuine substantial property of the truth-bearers, whereas according to the latter, truth does not have any deeper essence, but all that can be said about truth is contained in T-sentences (sentences having the form: ‘P’ is true if and only if P). There is no necessary analytic connection between the above theories of meaning and truth, but they have nevertheless some connections. Realists often favour some kind of truth-conditional theory of meaning and a substantial theory of truth (in particular, the correspondence theory). Minimalists and deflationists on truth characteristically advocate the use theory of meaning (e.g. Horwich). Semantical anti-realism (e.g. Dummett, Prawitz) forms an interesting middle case: its starting point is the use theory of meaning, but it usually accepts a substantial view on truth, namely that truth is to be equated with verifiability or warranted assertability. When truth is so understood, it is also possible to accept the idea that meaning is closely related to truth-conditions, and hence the conflict between use theories and truth-conditional theories in a sense disappears in this view. (shrink)

This essay critically assesses Roman Ingarden’s 1915 review of the second edition of Edmund Husserl’s Logical Investigations. I elucidate and critique Ingarden’s analysis of the differences between the 1901 first edition and the 1913 second edition. I specifically examine three tenets of Ingarden’s interpretation. First, I demonstrate that Ingarden correctly denounces Husserl’s claim that he only engages in an eidetic study of consciousness in 1913, as Husserl was already performing eidetic analyses in 1901. Second, I show that Ingarden is (...) misguided, when he asserts that Husserl had fully transformed his philosophy into a transcendental idealism in the second edition. While Husserl does appear to adopt a transcendental phenomenology by asserting–in his programmatic claims–that the intentional content and object are now included in his domain of research, he does not alter his actual descriptions of the intentional relationship in any pertinent manner. Third, I show Ingarden correctly predicts many of the insights Husserl would arrive at about logic in his late philosophy. This analysis augments current readings of the evolution of Ingarden’s philosophy, by more closely examining the development of his largely neglected early thought. I execute this critical assessment by drawing both from Husserl’s later writings and from recent literature on the Investigations. By doing so, I hope to additionally demonstrate how research on the Investigations has matured in the one hundred years since the release of that text, while also presenting my own views concerning these difficult interpretative issues. (shrink)

This paper is partly inspired by a well-known debate between Ruth Barcan Marcus, Terence Parsons and W. V. 0. Quine in the sixties> concerning the extent to which Quantified Modal Logic is committed to Essentialism; the issue nevertheless goes back to the origins of "analytic philosophy'', to the reflections of Frege, Russell, and the earlier Wittgenstein on the nature of logic. By elaborating on a suggestion by Quine, we purport to show that there is a relevant and interesting way to (...) look at the ontological commitments of logical systems such that they are stronger than they are usually taken to be. (shrink)

This paper offers a more comprehensive and accurate picture of Edmund Husserl’s semiotics. I not only clarify, as many have already done, Husserl’s theory of signs from the 1901 Logical Investigations, but also examine how he transforms that element of his philosophy in the 1913/14 Revisions to the Sixth Logical Investigation. Specifically, the paper examines the evolution of two central tenets of Husserl’s semiotics. I first look at how he modifies his classification of signs. I disclose why he (...) revised his 1901 distinction between indicators and expressions, instead claiming in 1913/14 that the divisions should be drawn between indicators, signals, and categorial signs. Second, I elucidate why Husserl overturned his conclusion from the Investigations, that signs execute their signitive operations in three steps, because he recognizes that categorial signs and their meant object are experienced all at once. By exploring the transformation of these two tenets of Husserl’s semiotics, we will see that he conceived of the First Investigation only as a starting or jumping off point for future analyses of signitive experience, rather than as his final account. This analysis will further reveal novel insights about Husserl’s understanding of intersubjectivity, passivity, and temporality. (shrink)

What are people who disagree about logic disagreeing about? The paper argues that (in a wide range of cases) they are primarily disagreeing about how to regulate their degrees of belief. An analogy is drawn between beliefs about validity and beliefs about chance: both sorts of belief serve primarily to regulate degrees of belief about other matters, but in both cases the concepts have a kind of objectivity nonetheless.

The paper argues against a commitment to metaphysical necessity, semantic modalities are enough. The best approaches to elucidate the semantic modalities are (still) versions of lingustic ersatzism and fictionalism, even if only developed in parts. Within these necessary properties and the difference between natural and semantic laws can be accounted for. The proper background theory for this is an updated version of Logical Empiricism, which is congenial to recent trends in Structural Realism. The anti-metaphysical attitude of Logical Empiricism (...) deserves revitalization. Another target besides metaphysical necessity are substantial forms of iterated modalities, as used, for instance, in the philosophy of religion. (shrink)

This paper illustrates what a philosophical and a logical investigation of colors amounts to in contrast to other kinds of color analysis such as physical, physiological, chemical, psychological or cultural analysis of colors. Neither a philosophical nor a logical analysis of colors is concerned with specific aspects of colors. Rather, these kinds of color analysis are concerned with what one might call “logical foundations of color theory”. I will illustrate this first by considering philosophical and then (...) class='Hi'>logical analysis of colors. (shrink)

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his (...) understanding of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

The purpose of this article is to support the logical incompatibility of the opposing views as a criterion for characterizing disagreements as genuinely metaphysical. That is, I intend to argue that a specific dispute is a metaphysical disagreement only when the conflicting views are governed by different logics. If correct, this criterion would not only help to separate merely verbal from genuine metaphysical debates, but it also would ground an argument against deflationism, guaranteeing the substantiality and relevance of metaphysics. (...) I intend to clarify the criterion, to present its basic foundations and commitments, to give some logical and metaphysical motivations for its adoption and some examples of its application. (shrink)

The beauty of Anselm’s ontological argument is, I believe, that no matter how one approaches it, one cannot refute it without making a significant metaphysical assumption, one that is likely to be contentious in its own right. Peter Millican disagrees. He introduces an objection according to which one can refute the argument merely by analysing its shallow logical details, without making any significant metaphysical assumption. He maintains, moreover, that his objection does not depend on a specific reading of the (...) relevant Anselmian text; in fact, Millican claims that his objection is applicable to every version of the ontological argument. In this paper, I argue that millican’s objection does not succeed, because, contrary to what he says, in order to justify his objection he does have to make a deep metaphysical assumption and rely on a specific reading of Anselm’s text. (shrink)

In this article, the attempts by David Lewis and Brian Loar to make perspicuous the logical form of sentences ascribing propositional attitudes to individuals are set out and criticized. Both work within the assumption of the truth of 'type' physicalism, and require that logically perspicuous attitude ascriptions be compatible with the demands of such a doctrine. It is argued that neither carry out this task successfully - Lewis's perspicuous ascriptions have counter-intuitive implications, while Loar's avoidance of these undermines type (...) physicalism itself. (shrink)

This paper presents an attempt to bridge the gap between logical and cognitive treatments of strategic reasoning in games. There have been extensive formal debates about the merits of the principle of backward induction among game theorists and logicians. Experimental economists and psychologists have shown that human subjects, perhaps due to their bounded resources, do not always follow the backward induction strategy, leading to unexpected outcomes. Recently, based on an eye-tracking study, it has turned out that even human subjects (...) who produce the outwardly correct ‘backward induction answer’ use a different internal reasoning strategy to achieve it. The paper presents a formal language to represent different strategies on a finer-grained level than was possible before. The language and its semantics help to precisely distinguish different cognitive reasoning strategies, that can then be tested on the basis of computational cognitive models and experiments with human subjects. The syntactic framework of the formal system provides a generic way of constructing computational cognitive models of the participants of the Marble Drop game. (shrink)

This essay presents a heterodox reading of the issue of solipsism in Wittgenstein’s Tractatus Logico-Philosophicus, out of which the whole of the TLP can be re-read. Inspired by, though not dependent on, the themes of virtuality and singularity found in Deleuze’s ‘transcendental empiricism’, Wittgenstein’s concept of ‘logical space’ is here complexly related to the paradoxes of the ‘metaphysical subject’ and ‘solipsism,’ within which the strictures of sense are defined, and through which the logico-pictorial scaffolding of the TLP precipitates its (...) own systematic dissolution. It shows how nonsense envelopes not only not idle chatter, and metaphysical confusion, but sense itself. (shrink)

This paper discusses critically what simulation models of the evolution ofcooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” and the modeling tradition it has inspired. Hardly any of the many simulation models of the evolution of cooperation in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this research design was (...) fundamentally flawed, because it is not possible to draw general empirical conclusions from theoretical simulations. At best such simulations can claim to prove logical possibilities, i.e. they prove that certain phenomena are possible as the consequence of the modeling assumptions built into the simulation, but not that they are possible or can be expected to occur in reality I suggest several requirements under which proofs of logical possibilities can nevertheless be considered useful. Sadly, most Axelrod-style simulations do not meet these requirements. I contrast this with Schelling’s neighborhood segregation model, thecore mechanism of which can be retraced empirically. (shrink)

In this work, we propose a definition of logical consequence based on the relation between the quantity of information present in a particular set of formulae and a particular formula. As a starting point, we use Shannon‟s quantitative notion of information, founded on the concepts of logarithmic function and probability value. We first consider some of the basic elements of an axiomatic probability theory, and then construct a probabilistic semantics for languages of classical propositional logic. We define the quantity (...) of information for the formulae of these languages and introduce the concept of informational logical consequence, identifying some important results, among them: certain arguments that have traditionally been considered valid, such as modus ponens, are not valid from the informational perspective; the logic underlying informational logical consequence is not classical, and is at the least paraconsistent sensu lato; informational logical consequence is not a Tarskian logical consequence. (shrink)

In this paper, I argue that Goff's view that universal consciousness grounds logical laws such as the law of non-contradiction cannot be true on the grounds that we cannot guarantee the classical logic loving nature of universal consciousness that Goff desires in order to ground logical laws. I will present three arguments to show this.

Starting from certain metalogical results, I argue that first-order logical truths of classical logic are a priori and necessary. Afterwards, I formulate two arguments for the idea that first-order logical truths are also analytic, namely, I first argue that there is a conceptual connection between aprioricity, necessity, and analyticity, such that aprioricity together with necessity entails analyticity; then, I argue that the structure of natural deduction systems for FOL displays the analyticity of its truths. Consequently, each philosophical approach (...) to these truths should account for this evidence, i.e., that first-order logical truths are a priori, necessary, and analytic, and it is my contention that the semantic account is a better candidate. (shrink)

It has been argued recently that classical theism and Lewisian modal realism are incompatible theses. The most substantial argument to this effect takes the form of a trilemma. It argues that no sense can be made of God’s being a necessary being in the modal realistic picture, on pain of, among other things, modal collapse. The question of this essay is: Is that so? My goal here is to detail the reasons that have been offered in support of this contention (...) and then defend the coherence of theistic modal realism from the trilemma. I call my reply to the argument an “Anselmian-Thomistic” defense, since it appeals to resources from classical medieval philosophy, especially from Anselm and Aquinas. (shrink)

Traditionally, pronouns are treated as ambiguous between bound and demonstrative uses. Bound uses are non-referential and function as bound variables, and demonstrative uses are referential and take as a semantic value their referent, an object picked out jointly by linguistic meaning and a further cue—an accompanying demonstration, an appropriate and adequately transparent speaker’s intention, or both. In this paper, we challenge tradition and argue that both demonstrative and bound pronouns are dependent on, and co-vary with, antecedent expressions. Moreover, the semantic (...) value of a pronoun is never determined, even partly, by extra-linguistic cues; it is fixed, invariably and unambiguously, by features of its context of use governed entirely by linguistic rules. We exploit the mechanisms of Centering and Coherence theories to develop a precise and general meta-semantics for pronouns, according to which the semantic value of a pronoun is determined by what is at the center of attention in a coherent discourse. Since the notions of attention and coherence are, we argue, governed by linguistic rules, we can give a uniform analysis of pronoun resolution that covers bound, demonstrative, and even discourse bound readings. Just as the semantic value of the first-person pronoun ‘I’ is conventionally set by a particular feature of its context of use—namely, the speaker—so too, we will argue, the semantic values of other pronouns, including ‘he’, are conventionally set by particular features of the context of use. (shrink)

There are two ways of thinking about instants of time: "spatial" accounts emphasize the similarities between instants and places; "modal" accounts focus on the parallels between times and possible worlds. My aim in this paper is to draw attention to one respect in which times are more similar to possible worlds than they are to places.

In this paper we discuss three examples of the appropriation of Kuhn’s ideas in philosophy of science. First we deal with classical logical empiricism. Perhaps somewhat surprisingly, the arch-logical empiricist Carnap considered Kuhn’s socio-historical account as a useful complementation, and not as a threat of the philosophy of science of logical empiricism. As a second example we consider the attempt of the so-called struc- turalist philosophy of science to provide a “rational reconstruction” of Kuhn’s approach. Finally, we (...) will deal with Friedman’s proposal to apply Kuhn’s ideas to the formulation of a modernized, historically enlightened Kantian approach that is based on the concept of a non-apodictic constitutive and historically moving a priori. (shrink)

In appearance, Husserl’s writings seem not to have had any influence on linguistic research, nor does what the German philosopher wrote about language seem to be worth a place in the history of linguistics. The purpose of the paper is exactly to contrast this view, by reassessing both the position and the role of Husserl’s early masterpiece — the Logical Investigations — within the history of linguistics. To this end, I will focus mainly on the third (On the theory (...) of wholes and parts) and fourth (The distinction between independent and non-independent meanings) Investigations, paying special attention to Husserl’s mereology and to the idea of a general pure grammar. The paper tries to situate the third and fourth Logical Investigation within the general context of late nineteenth-century and early twentieth-century linguistics and furthermore attempts to show the historical and theoretical importance of the Logical Investigations for the birth and the development of one of the most important linguistic “schools” of the twentieth century, namely structural linguistics. (shrink)

According to Aristotle if a universal proposition (for example: “All men are white”) is true, its contrary proposition (“All men are not white”) must be false; and, according to Aristotle, if a universal proposition (for example: “All men are white”) is true, its contradictory proposition (“Not all men are white”) must be false. I agree with what Aristotle wrote about universal propositions, but there are universal propositions which have no contrary proposition and have no contradictory proposition. The proposition X “All (...) the propositions that contradict this proposition are true” does not have the contrary proposition and does not have the contradictory proposition. In fact: FEX “All the propositions that contradict this proposition are not true” has a different subject: the subject of the proposition X is constituted by all the propositions that contradict the proposition X; by contrast, the subject of the proposition FEX is constituted by all the propositions that contradict the proposition FEX. And FOX “Not all the propositions that contradict this proposition are true” has a different subject: the subject of the proposition X is constituted by the propositions that contradict the proposition X; by contrast, the subject of the proposition FOX is constituted by the propositions that contradict the proposition FOX. According to Aristotle, a singular proposition (in his example: "Socrates is white") which is true must have its negative proposition ("Socrates is not white") which is false. I agree with Aristotle, but there are singular propositions which do not have the corresponding negative proposition. The proposition (or, rather, the pseudo-proposition) L “This same statement is not true” does not have the negative proposition because the proposition FNL “This same statement is true” has a different subject from the subject of the proposition L: the subject of the proposition L is the proposition L; by contrast, the subject of the proposition FNL is the proposition FNL. L and FNL cannot have the same subject. By contrast, the proposition M “This mount is entirely in Swiss territory” and the proposition NM “This mount is not entirely in Swiss territory” can have the same subject (for example, the Mount Eiger): in case the subject of the proposition M and the subject of the proposition NM is the same, M and NM are opposite propositions, NM is the negative proposition of M. By contrast, the proposition (or, rather, the pseudo-proposition) L "This same statement is not true" cannot have the corresponding negative proposition because FNL "This same statement is true" has a different subject: the subject of L is L ; by contrast, the subject of FNL is FNL. Then the paper continues by analyzing some variants of the liar’s paradox: L1 “The statement L1 is not true”; the so-called liar cycle; and the so-called Yablo’s paradox. (shrink)

In this paper I will show the problems that are encountered when dealing with uniqueness of connectives in a bilateralist setting within the larger framework of proof-theoretic semantics and suggest a solution. Therefore, the logic 2Int is suitable, for which I introduce a sequent calculus system, displaying - just like the corresponding natural deduction system - a consequence relation for provability as well as one dual to provability. I will propose a modified characterization of uniqueness incorporating such a duality of (...) consequence relations, with which we can maintain uniqueness in a bilateralist setting. (shrink)

This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...) notions and proposes a more physical treatment of mathematical objects separating the objects from tools used to study them. It both offers a possibility to create new numerical methods using infinities and infinitesimals in floating-point computations and allows one to study certain mathematical objects dealing with infinity more accurately than it is done traditionally. In these notes, we explain that even though both methodologies deal with infinities and infinitesimals, they are independent and represent two different philosophies of Mathematics that are not in a conflict. It is proved that texts :539–555, 2017; Gutman and Kutateladze in Sib Math J 49:835–841, 2008; Kutateladze in J Appl Ind Math 5:73–75, 2011) asserting that the ①-based methodology is a part of non-standard analysis unfortunately contain several logical fallacies. Their attempt to show that the ①-based methodology can be formalized within non-standard analysis is similar to trying to show that constructivism can be reduced to the traditional Mathematics. (shrink)

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation (...) into conditional connectives may show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

This paper proposes substitutional definitions of logical truth and consequence in terms of relative interpretations that are extensionally equivalent to the model-theoretic definitions for any relational first-order language. Our philosophical motivation to consider substitutional definitions is based on the hope to simplify the meta-theory of logical consequence. We discuss to what extent our definitions can contribute to that.

Dutch Book Arguments (DBAs) have been invoked to support various requirements of rationality. Some are plausible: probabilism and conditionalization. Others are less so: credal transparency and reflection. Anna Mahtani has argued for a new understanding of DBAs which, she claims, allow us to keep the DBAs for probabilism (and perhaps conditionalization) and reject the DBAs for credal transparency and reflection. I argue that Mahtani’s new account fails as (a) it does not support highly plausible requirements of rational coherence and (b) (...) it does not, even setting aside the first objection, succeed in undermining the DBAs for credal transparency or reflection. (shrink)