Alan Musgrave, Michael Friedman, Jeffrey Foss, and Richard Creath raised different objections against the Distinction between observables and unobservables when drawn within the confines of Bas C. van Fraassen's Constructive Empiricism, to the effect that the Distinction cannot be drawn there coherently. Van Fraassen has only responded to Musgrave but Musgrave claimed not to understand van Fraassen's succinct response. I argue that van Fraassen's response is not enough. What remains in the end is an unsolved problem which CE cannot (...) afford to leave unsolved, or so I argue; I then strengthen Musgrave's criticism and indicate that an extension of the epistemic policy of CE is mandatory to solve the problem. I also argue that Friedman's and Foss' objection against the Distinction in CE misses the mark on closer inspection. An objection due to Creath does hit the mark but can be taken care of without too much ado. All these objections seem alive and kicking until the present day; I try to put them all to rest. (shrink)

Active, constructive, and interactive are terms that are commonly used in the cognitive and learning sciences. They describe activities that can be undertaken by learners. However, the literature is actually not explicit about how these terms can be defined; whether they are distinct; and whether they refer to overt manifestations, learning processes, or learning outcomes. Thus, a framework is provided here that offers a way to differentiate active, constructive, and interactive in terms of observable overt activities and underlying (...) learning processes. The framework generates a testable hypothesis for learning: that interactive activities are most likely to be better than constructive activities, which in turn might be better than active activities, which are better than being passive. Studies from the literature are cited to provide evidence in support of this hypothesis. Moreover, postulating underlying learning processes allows us to interpret evidence in the literature more accurately. Specifying distinct overt activities for active, constructive, and interactive also offers suggestions for how learning activities can be coded and how each kind of activity might be elicited. (shrink)

We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin.One level is given by an intensional type theory, called Minimal type theory. This theory extends a previous version with collections.The other level is given by an extensional set theory that is interpreted in the first one by means of a quotient model.This two-level theory has two main features: it is minimal among the most relevant foundations for constructive mathematics; it is (...) constructive thanks to the way the extensional level is linked to the intensional one which fulfills the “proofs-as-programs” paradigm and acts as a programming language. (shrink)

This paper proposes that existing computational modeling research programs may be combined into platforms for the information of public policy. The main idea is that computational models at select levels of organization may be integrated in natural terms describing biological cognition, thereby normalizing a platform for predictive simulations able to account for both human and environmental costs associated with different action plans and institutional arrangements over short and long time spans while minimizing computational requirements. Building from established research programs, the (...) proposal aims to take advantage of current momentum in the direction of the integration of the cognitive with social and natural sciences, reduce start-up costs and increase speed of development. These are all important upshots given rising unease over the potential for AI and related technologies to shape the world going forward. (shrink)

Constructive empiricism implies that if van Fraassen does not believe that scientific theories and his positive philosophical theories, including his contextual theory of explanation, are empirically adequate, he cannot accept them, and hence he cannot use them for scientific and philosophical purposes. Moreover, his epistemic colleagues, who embrace epistemic reciprocalism, would not believe that his positive philosophical theories are empirically adequate. This epistemic disadvantage comes with practical disadvantages in a social world.

The present volume is intended as an all-round introduction to constructivism. Here constructivism is to be understood in the wide sense, and covers in particular Brouwer's intuitionism, Bishop's constructivism and A.A. Markov's constructive recursive mathematics. The ending "-ism" has ideological overtones: "constructive mathematics is the (only) right mathematics"; we hasten, however, to declare that we do not subscribe to this ideology, and that we do not intend to present our material on such a basis.

I develop a concept of observability that pertains to qualities rather than objects: a quality is observable if it can be registered by human sensation (possibly with the aid of instruments) without involving optional interpretations. This concept supports a better description of observations in science and everyday life than the object-based observability concepts presupposing causal information-transfer from the object to the observer. It also allows a rehabilitation of the traditional empiricist distinction between observations and their interpretations, but without a presumption (...) that observations are infallible. Using this concept of observability, I also propose a re-formulation of constructive empiricism that is easier to defend against realist attacks, while open to reasonable realist intuitions. (shrink)

Martin-Löf’s Constructive Type Theory (CTT) is a formal language developed in order to reason constructively about mathematics. It is thus a formal language conceived primarily as a tool to reason with rather than a formal language conceived primarily as a mathematical system to reason about. Constructive Type Theory is therefore much closer in spirit to Frege’s ideography and to the language of Russell and Whitehead’s Principia Mathematica than to the majority of logical systems (“logics”) studied by contemporary logicians. (...) Since CTT is designed as a language to reason with, much attention is paid to the explanation of basic concepts. This is perhaps the main reason why the style of presentation of CTT differs somewhat from the style of presentation typically found in, for instance, ordinary logic textbooks. For those new to the system it might be useful to approach an introduction, such as the one given below, more as a language course than as a course in mathematics. (shrink)

The morality of virtual representations and the enactment of prohibited activities within single-player gamespace (e.g., murder, rape, paedophilia) continues to be debated and, to date, a consensus is not forthcoming. Various moral arguments have been presented (e.g., virtue theory and utilitarianism) to support the moral prohibition of virtual enactments, but their applicability to gamespace is questioned. In this paper, I adopt a meta-ethical approach to moral utterances about virtual representations, and ask what it means when one declares that a virtual (...) interaction ‘is morally wrong’. In response, I present constructive ecumenical expressivism to (i) explain what moral utterances should be taken to mean, (ii) argue that they mean the same when referring to virtual and non-virtual interactions and (iii), given (ii), explain why consensus with regard to virtual murder, rape and paedophilia is not forthcoming even though such consensus is readily found with regard to their non-virtual equivalents. (shrink)

Now in its fifth edition, Good Reasoning Matters! is a practical guide to recognizing, evaluating, and constructing arguments. Combining straightforward instruction with abundant exercises and examples, this innovative introduction to argument schemes and rhetorical techniques will help students learn to think critically both within and beyond the classroom.

In this paper, I explore Rosen’s ‘transcendental’ objection to constructive empiricism—the argument that in order to be a constructive empiricist, one must be ontologically committed to just the sort of abstract, mathematical objects constructive empiricism seems committed to denying. In particular, I assess Bueno’s ‘partial structures’ response to Rosen, and argue that such a strategy cannot succeed, on the grounds that it cannot provide an adequate metalogic for our scientific discourse. I conclude by arguing that this result (...) provides some interesting consequences in general for anti-realist programmes in the philosophy of science.Keywords: Constructive empiricism; Mathematical fictionalism; Partial structures; Modality. (shrink)

The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett’s logic LC.

Certain extensions of Nelson's constructive logic N with strong negation have recently become important in arti.cial intelligence and nonmonotonic reasoning, since they yield a logical foundation for answer set programming (ASP). In this paper we look at some extensions of Nelson's .rst-order logic as a basis for de.ning nonmonotonic inference relations that underlie the answer set programming semantics. The extensions we consider are those based on 2-element, here-and-there Kripke frames. In particular, we prove completeness for .rst-order here-and-there logics, and (...) their minimal strong negation extensions, for both constant and varying domains. We choose the constant domain version, which we denote by QNc5, as a basis for de.ning a .rst-order nonmonotonic extension called equilibrium logic. We establish several metatheoretic properties of QNc5, including Skolem forms and Herbrand theorems and Interpolation, and show that the .rst-oder version of equilibrium logic can be used as a foundation for answer set inference. (shrink)

Sometimes one’s greatest academic disappointments can have unexpected outcomes. This is especially true when one is trying to change career trajectories or do something that others did not take seriously. My path into neuroethics was an unexpected journey catalyzed in part by constructive disappointment and the disbelief of colleagues who thought that the work I was pursuing nearly two decades prior was a fool’s errand. After all, could anyone—in his or her right mind—ever conceive of waking up a person (...) unconscious from brain injury and getting him to speak?1. (shrink)

Open peer commentary on the article “Perception-Action Mutuality Obviates Mental Construction” by Martin Flament Fultot, Lin Nie & Claudia Carello. Upshot: In my view, the clash between ecological psychology, enactivism, and constructivism in general has more to do with irreconcilable metaphysical and theoretical incommensurabilities than disagreements about specific mechanisms or processes of perception. Even with mutual enabling of action and perception, some internal process of self-modification is still needed if novel behavior is to be adequately explained.

We re-express a previous general result in a way which seems easier to remember, using the terminology of infinite games. We show how this can be applied to construct recursive linear orderings, showing, for example, that if there is a ▵ 0 2β + 1 linear ordering of type τ, then there is a recursive ordering of type ω β · τ.

Name der Zeitschrift: Kierkegaard Studies Yearbook Jahrgang: 2013 Heft: 1 Seiten: 451-472.

We represent the well-known surprise exam paradox in constructive and computable mathematics and offer solutions. One solution is based on Brouwer’s continuity principle in constructive mathematics, and the other involves type 2 Turing computability in classical mathematics. We also discuss the backward induction paradox for extensive form games in constructive logic.

In this paper, we deal with compact operators on a Hilbert space, within the framework of Bishop's constructive mathematics. We characterize the compactness of a bounded linear mapping of a Hilbert space into C n , and prove the theorems: Let A and B be compact operators on a Hilbert space H , let C be an operator on H and let α ϵ C . Then α A is compact, A + B is compact, A ∗ is compact, (...) CA is compact and if C ∗ exists, then AC is compact; An operator on a Hilbert space has an adjoint if and only if it is weakly compact. (shrink)

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL ew of the substructural logic FL ew. The main result of Part I of this series [41] shows that the equivalent variety semantics of N and the equivalent variety semantics of NFL ew are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of (...) deductive systems to establish the definitional equivalence of the logics N and NFL ew. It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural logic. (shrink)

According to van Fraassen, constructive empiricism (CE) makes better sense of scientific activity than scientific realism (SR). I discuss a recent episode in biomedical research - investigations about Helicobacter Pylori and its relation to peptic ulcer. CE's expedient to cope with it is a sort of belief substitution. I argue that replacing realist beliefs by empiricist surrogates (as-if beliefs) could accommodate scientists' expectations and behavior. Nonetheless, theoretical agnosticism could hardly motivate scientists to focus just on the observational consequences derived (...) from the theory at issue. Contrary to van Fraassen, I conclude then that, concerning scientific practice, realist beliefs cannot be considered as a gratuitious surplus which should be rejected. (shrink)

We present a new and constructive proof of the Peter-Weyl theorem on the representations of compact groups. We use the Gelfand representation theorem for commutative C*-algebras to give a proof which may be seen as a direct generalization of Burnside's algorithm [3]. This algorithm computes the characters of a finite group. We use this proof as a basis for a constructive proof in the style of Bishop. In fact, the present theory of compact groups may be seen as (...) a natural continuation in the line of Bishop's work on locally compact, but Abelian, groups [2]. (shrink)

My reply to the comments of Parkinson (2010) and Kuppens (2010) is organized in three parts. The first part deals with Parkinson’s claim that the scope of our research is limited because no real emotions were elicited. I suggest that the outcomes in our studies are structurally similar to real emotions but that they lack intensity. In the second part, I try to correct three potential misunderstandings regarding the nature of the comparison process that I proposed. In the third part, (...) I respond to Kuppens’ suggestion that we also need to consider the transition of appraisal values into the other components of emotion (actions tendencies, responses, and subjective experience). (shrink)

We give a constructive proof of McNaughton's theorem stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of Lukasiewicz. For the proof we only use Minkowski's convex body theorem and the rudiments of piecewise linear topology.

Sheaf semantics is developed within a constructive and predicative framework, Martin‐Löf's type theory. We prove strong completeness of many sorted, first order intuitionistic logic with respect to this semantics, by using sites of provably functional relations.

Philosophers use disagreement as a way to discover truth. It is constructive. It can lead one to refine one's own position and/or better understand the opposing position. When you are comfortable with the people you disagree with, it can be a fun way to learn. It can even build community. Yet students often see disagreement as divisive. There are winners and losers, and it's not much fun when you are losing. Rarely do students actively use it as a tool (...) for better understanding their own positions and arguments. In this one-page handout, I provide some tips to help students have constructive and respectful disagreement. It is intended for use in the philosophy classroom, but it may have other uses. [If you use the guide in your class, it would be nice to let me know but not required. Feedback and criticism are welcome.]. (shrink)

J. N. Crossley [1] raised the question of whether the implication 2 + A = A ⇒ 1 + A = A is true for constructive order types (C.O.T.'s). Using an earlier definition of constructive order type, A. G. Hamilton [2] presented a counterexample. Hamilton left open the general question, however, since he pointed out that Crossley considers only orderings which can be embedded in a standard dense r.e. ordering by a partial recursive function, and that his counterexample (...) fails to meet this requirement. We resolve the question by finding a C.O.T. A which meets Crossley's requirement and such that 2 + A = A but 1 + A ≠ A. At the suggestion of A. B. Manaster and A. G. Hamilton we easily extend this construction to show that for any n ≧ 2, there is a C.O.T. A such that n + A = A but m + A ≠ A for 0 < m < n. Hence, Theorem 3 of [2] and all of its corollaries hold with the new definition of C.O.T. The construction is not difficult and requires no priority argument. The techniques are similar to those developed in [3], but no outside results are needed here. (shrink)

Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms 'construction' and 'proof' has never been adequately explained (although Kreisel, Goodman and Martin-Löf have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and (...) constructive analysis are given. The philosophical basis of constructivism is explored thoroughly in Part I. The author seeks to answer objections from platonists and to reconcile his position with the central insights of Hilbert's formalism and logic. Audience: Philosophers of mathematics and logicians, both academic and graduate students, particularly those interested in Brouwer and Hilbert; theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi. (shrink)

In the present paper we introduce a constructive theory of nonstandard arithmetic in higher types. The theory is intended as a framework for developing elementary nonstandard analysis constructively. More specifically, the theory introduced is a conservative extension of HAω + AC. A predicate for distinguishing standard objects is added as in Nelson's internal set theory. Weak transfer and idealisation principles are proved from the axioms. Finally, the use of the theory is illustrated by extending Bishop's constructive analysis with (...) infinitesimals. (shrink)

This essay explores the possibility that religiously motivated intolerance and conflict can be reframed and positively utilized for constructive social-political purposes. After reviewing efforts by political philosophers over the past two decades to accommodate religious voices in political discourse, I scrutinize Charles Taylor’s attempt to improve upon the limits of “accommodationist” approaches to religious intolerance and conflict. I argue that both accommodationist and Taylor’s recognition-based approaches to religiously motivated conflict take the gravity of such conflict with insufficient seriousness. I (...) then explore the potential goods of intentional conflict by examining Chantal Mouffe’s account of agonistic pluralism as a proposal for thinking beyond tolerance as an orienting value for resolving intransigent conflict. While I argue that Mouffe’s account finally suffers from certain of the same misgivings as the accommodationist and recognition-based approaches, I conclude that agonistic pluralism’s aim to conceptually reframe (rather than eliminate) intolerance and conflict moves in an important and promising direction. (shrink)

In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for testing (...) scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

The child directed speech of twelve English‐speaking motherswas analyzed in terms of utterance‐level constructions. First, the mothers' utterances were categorized in terms of general constructional categories such as Wh‐questions, copulas and transitives. Second, mothers' utterances within these categories were further specified in terms of the initial words that framed the utterance, item‐based phrases such as Are you …, I'll …, It's …, Let's …, What did … The findings were: (i) overall, only about 15% of all maternal utterances had SVO (...) form (most were questions, imperatives, copulas, and fragments); (ii) 51% of all maternal utterances began with one of 52 item‐based phrases, mostly consisting of two words or morphemes (45% began with one of just 17 words); and (iii) children used many of these same item‐based phrases, in some cases at a rate that correlated highly with their own mother's frequency of use. We suggest that analyses of adult–child linguistic interaction should take into account not just general constructional categories, but also the item‐based constructions that adults and children use and the frequency with which they use them. (shrink)