The terms ‘compatibilism’ and ‘incompatibilism’ were introduced in the mid-20th century to name conflicting views about the logical relationship between the thesis of determinism and the thesis that someone has free will. These technical terms were originally introduced within a specific research paradigm, the classical analytic paradigm. This paradigm is now in its final stages of degeneration and few free-will theorists still work within it (i.e. using its methods, granting its substantive background assumptions, etc.). This chapter discusses how the ambiguity (...) of the terms ‘incompatibilism’ and ‘compatibilism’ took root as the classical analytic paradigm declined and why this matters to the contemporary debate. Among other things, I explain why the ambiguity of these anachronistic terms, though relatively innocuous when they were first introduced, is now encouraging theorists to tolerate and perpetuate serious philosophical errors (e.g. to conflate relations as different in kind and importance as correlation and causation, to promote uncontentiously invalid arguments, and to equivocate in ways that keep the free-will debate mired in pseudo-stalemates). I also suggest a new framework for anyone looking for relief from the confusion and deadlock created by quixotic attempts to redefine classical narratives and jargon so that they adequately describe the dialectical contours of the contemporary free-will debate. In addition, this new framework allows philosophers to start cross-pollinating work on free will and other famous problems of luck and control, e.g. the paradox of moral luck. (To see the distinctions applied to the philosophical problems of causal luck, constitutive luck, and moral luck, please see my essay "Free Will, Self-Creation, and the Paradox of Moral Luck" (Midwest Studies in Philosophy, 2019). -/- . (shrink)

There is no concept more central to logic and critical thinking than the concept of an argument. I here address the definition of ‘argument’ in the logical sense of the term and defend the claim that many current proposals, once they are interpreted in a way that makes them sufficiently precise, are extensionally inadequate. Definitions found in some contemporary, prominent critical thinking textbooks will serve as a springboard. I claim that each may be interpreted in an absolutist way or a (...) relativistic way, yet all turn out to be objectionable no matter which route is taken. I finish with a proposal on which the definition of ‘argument’ is an absolutist one, yet one that avoids the problems discussed for the earlier proposals. (shrink)

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...) in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (shrink)

This volume presents a selection of papers reflecting key theoretical issues in argumentation theory. Its six sections are devoted to specific themes, including the analysis and evaluation of argumentation, argument schemes and the contextual embedding of argumentation. The section on general perspectives on argumentation discusses the trends of empiricalization, contextualization and formalization, offers descriptions of the analytical and evaluative tools of informal logic, and highlights selected principles that argumentation theorists do and do not agree upon. In turn, the section on (...) linguistic approaches to argumentation focuses on the problem of distinguishing between explanation and argument, while also elaborating on the role of verbal indicators of argument schemes. All essays included in this volume point out notable recent developments in the study of argumentation. (shrink)

One of us has previously argued that the Church-Turing Thesis (CTT), contra Elliot Mendelson, is not provable, and is — light of the mind’s capacity for effortless hypercomputation — moreover false (e.g., [13]). But a new, more serious challenge has appeared on the scene: an attempt by Smith [28] to prove CTT. His case is a clever “squeezing argument” that makes crucial use of Kolmogorov-Uspenskii (KU) machines. The plan for the present paper is as follows. After covering some necessary preliminaries (...) regarding the nature of CTT, and taking note of the fact that this thesis is “intrinsically cognitive” (§2), we: sketch out, for context, an open-minded position on CTT and related matters (§3); explain the formal structure of squeezing arguments (§4); after a review of KU-machines, formalize Smith’s case (§5); give our objections to certain assumptions in Smith’s argument (§6); support these objections with some evidence from general but limited-agent problem solving (§7); and explain why Smith’s argument is inconclusive (§8). We end with some brief, concluding remarks, some of which point toward near-future work that will build on the present paper (§9). (shrink)

The power of Wittgenstein's N operator described in the Tractatus is that every proposition which can be expressed in the Russellian variant of the predicate calculus familiar to him has an equivalent proposition in an extended variant of his N operator notation. This remains true if the bound variables are understood in the usual inclusive sense or in Wittgenstein's restrictive exclusive sense. The problematic limit of Wittgenstein's N operator comes from his claim that symbols alone reveal the logical status of (...) propositions. This would require knowledge of the size of the Tractarian domain of unchangeable, simple objects, and this, Wittgenstein maintained, cannot be known. (shrink)

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...) We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference. (shrink)

This article examines the traditional and modern doctrines of categorical propositions and argues that both doctrines have serious problems. While the doctrines disagree about existential imports...

When modeling informal proofs like that of Euclid’s Elements using a sound logical system, we go from proofs seen as somewhat unrigorous – even having gaps to be filled – to rigorous proofs. However, metalogic grounds the soundness of our logical system, and proofs in metalogic are not like formal proofs and look suspiciously like the informal proofs. This brings about what I am calling here the groundedness problem: how can we decide with certainty that our metalogical proofs are rigorous (...) and sustain our logical system? In this paper, I will expose this problem. I will not try to solve it here. (shrink)

Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...) considering a Sheffer function for intuitionistic logic. (shrink)

This paper has three main concerns. First, it proposes a deflationary theory of the concept of truth, arguing thatthe concept can be explicitly defined in terms of substitutionalquantification. Second, it attempts to describe and explainthe intuitions that have traditionally been thought tofavor correspondence theories of truth over deflationarytheories. And third, it argues that these intuitions areultimately compatible with deflationism, maintaining,among other things, that the relation of semantic correspondence can itself be characterized in terms ofsubstitutional quantification.

The essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of (...) particular sciences. A fruitful approach to these problems combines the study of scientific detail with the kind of conceptual analysis that is characteristic of the modern analytic tradition. Such an approach is shared by these contributors: some primarily known as analytic philosophers, some as philosophers of science, but all deeply aware that the problems of analysis and interpretation link these fields together. (shrink)

Esta investigación se emprende motivada por la necesidad de desentrañar la progresión delos modelos de aprendizaje, los cuales se han ido adaptando para responder a las demandas de lasociedad en su dinámica constante de fluctuación y transformaciones. El objetivo de este trabajo es examinar de forma sistemática la evolución de los modelos de aprendizaje, destacando los cambios paradigmáticos que han favorecido la transición de enfoques de aprendizaje tradicionales hacia propuestas más innovadoras y transdisciplinarias. Para lograrlo, se lleva a cabo un (...) análisis bibliográfico apoyado en el método hermenéutico para la interpretación contextual de la literatura y los discursos, a fin de desentrañar las complejidades inherentes en la evolución de los modelos de aprendizaje. Los resultados resaltan la influencia limitante del paradigma de la simplicidad en laformación educativa tradicional y la necesidad de un giro hacia la dialogicidad y la colaboración eintegración disciplinaria para avanzar hacia la complejidad. Se concluye argumentando a favor de la adopción del paradigma de la complejidad, abogando por una epistemología transdisciplinariay un enfoque de aprendizaje interestructurante, que permitan el desarrollo humano integral.El reconocimiento de la complejidad humana en la enseñanza y el aprendizaje exige una transformación radical de la educación hacia prácticas más holísticas y transformadoras, esenciales para construir una sociedad equitativa y justa. (shrink)

Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Jaśkowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks—the standard conduits of (...) the method to a generation of philosophers—with an eye to determining what the ‘essential characteristics’ of natural deduction are. (shrink)

Although resolution-based inference is perhaps the industry standard in automated theorem proving, there have always been systems that employed a different format. For example, the Logic Theorist of 1957 produced proofs by using an axiomatic system, and the proofs it generated would be considered legitimate axiomatic proofs; Wang’s systems of the late 1950’s employed a Gentzen-sequent proof strategy; Beth’s systems written about the same time employed his semantic tableaux method; and Prawitz’s systems of again about the same time are often (...) said to employ a natural deduction format. [See Newell, et al (1957), Beth (1958), Wang (1960), and Prawitz et al (1960)]. Like sequent proof systems and tableaux proof systems, natural deduction systems retain.. (shrink)

The argument from design is one of the most widely debated arguments for the existence of God. There has been much written in support of and in criticism of the argument's basic structure and conclusion. I shall attempt to clarify these positions, and to argue that the theistic account provides a more rationally justified explanation of human life on earth than the atheistic account. Many philosophers think that any proof for the existence of God is mere "metaphysical speculation." Many times (...) these philosophers use the criteria of scientific empiricism as the standard for an "acceptable" scientific theory, regardless of the subject matter. I shall formulate the argument from design as an empirical scientific theory according to the school of scientific falsificationism as stated by Karl Popper. The principal literature to be investigated in this study will be the most recent articles and texts which discuss relevant scientific data, and their philosophical implications for the argument from design. The results of this investigation demonstrate that it is possible to formulate an argument for the existence of God which meets all of the criteria of the falsificationists school of scientific empiricism. (shrink)

We present the design goals and metatheory of the Monadic Hybrid Calculus, a new formal system that has the same power as the Monadic Predicate Calculus. MHC allows quantification, including relative quantification, in a straightforward way without the use of bound variables, using a simple adaptation of modal logic notation. Thus “all Greeks are mortal” can be written as [G]M. MHC is also ‘hybrid’ in that it has individual constants, which allow us to formulate statements about particular individuals. Thus “Socrates (...) is Athenian and mortal” can be formalised as s.For our proof system, we use a simple adaptation of Beth-style tableaus. The availability of individual constants eliminates the need for labelled deduction.We discuss first the pragmatic and pedagogical advantages of MHC. Then we present the metatheory: formal syntax, semantics, proof rules, soundness, completeness and expressive equivalence with the Monadic Predicate Calculus. (shrink)