Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.

Logic and psychology overlap in judgment, inference and proof. The problems raised by this commonality are notoriously difficult, both from a historical and from a philosophical point of view. Sundholm has for a long time addressed these issues. His beautiful piece of work [A Century of Inference: 1837-1936] begins by summarizing the main difficulty in the usual provocative manner of the author: one can start, he says, by the act of knowledge to go to the object, as the Idealist does; (...) one can also start by the object to go to the act, in the Realist mood; never the two shall meet. He is himself inclined to accept the first perspective as the right one and he has eventually developed an original version of antirealism which starts, not from considerations about the publicity of meaning, in the manner of Dummett, but from an epistemic standpoint, trying to search in a non-Fregean tradition of analysis of judgement and cognate notions a way of founding constructivist semantics. The present paper ploughes the same field. We concentrate on the significance, for Sundholm’s program, of the perspective that has been opened by Twardowski in his important essay on acts and products (1912. (shrink)

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...) a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. (shrink)

In “A new proof of the completeness of the Lukasiewicz axioms” Chang proved that any totally ordered MV-algebra A was isomorphic to the segment \}\) of a totally ordered l-group with strong unit A *. This was done by the simple intuitive idea of putting denumerable copies of A on top of each other. Moreover, he also show that any such group G can be recovered from its segment since \^*}\), establishing an equivalence of categories. In “Interpretation of AF C (...) *-algebras in Lukasiewicz sentential calculus” Mundici extended this result to arbitrary MV-algebras and l-groups with strong unit. He takes the representation of A as a sub-direct product of chains A i, and observes that \ where \. Then he let A * be the l-subgroup generated by A inside \. He proves that this idea works, and establish an equivalence of categories in a rather elaborate way by means of his concept of good sequences and its complicated arithmetics. In this note, essentially self-contained except for Chang’s result, we give a simple proof of this equivalence taking advantage directly of the arithmetics of the the product l-group \, avoiding entirely the notion of good sequence. (shrink)

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...) a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. (shrink)

Conversational Artificial Intelligence (CAI) systems (also known as AI “chatbots”) are among the most promising examples of the use of technology in mental health care. With already millions of users worldwide, CAI is likely to change the landscape of psychological help. Most researchers agree that existing CAIs are not “digital therapists” and using them is not a substitute for psychotherapy delivered by a human. But if they are not therapists, what are they, and what role can they play in mental (...) health care? To answer these questions, we appeal to two well-established and widely discussed concepts: cognitive and affective artifacts. Cognitive artifacts are artificial devices contributing functionally to the performance of a cognitive task. Affective artifacts are objects which have the capacity to alter subjects’ affective state. We argue that therapeutic CAIs are a kind of cognitive-affective artifacts which contribute to positive therapeutic change by (i) simulating a (quasi-)therapeutic interaction, (ii) supporting the performance of cognitive tasks, and (iii) altering the affective condition of their users. This sheds new light on why virtually all existing mental health CAIs implement principles and techniques of Cognitive Behavioral Therapy — a therapeutic orientation according to which affective change and, ultimately, positive therapeutic change is mediated by cognitive change. Simultaneously, it allows us to conceptualize better the potential and limitations of applying these technologies in therapy. (shrink)

According to the cognitive model of psychopathology, maladaptive beliefs about oneself, others, and the world are the main factors contributing to the development and persistence of various forms of mental suffering. Therefore, the key therapeutic process of Cognitive Behavioral Therapy (CBT)—a therapeutic approach rooted in the cognitive model—is cognitive restructuring, i.e., a process of revision of such maladaptive beliefs. In this paper, I examine the philosophical assumptions underlying CBT and offer theoretical reasons to think that the effectiveness of belief revision (...) in psychotherapy is very limited. This is the case, I argue, because the cognitive model wrongly assumes that our body of beliefs is unified, while it is in fact fragmented. (shrink)

We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a simple proof of this theorem inspired in Ferraioli (...) and Lettieri (Math Logic Q 1:27–43, 2011). (shrink)

I-theories of bare demonstratives take the semantic referent of a demonstrative to be determined by an inner state of the utterer. E-theories take the referent to be determined by factors external to the utterer. I argue that, on the Standard view of communication, neither of these theories can be right. Firstly, both are committed to the existence of conventions with superfluous content. Secondly, any claim to the effect that a speaker employs the conventions associated with these theories cannot have any (...) content, i.e. nothing can count as following these conventions. Bare demonstratives may well not be devices of semantic reference at all, i.e. may not actually contribute a referent to the proposition semantically expressed by an utterance. (shrink)

Declarations like “this meeting is adjourned” make certain facts the case by representing them as being the case. Yet surprisingly little attention has been paid to the mechanism whereby the utterance of a declaration can bring about a new state of affairs. In this paper, we use the incentivization account of institutional facts to address this issue. We argue that declarations can serve to bring about new states of affairs as their utterance have game theoretical import, typically in virtue of (...) the utterer signaling a commitment to act in an incentive-changing way. (shrink)

Three experiments explore the role of working memory in motor skill acquisition and performance. Traditional theories postulate that skill acquisition proceeds through stages of knowing, which are initially declarative but later procedural. The reported experiments challenge that view and support an independent, parallel processing model, which predicts that procedural and declarative knowledge can be acquired separately and that the former does not depend on the availability of working memory, whereas, the latter does. The behaviour of these two processes was manipulated (...) by providing or withholding visual (and auditory) appraisal of outcome feedback. Withholding feedback was predicted to inhibit the use of working memory to appraise success and, thus, prevent the formation of declarative knowledge without affecting the accumulation of procedural knowledge. While the first experiment failed to support these predictions, the second and third experiments demonstrated that procedural and declarative knowledge can be acquired independently. It is suggested that the availability of working memory is crucial to motor performance only when the learner has come to rely on its use. (shrink)

There are two tasks for any adequate philosophy of mind: (1) articulate one’s position and explain why dualism is the commonsense view; (2) defend one’s position. I believe that there is an argument that simultaneously satisfies both desiderata in a non–ad hoc way and, thus, the argument can thereby claim the virtue of theoretical simplicity in its favor. In what follows, I shall present the argument and defend its most crucial premise, respond to three criticisms that have been raised against (...) it, and draw out one dialectical implication of the argument. (shrink)

While my own philosophical views are largely in keeping with my mentor, Dallas Willard, nevertheless, I find his conception of the human person puzzling, hard to specify precisely, and prima facie contradictory in a few places. Dallas's central goal in formulating his anthropology was to develop a model that shed light on, allowed for deeper insight into, and fostered interest in spiritual formation, especially the role of the body in spiritual maturation. I share this goal, and agree with most of (...) his model. But in what follows, I will make more precise what his views were, try to clear up what, prima facie, seem to be contradictions in his theory, and, finally, recommend an alternative that captures the central concerns Dallas had for his own position. Thus, I will lay out a few general points of Dallas's ontology, provide a description of his philosophical/theological anthropology, along with two problems that seem to be present, and offer a slightly adjusted alternative to his position that accomplishes his main goal in a way with which I believe he would be satisfied. (shrink)

I argue that Kant’s mature political philosophy entails the provisionality thesis. The provisionality thesis asserts that in a world like ours, populated with beings sufficiently like us, acquired rights (rights to external objects of choice, including property, sovereignty and territory) are necessarily provisional. I motivate the standard view, which restricts the notion of provisional right to the state of nature and the transition from the state of nature to the civil condition. I then provide two textual arguments against it. I (...) conclude by reflecting on the normative implications of the provisionality thesis, arguing that they are more modest than has been formerly appreciated. (shrink)

Transcranial Magnetic Stimulation is a technique that may aid researchers in their attempts to elucidate the underlying brain functions involved in consciousness. By employing TMS along with other neuroimaging methods and case studies, researchers may be aided in addressing their various hypotheses. Employing the ‘brain as mobile’ analogy, it may be possible to determine the individual contributions of single elements of the brain without upsetting the overall balance.

Semantic theories that violate semantic innocence, that is require reference shifts when terms are embedded in ‘that’ clauses and the like, are often challenged by producing sentences where an anaphoric expression, while not itself embedded in a context in which reference shifts, is anaphoric on an antecedent expression that is embedded in such a context. This, in conjunction with a widely accepted principle concerning unproblematic anaphora (the ‘Principle of Anaphoric Reference’), is used to show that such reference shifting has absurd (...) consequences. We show that it is the widely accepted principle concerning anaphora that is to be blamed for these consequences and not the supposed sin of reference shifting. (shrink)

Construed metaphysically, the problem of individuation is the problem of offering an ontological assay of two entities that share all their pure properties in common so as to offer an account of what makes them distinct particulars. This article provides a survey of the major contemporary attempts to answer this problem. To accomplish this goal, the most important contemporary advocates of each solution is analyzed: the trope nominalism of Keith Campbell, the realism of D. M. Armstrong, the Leibnizian essence view (...) of Alvin Plantinga, and the bare particular position of Gustav Bergmann. As a secondary purpose, the article provides a brief critique of the first three solutions and a brief defense of the fourth. (shrink)

Of the early Roman historians who wrote in Greek, A. Postumius Albinus was not necessarily alone in realizing that his Greek was not the best Greek; while, on the other hand, Cato and those who followed the new fashion of writing in Latin would have resented, we may assume, could they have foreknown, the statement of Q,. Catulus in Cicero's De Oratore that they had no literary or rather ‘oratorical’ merit; though Cato might have approved Catulus' caustic comment on Roman (...) historical writing, ‘Satis est non esse mendacem’. That an historian should not, consciously and deliberately, lie all second-century historians would no doubt have agreed; and they would have endorsed Polybius' condemnation of masquerading as history in a story whose falseness was self-evident, because it assumed, on the part of the young sons of senators at Rome, a gravitas such as no young boy could possibly possess. (shrink)

The paper shows a new example of nonuniqueness of the solutionto Newtonian equations of motion for infinite gravitational systems. Unlike otherexamples, the gravitational field presents no singularity, nor are the non-gravitational forcesintroduced in the model singular (in particular, there are no collisions). The result is also ofinterest because it points to an interesting limitation of the elementary (Newtonian) formulationof classical mechanics.

This paper responds to the recent situationist critique of practical rationality and decision-making. According to that critique, empirical evidence indicates that our choices are governed by morally irrelevant situational factors and not durable character traits, and rarely result from overt rational deliberation. This critique is taken to indicate that popular moral theories in the Western tradition are descriptively deficient, even if normatively plausible or desirable. But we believe that the situationist findings regarding the sources of, or influences over, our moral (...) agency do not reflect durable features of human nature, and claim that these findings are a byproduct of a deficient approach to moral education. Existing models of moral education, which are “positive” in nature, do a poor job of developing virtuous people. Instead, we argue that a “negative” approach to moral education, traceable to Locke, Smith, and Rousseau, would be more successful. This strategy represents something of a compromise between the strategies adopted by thinkers like Rachana Kamtekar : 458–491 2004), who argues that traditional moral categories escape largely untouched by findings in social psychology, and John Doris :504–530 1998) and Gilbert Harman : 87–94 2003), who argue that findings in psychology prove our traditional moral theories are defective. (shrink)

The classical wave-particle problem is resolved in accord with Newton's concept of the particle nature of light by associating particle density and flux with the classical wave energy density and flux. Point particles flowing along discrete trajectories yield interference and diffraction patterns, as illustrated by Young's double pinhole interference. Bound particle motion is prescribed by standing waves. Particle motion as a function of time is presented for the case of a “particle in a box.” Initial conditions uniquely determine the subsequent (...) motion. Some discussion regarding quantum theory is preseted. (shrink)

i) We show for each context-free language L that by considering each word of L as a structure in a natural way, one turns L into a finite union of classes which satisfy a finitary analog of the characteristic properties of complete universal first order classes of structures equipped with elementary embeddings. We show this to hold for a much larger class of languages which we call free local languages. ii) We define local languages, a class of languages between free (...) local and context-sensitive languages. Each local language L has a natural extension L ∞ to infinite words, and we prove a series of "pumping lemmas", analogs for each local language L of the "uvxyz theorem" of context free languages: they relate the existence of large words in L or L ∞ to the existence of infinite "progressions" of words included in L, and they imply the decidability of various questions about L or L ∞ . iii) We show that the pumping lemmas of ii) are independent from strong axioms, ranging from Peano arithmetic to ZF + Mahlo cardinals. We hope that these results are useful for a model-theoretic approach to the theory of formal languages. (shrink)

Les sciences cognitives poursuivent un objectif fort ancien, qui consiste, sommairement dit, à décrire et à expliquer les comportements intelligents. Elles appliquent à cet effet des principes méthodologiques moins traditionnels, dont l'adoption définit ce qu'il est convenu d'appeler le "tournant cognitif". Je me propose ici d'exposer brièvement ces principes, de les illustrer par des exemples appropriés et d’en discuter la signification philosophique. Pour l’essentiel, j’ai mis en avant un domaine qui me semble particulièrement pertinent pour les philosophes: l'analyse de la (...) catégorisation, c'est-à-dire du processus par lequel un ensemble d'entités (stimuli sonores ou visuels, objets concrets ou abstraits) en vient à être classifié en catégories séparées, qui peuvent être de type perceptif (phonèmes, couleurs) ou conceptuel (espèces naturelles, types d'événements, catégories esthétiques et morales). (shrink)

Takeuti introduced an infinitary proof system for determinate logic and showed that for transitive models of Zermelo-Fraenkel set theory with the Axiom of Dependent Choice that contain all reals, the cut-elimination theorem is equivalent to the Axiom of Determinacy, and in particular contradicts the Axiom of Choice. We consider variants of Takeuti's theorem without assuming the failure of the Axiom of Choice. For instance, we show that if one removes atomic formulae of infinite arity from the language of Takeuti's proof (...) system, then cut elimination is equivalent to a determinacy hypothesis provable, e.g., in ZFC + “there are infinitely many Woodin cardinals.” A slight extension of the proof system admits cut elimination for countable sequents under the same assumptions. A simple modification of the proof system yields analogs of the results above for the Axiom of Real Determinacy and uncountably many Woodin cardinals. (shrink)