Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

Edward Nieznański developed two logical systems to deal with the problem of evil and to refute religious determinism. However, when formalized in first-order modal logic, two axioms of each system contradict one another, revealing that there is an underlying minimal set of axioms enough to settle the questions. In this article, we develop this minimal system, called N3, which is based on Nieznański’s contribution. The purpose of N3 is to solve the logical problem of evil through the (...) defeat of a version of religious determinism. On the one hand, these questions are also addressed by Nieznański’s systems, but, on the other hand, they are obtained in N3 with fewer assumptions. Our approach can be considered a case of logic of religion, that is, of logic applied to religious discourse, as proposed by Józef Maria Bocheński; in this particular case, it is a discourse in theodicy, which is situated in the context of the philosophy of religion. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a (...) larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In this paper, we (...) propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

Łukasiewicz has often been criticized for his motive for inventing his three-valued logic, namely the avoidance of determinism. First of all, I want to show that almost all of the critcism along this line was wrong. Second I will indicate that he made mistakes, however, in constructing his system, because he had other motives at the same time. Finally I will propose some modification of his system and its interpretation which can attain his original purpose in some sense.

I have three main objectives in this essay. First, in chapter 2, I shall put forward and justify what I call worldlessness, by which I mean the following: All truths (as well as falsehoods) are wholly independent of any circumstances, not only time and place but also possible worlds. It follows from this view that whatever is actually true must be taken as true with respect to every possible world, which means that all truths are (in a sense) necessary. However, (...) the account I shall propound is different from what is known in the trade as necessitarianism, i.e. the view that there is only one possible world, viz. the actual one, for the doctrine of the worldlessness of truth values, despite its commitment to the necessity of truths and falsehoods, is quite compatible with the idea of there being other possible worlds. Another important issue in chapter 2, explored in particular in section 2.12, is the claim that there is no real change in the world. Secondly, in chapter 3 I consider the eminent traditional argument for determinism, deriving from Aristotle, namely, logical determinism, i.e. determinism justified by an appeal to the logical principle of bivalence (that all proper statements, including those concerning the future, are either true or false). In this connection I try to show that, (i), the formulation of the conclusion of this argument as "Whatever will happen will happen of necessity" is implausible, at least from the modern point of view, (ii), the formulation as "Whatever will happen will happen inevitably" is more to the point, and (iii), on the basis of the worldless and timeless aspect advocated in chapter 2, this latter formulation is quite harmless, essentially amounting to the trivial statement, "Whatever will happen will happen". Thirdly, in chapter 4 I study theological determinism, or determinism that arises from God's supposed providential control over everything that happens. In this connection, I shall survey some historical accounts of the relation between human free will and determinism (not only theological but also causal determinism); the philosophers the views of whom I shall attend to include Chrysippus, St. Augustine, Boethius and Aquinas. I shall in particular consider G.W. Leibniz' theodicean aspirations, viz. his solution to the problem of evil and, especially, his compatibilist attempts to reconcile human free will with the strictly deterministic flow of actual events. I think it is important to try to explicate Leibniz' ingenious account of these matters, since it seems that it has not been fully appreciated in the literature, not even by contemporary Leibniz scholars (such as B. Mates, R.C. Sleigh, C. Wilson, R.M. Adams and D. Rutherford). In providing the Leibnizian compatibilist solution of the problem of determinism and freedom in chapter 4, I shall utilize the approach of chapter 2. (shrink)

In the current philosophical literature, determinism is rarely defined explicitly. This paper attempts to show that there are in fact many forms of determinism, most of which are familiar, and that these can be differentiated according to their particular components. Recognizing the composite character of determinism is thus central to demarcating its various forms.

In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based (...) in orthomodular lattices, allowing to study post-quantum models using logical techniques. (shrink)

Edward Nieznanski developed in 2007 and 2008 two different systems in formal logic which deal with the problem of evil. Particularly, his aim is to refute a version of the logical problem of evil associated with a form of religious determinism. In this paper, we revisit his first system to give a more suitable form to it, reformulating it in first-order modal logic. The new resulting system, called N1, has much of the original basic structure, and many axioms, (...) definitions, and theorems still remain; however, some new results are obtained. If the conclusions attained are correct and true, then N1 solves the problem of evil through the refutation of a version of religious determinism, showing that the attributes of God in Classical Theism, namely, those of omniscience, omnipotence, infallibility, and omnibenevolence, when adequately formalized, are consistent with the existence of evil in the world. We consider that N1 is a good example of how formal systems can be applied in solving interesting philosophical issues, particularly in Philosophy of Religion and Analytic Theology, establishing bridges between such disciplines. (shrink)

The radical redefinition of the landscape of physics that followed the contributions of Niels Bohr and Werner Heisenberg at the start of the 20th century led to plethora [of] new perspectives on age-old metaphysical questions on determinism and the nature of reality. The main contention of this article is that the work of Gilbert Simondon - whose magnum opus possesses a scope uniting the most basic philosophical concerns with the most recent breakthroughs in natural sciences - is highly relevant (...) for an adequate understanding of the split between determinism and indeterminism, as well as the underlying presuppositions which have driven some influential contributions to this topic. To this end, the article shows that the more deterministic interpretation of quantum mechanics offered by David Bohm and Louis de Broglie proves to be a valuable reference point for a more precise use and understanding of Simondon'ss transductive logic - especially when its philosophical lapses are considered closely. Finally, following the considerations of both thinkers, we aim at a more precise reconsideration of the stakes of indeterminism in modern physics, as well as a restructuration of what is often understood as a polarization. (shrink)

At the heart of the Stoic theory of modality is a strict commitment to bivalence, even for future contingents. A commitment to both future truth and contingency has often been thought paradoxical. This paper argues that the Stoic retreat from necessity is successful. it maintains that the Stoics recognized three distinct senses of necessity and possibility: logical, metaphysical and providential. Logical necessity consists of truths that are knowable a priori. Metaphysical necessity consists of truths that are knowable a (...) posteriori, a world order according to certain metaphysical principles and natures that god crafts within the constraints of matter. Finally, what is providentially necessary is what occurs according to the chain of fate, but only once it is in process or past. -/- The method of the paper is a close reading of Diogenes Laertius 7.75, adducing broad textual evidence along the way, to show that the Stoic theory of modality embraces Philonian possibility, both that which is capable of being true as a matter of logical consistency, and that which is possible according to the bare fitness of the entity. What differentiates the Stoics from Philo is their additional commitment to possibility as opportunity, resisting the collapse of determinism into necessity. (shrink)

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results (...) hold for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

Mark David Webster ABSTRACT: Using qualitative methods, the author sought to better understand how philosophical assumptions about technology affect the thinking, and influence the decision making, of educational technology leaders in their professional practice. One of the research questions focused on examining whether assumptions of technological determinism were present in thinking and influenced the decisions that leaders make. The core category that emerged from data analysis, Keep up with technology (or be left behind), was interpreted to be a manifestation (...) of the technological imperative, an assumption associated with the philosophical perspective of technological determinism. The article presents a literature review and critique of philosophical issues surrounding technological determinism. Data analysis led to the conclusion that technology leaders working in K-12 education place weighted priority on the technological imperative, and there is philosophical tension between Keep up with technology (or be left behind), and a concurrently held perspective based on the logic of the instrumental view of technology. The findings suggest that different accounts of technological determinism, including Bimber’s three accounts of normative, nomological, and unintended consequences, are significant in the thinking of participants. School technology leaders placed priority on embracing technological change, sometimes adopting technology for its own sake. (shrink)

The present paper has two main aims. The first one is philosophical and is related to the general topic of this volume (Logical Empiricism and Pragmatism): I would like to draw attention to the fact that the issue of classical scientific determinism, despite being ‘metaphysical’ and thereby ‘nonsensical’ according to the Vienna Circle's ‘scientific world conception’, bothered philosophers, like William James and Charles Peirce, who were deeply involved in scientific practice. At the end of the paper I shall (...) raise the question of why it was so and what this fact may suggest about the relationship between science and metaphysics. The second main aim of this paper is historico-philosophical: in the time span between the late 1870s and by the turn of 1900 James (1842–1910) and Peirce (1839–1914) contributed repeatedly to the ongoing discussions about scientific determinism. In this paper I give a general overview of their positions based mainly on primary sources and I embed them into the broader context of the history of the concept of scientific determinism, dedicating special attention to their relationship with a particular French anti-deterministic tradition (Renouvier, Poincaré, Boutroux and Bergson). (shrink)

Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the context (...) of nested sequents, referred to as "coloring," which consists of taking a formula as input, guessing a certain coloring of its subformulae, and then running proof-search in a nested sequent calculus on the colored input. Our technique lets us decide the validity of standpoint formulae in CoNP since proof-search only produces a partial proof relative to each permitted coloring of the input. We show how all partial proofs can be fused together to construct a complete proof when the input is valid, and how certain partial proofs can be transformed into a counter-model when the input is invalid. These "certificates" (i.e. proofs and counter-models) serve as explanations of the (in)validity of the input. (shrink)

The main thesis of this paper is that Pap’s The Functional A Priori of Physical Theory (Pap 1946, henceforth FAP) and Cassirer’s Determinism and Indeterminism in Modern Physics (Cassirer 1937, henceforth DI) may be conceived as two kindred accounts of a late Neo-Kantian philosophy of science. They elucidate and clarify each other mutually by elaborating conceptual possibilities and pointing out affinities of neo-Kantian ideas with other currents of 20th century’s philosophy of science, namely, pragmatism, conventionalism, and logical empiricism. (...) Taking into account these facts, it seems not too far fetched to conjecture that under more favorable circumstances Pap could have served as a mediator between the “analytic” and “continental” tradition thereby overcoming the dogmatic dualism of these two philosophical currents that has characterized philosophy in the second half the 20th century. (shrink)

NOTE TO READERS: My current research program is firmly grounded in the technical aspects of this dissertation. That said, my views have evolved significantly since writing it, e.g. I've flipped my views on the best working definition of 'determinism', and I no longer defend the viability of incompatibilist-impossibilism (I still grant the superficial logical consistency of the two views, but now contend that there is no way to defend one without rejecting the other). I have also given up (...) on the general project of rehabilitating the terms 'compatibilism' and 'incompatibilism', as I now see them as unhelpful hangovers from a degenerated research program. (shrink)

Logic has sometimes been seen as an alternative to metaphysics and to speculation. In this paper it is argued that a different story should be told when it comes to temporal logic and tense-logic in particular. A. N. Prior’s first formulation of tense logic was mainly established in order to qualify the discussion of certain metaphysical and conceptual problems. Although temporal logic has now been developed in various abstract and rather technical ways, it may still serve as a great help (...) for anyone who wants to clarify the discussion of important existential questions like the nature of time, determinism, future contingency or freedom of choice. (shrink)

A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and (...) of Everett’s many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory. (shrink)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach can be (...) naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (shrink)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a (...) non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...) the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)

A number of philosophers and theologians have argued that if God has knowledge of future human actions then human agents cannot be free. This argument rests on the assumption that, since God is essentially omniscient, God cannot be wrong about what human agents will do. It is this assumption that I challenge in this paper. My aim is to develop an interpretation of God’s essential omniscience according to which God can be wrong even though God never is wrong. If this (...) interpretation of essential omniscience is coherent, as I claim it is, then there is a logically consistent position according to which God is essentially omniscient, God foreknows what human agents will do, and yet it is possible for human agents to do otherwise. Thus, the argument for theological fatalism fails. (shrink)

This paper introduces and discusses three models of future: a determinist model, a stochastic model, and the model of True Prophetic Knowledge. All three models coexist in natural languages and are represented both in their grammatical systems and in the text-building discourse strategies speakers and authors apply to.

The assumption that known physical laws are sufficient for explaining mental phenomena is flawed from the outset. Qualities such as phenomenal redness do not exist within the known physical laws so by definition they are incomplete. Now assuming a new law was added that could explain how some physical property or vibration causes or is associated with phenomenal redness it would not be enough because it still wouldn’t explain how different qualities are bound together into a subjective unity. Assuming more (...) additional laws could now explain the popping into existence of subjective selves this also would still not be enough because a subjective self that cannot be directly observed nor indirectly observed via its effects vanishes into non-existence. This implies that subjective selves must have causal efficacy. But this would require still additional physical laws or perhaps an accommodated interpretation of quantum physics because there is no current understanding of how a mind can change the probability distribution of matter. But even if an expanded quantum physics was understood this would still not be enough because no general law can determine the indexical fact that I am me and you are you. -/- Then the hard problem of consciousness is real, non-trivial and when taken seriously appears to be actually separate problems. 1. How are qualia generated from purely physical activity? This appears to be a strictly deterministic process. 2. The so called binding problem. That is how is that I hear a sound and see a visual scene and feel a bodily sensation, all separate modalities that are unrelated, and yet I experience them all at the same time? 3. Can it be that I am causally efficacious? It certainly seems that the actual feelings of pain and pleasure serve some real purpose. Since conscious entities can never be directly observed and are only known through their effects, if they have no effects they disappear altogether. 4. The so called problem of indexicality. That is why I am me and not you. This seems to be a real fact above and beyond any objective fact. Eliminative materialism ignores the empirical evidence that phenomenal qualities exist and in doing so attains logical consistency. Other forms of emergence that try to explain qualia and give it a meaning while being restricted to physical closure are illogical. I explore these hard problems and arrive at a justification for a panpsychic interactive dualism. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an (...) m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. (shrink)

ABSTRACT: This is a little piece directed at the newcomer to Aristotle, making some general remarks about reading Aristotle at the beginning and end, with sandwiched in between, a brief and much simplified discussion of some common misunderstandings of Aristotle's philosophy, concerning spontaneity, causal indeterminism, freedom-to-do-otherwise, free choice, agent causation, logical determinism, teleological determinism, artistic creativity and freedom (eleutheria).

In the paper we provide an overview of issues related to the models used in the research on the logic of norms and actions. We present two models of the variability of the world: temporal (acyclic) and atemporal (cyclic). In the first one the past is always clearly defined, and the future is potentially “branched”. The second type of model allows for a return to the situation that took place. Next we describe different approaches towards agency modeling. We present the (...) most important paradigms, including the logic of actions, where actions are interpreted as transitions between the situations and STIT logic, which states only the responsibility of the agent for particular states of affairs. We discuss questions of determinism and indeterminism of actions, identification of basic actions and operations and the issue of identity. The final part of the paper is devoted to deontic categories. In particular, the applicability of the concepts of strong and weak permission and prohibition in different situational contexts, and their relationship to the two concepts of obligation: abstract and derived. (shrink)

The famous EPR article of 1935 challenged the completeness of quantum mechanics and spurred decades of theoretical and experimental research into the foundations of quantum theory. A crowning achievement of this research is the demonstration that nature cannot in general consist in noncontextual pre-measurement properties that uniquely determine possible measurement outcomes, through experimental violations of Bell inequalities and Kochen-Specker theorems. In this article, I reconstruct an argument from Niels Bohr’s writings that the reality of the Einstein-Planck-de Broglie relations alone implies (...) that no such properties can exist for momentum and position measurements, show how this argument responds to the challenge of EPR on general physical grounds, and advance that this reconstruction shows that and how Bohr’s “complementarity” is a view of the objective content and logic of quantum theory. (shrink)

The Lazy Argument, as it is preserved in historical testimonies, is not logically conclusive. In this form, it appears to have been proposed in favor of part-time fatalism (including past time fatalism). The argument assumes that free will assumption is unacceptable from the standpoint of the logical fatalist but plausible for some of the nonuniversal or part-time fatalists. There are indications that the layout of argument is not genuine, but taken over from a Megarian source and later transformed. The (...) genuine form of the argument seems to be given in different form and far closer to Megarian logical fatalism and its purpose is not to defend laziness. If the historical argument has to lead to a logically satisfactory solution, some additional assumptions and additional tuning is needed. (shrink)

In the contemporary philosophical debate about probability, one of the main problems con‐ cerns the relation between objective probability and determinism. Is it possible for objective probability and determinism to co‐exist? this is one of the questions this dispute tries to answer. the scope of discussion is conducted between advocates of a positive answer (com‐ patibilist) and co‐existence opponents (incompatibilist). In the early twentieth century, many logicians also developed topics regarding probability and determinism. One of them was (...) the outstanding Polish logician and philosopher — Jan Łukasiewicz. the general purpose of this paper is to analyse and implement Łukasiewicz’s views regarding determinism and probability in the contemporary eld of this problem. I will try to show the relation between his interpre‐ tations of these concepts and in consequence his attempt to con ont them. As a result of the above analysis, I present some di erent positions (located in the elds of logic and semantics) in the contemporary discourse about the relation between objective probability and determi‐ nism. moreover, I will present Łukasiewicz’s views about this relation and the consequence of these solutions in the eld of logic. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs (...) recover the validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)

In this paper, I challenge the traditional narrative that William James’s arguments against determinism were primarily motivated by his personal struggles with depression. I argue that James presents an alternative argument against determinism that is motivated by his commitment to sound scientific practice. James argues that determinism illegitimately extrapolates from observations of past events to predictions about future events without acknowledging the distinct metaphysical difference between them. This occupation with futurity suggests that James’s true target is better (...) understood as logical determinism rather than causal determinism. This has consequences for James’s proposed alternative, which I call his probabilistic underdeterminism, a conception of the universe that is built on chance, choice, and a local teleology. All of this forms part of a broader criticism of the scientific practices of his day based on their widespread failure to acknowledge the distorting effects of observation on that which is observed. (shrink)

In this paper we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics. We give a characterization of the degree of non-functionality which is compatible with the propositional structure of quantum theory, showing that having truth-functional connectives, together with some assumptions regarding the relation of logical consequence, commits us to the adequacy of the interpretation sets of these connectives. An advantage of our proof is that it is independent (...) of the number of truth values involved, generalizing previous works. We also show the failure of the adequacy of every Nmatrix that is a model of the non-distributive lattice of quantum propositions. En este trabajo discutimos las nociones de adecuación y veritativo-funcionalidad en la lógica cuántica, desde el punto de vista de una semántica no determinista. Damos una caracterización del grado de no-funcionalidad compatible con la estructura proposicional de la teoría cuántica, mostrando que tener conectivos veritativo-funcionales, junto con algunos presupuestos relativos a la relación de consecuencia lógica, nos compromete con la adecuación de los conjuntos de interpretación de estos conectivos. Un punto ventajoso de nuestra prueba es que se independiza de la cantidad de valores de verdad involucrados, generalizando trabajos previos. Probamos también que falla la adecuación de cualquier Nmatriz que sirva como modelo para el retículo no distributivo de proposiciones cuánticas. (shrink)

Demonstrates the sophistication of Seneca’s Stoicism by setting his contributions within the context of his school. Seneca’s contributions to physics, metaphysics, logic, determinism, theodicy and eschatology are set within a systematic reconstructions of Stoic positions. Ample documentation of sources and scholarship as well as the thematic, handbook-like structure allow for this book to be used as a look-up tool and introduction to the Stoic cosmos and the place of humans within it. -/- There are a number of new readings (...) and interpretations, e.g. concerning the corporeality of the principles; mixture (krasis di’ holôn); the elements and pneuma; identity; the relation of God and humans; Seneca’s attitude to logic; Seneca’s philosophy of time; the role of lekta in defining reality and action; Stoic and Senecan theodicy; Seneca’s contribution to the determinism debate. (shrink)

A general mathematical framework, based on countable partitions of Natural Numbers [1], is presented, that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy criteria to be used to assess formulas associated with the same connective, but that differ in their complexity. The presented method can be adapted potentially infinite number of connectives and truth values, (...) therefore, it can be considered a general framework to provide semantics to several of the known logic systems (eg, LC, L3 LP, FDE). The presented semantics allow to converge to different standard semantics if the separation complexity procedure is annulled. Therefore, it can be understood as a framework that allows greater precision (in complexity terms) with respect to formula satisfaction. Naturally, because of how it is built, it can be incorporated into non-deterministic semantics. The presented procedure also allows generating valuations that grant a different truth value to each formula of propositional language. As a positive side effect, our method allows a constructive proof of the equipotence between N and N^n for all Natural n. (shrink)

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in (...) exploring the foundations of multialgebras applied to the study of logic systems. -/- It is well known from universal algebra that, for every signature Sigma, there exist algebras over Sigma which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of Sigma-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms (or propositional formulas, in the context of logic). Equivalently, the forgetful functor, from the category of Sigma-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor U, from the category of Sigma-multialgebras to Set, does not have a left adjoint. -/- In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices (which selects how a homomorphism approaches indeterminacies), there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that U does not have a left adjoint. (shrink)

FDE, LP and K3 are closely related to each other and admit of an intuitive informational interpretation. However, all these logics are co-NP complete, and so idealized models of how an agent can think. We address this issue by shifting to signed formulae, where the signs express imprecise values associated with two bipartitions of the corresponding set of standard values. We present proof systems whose operational rules are all linear and have only two structural branching rules that express a generalized (...) Principle of Bivalence. Each of these systems leads to defining an infinite hierarchy of tractable approximations to the respective logic, in terms of the maximum number of allowed nested applications of the two branching rules. Further, each resulting hierarchy admits of an intuitive 5-valued non-deterministic semantics. (shrink)

It is a widely held principle that no one is able to do something that would require the past to have been different from how it actually is. This principle of the fixity of the past has been presented in numerous ways, playing a crucial role in arguments for logical and theological fatalism, and for the incompatibility of causal determinism and the ability to do otherwise. I will argue that, assuming bivalence, this principle is in conflict with standard (...) views about knowledge and the semantics for ‘actually’. I also consider many possible responses to the argument. (shrink)

This paper explores the liar paradox and its implications for logic and philosophical reasoning. It analyzes the paradox using classical logic principles and paraphrases it as "affirmation of the falsity of the very affirmation." The study draws connections between the liar paradox and Hegel's speculative sentence and suggests it functions as a "quasi-speculative sentence." Additionally, it examines parallels with the logocentric predicament and the determinist's assertion, highlighting their paradoxical nature. Through these analyses, the paper aims to illuminate the fundamental paradoxes (...) in our reasoning and logic. (shrink)

Edward Nieznański developed two logical systems in order to deal with a version of the problem of evil associated with two formulations of religious determinism. The aim of this research was to revisit these systems, providing them with a more appropriate formalization. The new resulting systems, namely, N1 and N2, were reformulated in first-order modal logic; they retain much of their original basic structures, but some additional results were obtained. Furthermore, our research found that an underlying minimal set (...) of axioms is enough to settle the questions proposed. Thus, we developed a minimal system, called N3, that solves the same issues tackled by N1 and N2, but with less assumptions than these systems. All of the systems developed here are proposed as solutions to the logical problem of evil through the refutation of two versions of religious determinism, showing that the attributes of God in Classical Theism, namely, those of omniscience, omnipotence, infallibility, and omnibenevolence, when formalized, are consistent with the existence of evil, providing one more response to this traditional issue. (shrink)

The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no (...) matter whether the proposition is about the past, present or future. In particular, the argument goes, whatever one does or does not do in the future is determined in the present by the truth or falsity of the corresponding proposition. The second argument coming from logic is much more modern and appeals to Gödel's incompleteness theorems to make the case against determinism and in favour of free will, insofar as that applies to the mathematical potentialities of human beings. The claim more precisely is that as a consequence of the incompleteness theorems, those potentialities cannot be exactly circumscribed by the output of any computing machine even allowing unlimited time and space for its work. The chapter concludes with some new considerations that may be in favour of a partial mechanist account of the mathematical mind. (shrink)

According to informal logic, the possibilities of deductive logic as a tool for analysing and evaluating ordinary arguments are very limited. While I agree with this claim in general, I question it in the case of the argument from cause to effect. In this paper I first show, on the basis of carefully chosen examples, that we usually react differently to falsification of the conclusion of the argument from cause to effect than we do to the falsification of the conclusion (...) of other defeasible arguments. I then identify general conditions and assumptions under which the causal argument from cause to effect can be reconstructed as deductive. Finally, I compare the causal argument with the expert argument, which is a typical example of a defeasible argument in the narrower sense. (shrink)

Necessity is a touchstone issue in the thought of Charles Peirce, not least because his pragmatist account of meaning relies upon modal terms. We here offer an overview of Peirce’s highly original and multi-faceted take on the matter. We begin by considering how a self-avowed pragmatist and fallibilist can even talk about necessary truth. We then outline the source of Peirce’s theory of representation in his three categories of Firstness, Secondness and Thirdness, (monadic, dyadic and triadic relations). These have modal (...) purport insofar as the first category corresponds to possibility, the second to mechanical necessity and the third to a kind of semantic or intentional necessity. We then turn to Peirce’s explicit modal epistemology and show how it began as information-relative, with different modalities (e.g. logical, physical, practical) distinguished in terms of respective ‘designated states of information’, and shifted later in his life towards a more robust realism founded in direct perception of ideas in their relations. We then turn to Peirce’s formal logic, focusing on his diagrammatic system of Existential Graphs where he did his most serious logical research. Finally we discuss Peirce’s modal metaphysics and its implications for determinism and realism about universals. (shrink)

The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Goedel's (first) incompleteness theorem. In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (i.e. uncorrelated measurement (...) settings, as in 't Hooft's cellular automaton interpretation of quantum mechanics). The main point is that Bell and others did not exploit the full empirical content of quantum mechanics, which consists of long series of outcomes of repeated measurements (idealized as infinite binary sequences): their arguments only used the long-run relative frequencies derived from such series, and hence merely asked hidden variable theories to reproduce single-case Born probabilities defined by certain entangled bipartite states. If we idealize binary outcome strings of a fair quantum coin flip as infinite sequences, quantum mechanics predicts that these typically (i.e. almost surely) have a property called 1-randomness in logic, which is much stronger than uncomputability. This is the key to my claim, which is admittedly based on a stronger (yet compelling) notion of determinism than what is common in the literature on hidden variable theories. (shrink)

The deterministic or probabilistic laws of our representations and our science do not link what “is” to what “will be” but what “I know” to what “I could know”. Consistency is not a predicate on the physical laws of the world but on the logical laws of Meaning. If you cannot convince yourself of that. If you want to believe that the Softmatter of the Meaning cannot be more consistent than the Hardmatter of the physical world. Think again ... (...) ...and try to answer this question : Why would it be less unlikely for a physical world to evolve from the big bang to individuated knowing persons than for an amorphous interdependence to assemble (logically) individuated representations of the world ? (shrink)

In this paper I present and evaluate van Inwagen’s famous Consequence Argument, as presented in An Essay on Free Will. The grounds for the incompatibility of freewill and determinism, as argued by van Inwagen, is dependent on our actions being logical consequences of events outside of our control. Particularly, his arguments depend upon, in one guise or another, the transference of the modal property of not being possibly rendered false through the logical consequence relation, i.e. the β-principle. (...) I argue that, due to the symmetric nature of determinism, van Inwagen is exposed to what I call “reversibility arguments” in the literature. Such arguments reverse the β-principle and start from our apparent control over our own actions to our control over the initial conditions. Since van Inwagen does not endorse a particular theory of laws or logical consequence, he is open to such counterarguments. The plausibility of such reversibility arguments depends on what would be called a Wittgensteinian conception of logical consequence. In the _Remarks on the Foundation of Mathematics_, one of Wittgenstein’s main concerns is the normativity of logical inference i.e. proof. Such concerns with normativity and rule-following are generally a feature of his later philosophy. In the _Remarks_ Wittgenstein resists a conception of logical deduction which places the source of normativity outside of human practice. (shrink)

Volition and Allied Causal Concepts is a work of aetiology and metapsychology. Aetiology is the branch of philosophy and logic devoted to the study of causality (the cause-effect relation) in all its forms; and metapsychology is the study of the basic concepts common to all psychological discourse, most of which are causal. Volition (or free will) is to be distinguished from causation and natural spontaneity. The latter categories, i.e. deterministic causality and its negation, have been treated in a separate work, (...) The Logic of Causation. Volition may be characterized as personal causality, a relation between an agent (the self or soul) and his actions (acts of will). Unlike causation, this relation cannot be entirely defined using conditional (if–then) propositions. Although we can say that the agent is a sine qua non of his actions, we cannot say that the agent is invariably (in all or specific circumstances) followed by his actions. It appears that both an act of will and its negation remain possible to a soul in any given set of circumstances. This defines freedom of the will, and implies the responsibility of the agent for his actions. Introspection provides knowledge of particular acts of will. The existence of freewill implies a distinction between necessary causation (determinism independent of volition) and inertial causation (determinism, except when some contrary will interferes). An act of will occurs on a spiritual plane. It may have natural (mental or physical) consequences; those that inevitably follow it may be regarded as directly willed, whereas those that vary according to circumstances must be considered indirectly willed. Volition presupposes some degree of consciousness. So-called involuntary acts of will involve a minimum of attention, whereas mindful acts are fully conscious. Even pure whim involves intention. Most volitions moreover involve valuation, some sort of projection of goals, deliberation on means, choice and decision. To judge responsibility, various distinctions are called for, like that between intentional, incidental and accidental consequences. Volitional action can be affected through the terms and conditions of the world surrounding its agent, but also more intimately through the influence of concrete or abstract aspects of that world that the subject has cognized. The causal concept of influence, and its implication of cognition (of inner or outer information, including emotions), are crucial to measuring the effort involved in volition. Influences make willing easier or harder, yet do not curtail its essential freedom. All the causal concepts used in psychological explanation – affections, appetites, instincts, habits, obsessions, compulsions, urges and impulses – can be elucidated thanks to this important finding. Much of human (and animal) behavior can thus be both acknowledged as volitional and as variously influenced. Volition and Allied Causal Concepts is a work of ambitious scope, intent on finally resolving philosophical and logical issues that have always impeded progress in psychology. It clarifies the structure and workings of the psyche, facilitating hygienic and therapeutic endeavors. The relation between volition and physical laws is discussed, as is the place of volition in biology. Concepts used in biology, analogous to that of purpose, are incidentally analyzed. Theological issues are also dealt with, as are some topics in ethics and law. (shrink)