Constructive empiricism, the view introduced in The Scientific Image, is a view of science, an answer to the question "what is science?" Arthur Fine's and Paul Teller's contributions to this symposium challenge especially two key ideas required to formulate that view, namely the observable/unobservable and acceptance/belief distinctions. I wish to thank them not only for their insightful critique but also for the support they include. For they illuminate and counter some misunderstandings of Constructive Empiricism along the way. That (...) leaves me free to focus on those two main challenges. (shrink)

Bas van Fraassen’s Constructive Empiricism (CE) has been much discussed. There is, however, a curious feature of van Fraassen’s writings that has been overlooked up until now. This is that he sometimes capitalises certain key terms, notably “Induction”. This is done to differentiate a pragmatic small ‘i’ induction (which has epistemic import) from a rule-bound capital ‘I’ induction (which does not). In this paper, I argue that van Fraassen’s small letter/capital letter distinction reveals an underlying dualism, one that is (...) reminiscent of the notoriously problematic semantic dualism in Logical Positivism (between a theoretical language and an observation language). Despite partly developing CE to overcome Logical Positivism’s kind of dualism, van Fraassen seems to have tacitly endorsed it anyway. If so, then CE requires revision. It is, however, not clear how to conduct such a revision. It is not clear what the way forward should be once CE is understood as innately dualistic. (shrink)

ONE Methodical Thinking Motto: When we teach men how to think, instead of what to think, then we also reduce misunderstanding. ...

We define and investigate Heyting-valued interpretations for Constructive Zermelo–Frankel set theory . These interpretations provide models for CZF that are analogous to Boolean-valued models for ZF and to Heyting-valued models for IZF. Heyting-valued interpretations are defined here using set-generated frames and formal topologies. As applications of Heyting-valued interpretations, we present a relative consistency result and an independence proof.

We consider the relation between past and future events from the perspective of the constructive episodic simulation hypothesis, which holds that episodic simulation of future events requires a memory system that allows the flexible recombination of details from past events into novel scenarios. We discuss recent neuroimaging and behavioral evidence that support this hypothesis in relation to the theater production metaphor.

We introduce a predicative version of topos based on the notion of small maps in algebraic set theory, developed by Joyal and one of the authors. Examples of stratified pseudotoposes can be constructed in Martin-Löf type theory, which is a predicative theory. A stratified pseudotopos admits construction of the internal category of sheaves, which is again a stratified pseudotopos. We also show how to build models of Aczel-Myhill constructive set theory using this categorical structure.

constructive empiricism asserts that it is not for science to reach a verdict on whether a theory is true or false, if the theory is about unobservable entities; science's only interest here, says Van Fraassen, is to discover whether the theory is ‘empirically adequate’. However, if a theory is soley about observables, empirical adequacy and truth are said to ‘coincide’, here discovering the theory's truth value is an appropriate scientific goal. Constructive empiricism thus rests an epistemological thesis on (...) a semantical distinction. This paper critically examines the notion of aboutness and its epistemological significance. * I am grateful to members of my philosophy of science seminar during Spring, 1983 for useful discussion and to the two anonymous referees of this journal for providing helpful suggestions. I also thank the University of Wisconsin, Madison Graduate School for support in the form of a Romnes Faculty Fellowship. (shrink)

Scholars of the emotions maintain that all anger requires an object of blame. In order to be angry, many writers argue, one must believe than an actor has done serious damage to something that one values. Yet an individual may be angered without blaming another. This kind of emotion, called situational anger, does not entail a corresponding object of blame. Situational anger can be a useful force in public life, enabling citizens to draw attention to the seriousness of social or (...) political problems, without necessarily vilifying political officials. (shrink)

This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.

James Ladyman has argued that constructive empiricism entails modal realism, and that this renders constructive empiricism untenable. We maintain that constructive empiricism is compatible with modal nominalism. Although the central term 'observable' has been analyzed in terms of counterfactuals, and in general counterfactuals do not have objective truth conditions, the property of being observable is not a modal property, and hence there are objective, non-modal facts about what is observable. Both modal nominalism and constructive empiricism require (...) clarification in the face of Ladyman's argument. But we also argue that, even if Ladyman were right that constructive empiricism entails modal realism, this would not be a problem for constructive empiricism. (shrink)

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)

In this paper, a family of paraconsistent propositional logics with constructive negation, constructive implication, and constructive co-implication is introduced. Although some fragments of these logics are known from the literature and although these logics emerge quite naturally, it seems that none of them has been considered so far. A relational possible worlds semantics as well as sound and complete display sequent calculi for the logics under consideration are presented.

Constructive Empiricism, the view introduced in The Scientific Image, is a view of science, an answer to the question “what is science?” Arthur Fine’s and Paul Teller’s contributions to this symposium challenge especially two key ideas required to formu- late that view, namely the observable/unobservable and accept- ance/belief distinctions. I wish to thank them not only for their insightful critique but also for the support they include. For they illuminate and counter some misunderstandings of Constructive Empiricism along the (...) way. That leaves me free to focus on those two main challenges. The three of us share a good deal of common history. So it is perhaps only remarkable, and not astonishing, that we now share a common leaning to Pragmatism in philosophy. Of us three I am clearly themost conservative in this respect, especially as pertaining to truth, reference, and belief.2 Arthur Fine showed very nicely how Constructive Empiricism could have been conceived under the canopy of Dewey’s Instrumentalism. Much of it could appear as a Corollary to that sort of Instrumentalism, I agree. But in fact Iwould not be happy to land in that general Pragmatist position. (shrink)

No doubt my earlier paper has struck a sensitive nerve among existing and prospective constructive empiricists – hence their united reply.1 I shall, for brevity, introduce an imaginary single author of their critique and call him CE. In this rejoinder, I try to show, first, that CE’s counter-arguments do not refute my original arguments; and second, that a claim of CE’s paper is very close to the conclusion of my original paper. A central point of my original piece was (...) that there is a symmetry between scientific realism and constructive empiricism vis à vis van Fraassen’s arguments from the bad lot and from indifference. Scholastic charges of an ‘apparent misunderstanding’ of ‘empirical adequacy’ do not cast any light on the issues at stake. (However, the notion of empirical adequacy I employed, p. 41, is the standard one: ‘a theory is empirically adequate if and only if it saves all phenomena, past, present and future, and squares with all actual and possible observations’.) The issue between CE and myself is more substantive: CE relies on the thesis that for any theory there are ‘indefinitely many empirically equivalent rivals’ (p. 307), in order to infer that there are infinitely many empirically adequate theories, and then to argue that if realists.. (shrink)

The use of contingent valuation methods for estimating the economic value of environmental improvements and damages has increased significantly. However, doubts exist regarding the validity of the usual willingness to pay CV methods. In this article, we examine the CV approach in light of recent findings from behavioral decision research regarding the constructive nature of human preferences. We argue that a principal source of problems with conventional CV methods is that they impose unrealistic cognitive demands upon respondents. We propose (...) a new CV approach, based on the value-structuring capabilities of multiattribute utility theory and decision analysis, and discuss its advantages and disadvantages. (shrink)

We put together several observations on constructive negation. First, Russell anticipated intuitionistic logic by clearly distinguishing propositional principles implying the law of the excluded middle from remaining valid principles. He stated what was later called Peirce’s law. This is important in connection with the method used later by Heyting for developing his axiomatization of intuitionistic logic. Second, a work by Dragalin and his students provides easy embeddings of classical arithmetic and analysis into intuitionistic negationless systems. In the last section, (...) we present in some detail a stepwise construction of negation which essentially concluded the formation of the logical base of the Russian constructivist school. Markov’s own proof of Markov’s principle (different from later proofs by Friedman and Dragalin) is described. (shrink)

The (dis)continuism debate—the debate over whether remembering is a form of imagining—is a prominent one in contemporary philosophy of memory. In recent work, Langland-Hassan (2021) has argued that this debate is best understood as a dispute over whether remembering is a form of constructive imagining. In this paper, I argue that remembering is not a form of constructive imagining because constructive processes in remembering and imagining are constrained, and hence controlled, in different ways at the level of (...) consciousness. More specifically, I argue that remembering and imagining differ in terms of the interventions we can make on the constructive processes as they unfold. If this is correct, then a form of discontinuism is vindicated: remembering and imagining are, on this view, processes of different kinds. (shrink)

Constructive and intuitionistic Zermelo-Fraenkel set theories are axiomatic theories of sets in the style of Zermelo-Fraenkel set theory (ZF) which are based on intuitionistic logic. They were introduced in the 1970's and they represent a formal context within which to codify mathematics based on intuitionistic logic. They are formulated on the basis of the standard first order language of Zermelo-Fraenkel set theory and make no direct use of inherently constructive ideas. In working in constructive and intuitionistic ZF (...) we can thus to some extent rely on our familiarity with ZF and its heuristics. -/- Notwithstanding the similarities with classical set theory, the concepts of set defined by constructive and intuitionistic set theories differ considerably from that of the classical tradition; they also differ from each other. The techniques utilised to work within them, as well as to obtain metamathematical results about them, also diverge in some respects from the classical tradition because of their commitment to intuitionistic logic. In fact, as is common in intuitionistic settings, a plethora of semantic and proof-theoretic methods are available for the study of constructive and intuitionistic set theories. -/- The entry introduces the main features of Constructive and Intuitionistic ZF and offers links to the relevant bibliography. (shrink)

We describe an explicit construction of algebraic models for theories with non-standard elements either with classical or constructive logic. The corresponding truthvalue algebra in our construction is a complete algebra of subsets of some concrete decidable set. This way we get a quite finitistic notion of true which reflects a notion of the deducibility of a given theory. It enables us to useconstructive, proof-theoretical methods for theories with non-standard elements. It is especially useful in the case of theories with (...) constructive logic where algorithmic properties are essential. (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 . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL ew (namely, a certain variety of FL ew -algebras) are term equivalent. This answers a longstanding question of Nelson (...) [30]. Extensive use is made of the automated theorem-prover Prover9 in order to establish the result. The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL ew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL ew. (shrink)

There are inequalities between cardinal characteristics of the continuum that are true in any model of ZFC, but without a Borel morphism proving the inequality. We answer some questions from Blass [1].

A defence of constructive empiricism against an attack of N. Maxwell by means of his pet-thesis that science implicitly and permanently accepts a metaphysical thesis about the nature of the universe. We argue that Maxwell's attack can be beaten off; that his arguments do not establish what Maxwell believes they establish; and that we can draw a number of valuable lessons from these attacks about the nature of science and of the libertatian nature of constructive empiricism.

, I argued that Bas van Fraassen's constructive empiricism was undermined in various ways by his antirealism about modality. Here I offer some comments and responses to the reply to my arguments by Bradley Monton and van Fraassen [2003]. In particular, after making some minor points, I argue that Monton and van Fraassen have not done enough to show that the context dependence of counterfactuals renders their truth conditions non-objective, and I also argue that adopting modal realism does after (...) all undermine the motivation for constructive empiricism. Introduction Underdetermination and epistemic modesty Counterfactual observations Modal realism and constructive empiricism. (shrink)

Constructive empiricism, Bas van fraassen's new variety of anti-Realism, Maintains that science aims at empirically adequate, Rather than true theories and that, In fully accepting a theory, One should believe only that it is empirically adequate. A theory is empirically adequate just in case it has a model in which all observable phenomena may be embedded. I challenge van fraassen's main arguments and argue that the observable/unobservable distinction will not bear the weight that van fraassen places on it.

Recent debates in metaphysics have highlighted the significance of type theories, such as Simple Type Theory (STT), for our philosophical analysis. In this chapter, I present the salient features of a constructive type theory in the style of Martin-Löf, termed CTT. My principal aim is to convey the flavour of this rich, flexible and sophisticated theory and compare it with STT. I especially focus on the forms of quantification which are available in CTT. A further aim is to argue (...) that a comparison between a plurality of theories is beneficial to the philosophical analysis. We may, for example, discover helpful features of one theory that we may want to import into another context, thus enriching our repertoire of formal tools. Or, through comparison with a less well-known theory, we may gain a better understanding of the characteristics of the theories we are familiar with. As argued in this chapter, CTT has much to offer in all of these respects. (shrink)

This is the first paper on constructive concurrent dynamic logic . For the first time, either for concurrent or sequential dynamic logic, we give a satisfactory treatment of what statements are forced to be true by partial information about the underlying computer. Dynamic logic was developed by Pratt [V. Pratt, Semantical considerations on Floyd–Hoare logic, in: 17th Annual IEEE Symp. on Found. Comp. Sci., New York, 1976, pp. 109–121, V. Pratt, Applications of modal logic to programming, Studia Logica 39 (...) 257–274] for nondeterministic sequential programs, and by Peleg [D. Peleg, Concurrent dynamic logic, Journal of the Association for Computing Machinery 34 , D. Peleg, Communication in concurrent dynamic logic, Journal of Computer and System Sciences 35 ] for concurrent programs, for the purpose of proving properties of programs such as correctness. Here we define what it means for a dynamic logic formula to be forced to be true knowing only partial information about the results of assignments and tests. This informal CCDL semantics is formalized by intuitionistic Kripke frames modeling this partial information, and each such frame is interpreted as an idealized concurrent machine . In CCDL, proofs and deductions are ω-height, ω-branching, well-founded labeled subtrees of ωω. These are a generalization of the signed tableaux of Nerode [A. Nerode, Some lectures in modal logic, Technical Report, M.S.I. Cornell University, 1989, CIME Logic and Computer Science Montecatini Volume, Springer-Verlag Lecture Notes, 1990, A. Nerode, Some lectures in intuitionistic logic, Technical Report, M.S.I. Cornell University, 1988, Marktoberdorf Logic and Computation NATO Summer School Volume, NATO Science Series, 1990 ] stemming from the prefix tableaux of Fitting [M.C. Fitting, Proof Methods for Modal and Intuitionistic Logic, Reidel, 1983]. We demonstrate the correctness of our tableau proofs, define consistency properties, prove that consistency properties yield models, construct systematic tableaux, prove that systematic tableaux yield a consistency property, and conclude that CCDL is complete. This infinitary semantics and proof procedure will be the primary guide for defining, in a sequel, the correct finitary CCDL based on induction principles. FCCDL is suitable for implementation in constructive logic software systems such as Constable’s NUPRL or Huet-Coquand’s CONSTRUCTIONS. Our goal is to develop a constructive logic programming tool for specification and modular verification of programs in any imperative concurrent language, and for the extraction of concurrent programs from constructive proofs. Subsequent papers will introduce analogous logics for declarative and functional concurrent languages. (shrink)

We argue that constructive approaches in epistemology and systems science, which are focused on normativity, knowledge, and communication of organisms and emphasize the primacy of activity, self-construction, and niche-construction in the cognitive agents, fit naturally to the both methodology and theory of biosemiotics. In particular, constructive view was already present in the works of the major precursors of biosemiotics: von Uexküll and Bateson, and to some extent Peirce. Biosemiotics has a chance to function as a mediating field in (...) the theoretical integration of semiotics with its construction-related sister disciplines (e.g., second order cybernetics, autopoiesis, constructivism, enactivism, and interactivism) because of its explicit assumption of the semiotic nature of life and agency and its objectified “first person” view to biosemiotic agents, the view that nevertheless avoids the agnostic attitude towards reality. (shrink)

Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. (...) Furthermore, we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum. (shrink)

In this paper, I argue that, contrary to the constructive empiricist’s position, observability is not an adequate criterion as a guide to ontological commitment in science. My argument has two parts. First, I argue that the constructive empiricist’s choice of observability as a criterion for ontological commitment is based on the assumption that belief in the existence of unobservable entities is unreasonable because belief in the existence of an entity can only be vindicated by its observation. Second, I (...) argue that the kind of ontological commitment that is under consideration when accepting a scientific theory is commitment to what I call theoretical kinds and that observation can vindicate commitment to kinds only in exceptional cases. (shrink)

The incorporation of post-event testimonial information into an agent’s memory representation of the event via constructive memory processes gives rise to the misinformation effect, in which the incorporation of inaccurate testimonial information results in the formation of a false memory belief. While psychological research has focussed primarily on the incorporation of inaccurate information, the incorporation of accurate information raises a particularly interesting epistemological question: do the resulting memory beliefs qualify as knowledge? It is intuitively plausible that they do not, (...) for they appear to be only luckily true. I argue, however, that, despite its intuitive plausibility, this view is mistaken: once we adopt an adequate (modal) conception of epistemic luck and an adequate (adaptive) general approach to memory, it becomes clear that memory beliefs resulting from the incorporation of accurate testimonial information are not in general luckily true. I conclude by sketching some implications of this argument for the psychology of memory, suggesting that the misinformation effect would better be investigated in the context of a broader “information effect”. (shrink)

In his recent “Expanding the Empirical Realm: Constructive Empiricism and Augmented Observation” (2024), Finnur Dellsén recalls a quite famous case that Gideon Rosen put forward against manifestationalism thirty years ago, and maintains that an analogous argument might be presented against Bas van Fraassen’s constructive empiricism. This study is meant as a response to Dellsén: while the idea behind his paper is sound, I do not think it actually works. In brief, the reason is that we do not have (...) God’s point of view and thus are in no condition to know whether a certain scientific theory is empirically adequate, let alone true. Once again, perhaps constructive empiricism still represents the best compromise so far presented between strict empiricism and the acknowledgment of the rationality of science. (shrink)

I present a semantics for the language of first-order additive-multiplicative linear logic, i.e. the language of classical first-order logic with two sorts of disjunction and conjunction. The semantics allows us to capture intuitions often associated with linear logic or constructivism such as sentences = games, SENTENCES = resources or sentences = problems, where “truth” means existence of an effective winning strategy.The paper introduces a decidable first-order logic ET in the above language and gives a proof of its soundness and completeness (...) with respect to this semantics. Allowing noneffective strategies in the latter is shown to lead to classical logic.The semantics presented here is very similar to Blass's game semantics. Although there is no straightforward reduction between the two corresponding notions of validity, my completeness proof can likely be adapted to the logic induced by Blass's semantics to show its decidability, which was the main problem left open in Blass's paper.The reader needs to be familiar with classical logic and arithmetic. (shrink)