Anti-exceptionalism about logic is the thesis that logic is not special. In this paper, I consider, and reject, a challenge to this thesis. According to this challenge, there are basic logical principles, and part of what makes such principles basic is that they are epistemically exceptional. Thus, according to this challenge, the existence of basic logical principles provides reason to reject anti-exceptionalism about logic. I argue that this challenge fails, and that the (...) exceptionalist positions motivated by it are thus unfounded. I make this case by disambiguating two senses of ‘basic’ and showing that, once this disambiguation is taken into account, the best reason we have for thinking that there are basic principles actually implies that those principles do not require a special epistemology. Consequently, the existence of basic logical principles provides reason to accept, rather than reject, anti-exceptionalism concerning the epistemology of logic. I conclude by explaining how an abductivist, anti-exceptionalist approach to the epistemology of logic can accommodate the notion of basic logical principles. (shrink)

Aristotle shares with Plato the attitude that the world, ‘the all,’ is a kosmos, a well-ordered and beautiful whole which, as such, can be rendered intelligible, or understood, by the intellect. One understands things, generally speaking, by tracing them back to their sources, origins or principles and causes or explanatory factors, and seeing in what manner they are related to these principles. We know, or understand, a thing when we grasp ‘the why’ or cause. Consequently, understanding is systematic. (...) Some things we understand through themselves - these are the first principles and as such are not understood by tracing them back to causes. We understand other things by systematically relating them in appropriate ways to what is known through itself. These other things are known through, or by means of, their causes and principles. (shrink)

We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility. A logical constant obeys to the principle of reflection if it is characterized semantically by an equation (...) binding it with a metalinguistic link between assertions, and if its syntactic inference rules are obtained by solving that equation. All connectives of basic logic satisfy reflection. To the control of weakening and contraction of linear logic, basic logic adds a strict control of contexts, by requiring that all active formulae in all rules are isolated, that is visible. From visibility, cut-elimination follows. The full, geometric symmetry of basic logic induces known symmetries of its extensions, and adds a symmetry among them, producing the structure of a cube. (shrink)

Fitch's basic logic is an untyped illative combinatory logic with unrestricted principles of abstraction effecting a type collapse between properties (or concepts) and individual elements of an abstract syntax. Fitch does not work axiomatically and the abstraction operation is not a primitive feature of the inductive clauses defining the logic. Fitch's proof that basic logic has unlimited abstraction is not clear and his proof contains a number of errors that have so far gone undetected. This paper corrects (...) these errors and presents a reasonably intuitive proof that Fitch's system K supports an implicit abstraction operation. Some general remarks on the philosophical significance of basic logic, especially with respect to neo-logicism, are offered, and the paper concludes that basic logic models a highly intensional form of logicism. (shrink)

In their Basic Logic, Sambin, Battilotti and Faggian give a foundation of logical inference rules by reference to certain reflection principles. We investigate the relationship between these principles and the principle of Definitional Reflection proposed by Hallnäs and Schroeder-Heister.

At least some of us, at least some of the time—when not in the grip of radical sceptical doubt—are inclined to believe that we know, for example, that if we infer a conclusion from two true premises, one a conditional whose consequent is that conclusion and the other the antecedent of that conditional, then our conclusion must be true, or that we know similar things about other simple patterns of inference. If we do indeed have knowledge of this sort, it (...) is what I mean by logical knowledge. Logical knowledge is, roughly speaking, knowledge about logic—such as knowledge that a certain principle of inference necessarily preserves truth, or that every proposition of a certain form must be true—and so is not the same thing as knowledge that is gained by using logic, i.e. inferential knowledge. That is not to say, of course, that logical knowledge can't be inferential. On the contrary, it is barely open to question that—if there is any logical knowledge at all—there is a lot of inferential logical knowledge. For example, if we know that the introduction and elimination principles for the conditional are truth-preserving, we can surely get to know, by inference, that the principle of hypothetical syllogism is so too, not to mention other, less obvious and more recondite, examples of putative logical knowledge. (shrink)

Critical examination of Alchourrón and Bulygin’s set-theoretic definition of normative system shows that deductive closure is not an inevitable property. Following von Wright’s conjecture that axioms of standard deontic logic describe perfection-properties of a norm-set, a translation algorithm from the modal to the set-theoretic language is introduced. The translations reveal that the plausibility of metanormative principles rests on different grounds. Using a methodological approach that distinguishes the actor roles in a norm governed interaction, it has been shown that metanormative (...) principles are directed second-order obligations and, in particular, that the requirement related to deductive closure is directed to the norm-applier role rather than to the norm-giver role. The approach has been applied to the case of pure derogation yielding a new result, namely, that an independence property is a perfection-property of a norm-set in view of possible derogation. This paper in a polemical way touches upon several points raised by Kristan in his recent paper. (shrink)

This article is a discussion of E. K. Emilsson, Plotinus (London and New York, 2017). Three themes are selected: causation; the holistic account of intelligible being; the status of matter and body. The discussion ends with some remarks about Emilsson’s approach to Plotinus’ philosophy. Emilsson’s account of Plotinus’ causation is based on the transmission model, what Emilsson calls ‘the principle of prior possession’. Here it is argued that the transmission model requires qualifications in order to be applied to Plotinus’ account (...) of causation. The section on Plotinus’ holism focuses on two analogies: that of science and its theorems and that of craftsmanship. The section on matter and body addresses the issue of Plotinus’ dualism as different from Cartesian dualism. The final remarks assess Emilsson’s philosophical approach to Plotinus, his use of contemporary philosophical notions, and the problem of Plotinus’ philosophical mysticism. (shrink)

This book concisely states the main laws and precepts of formal logic along with their immediate corollaries. Commentary is kept to a minimum.

Kritičko čitanje Alchourrónove i Bulyginove skupovnoteorijske defnicije normativnoga sustava pokazuje da njegova deduktivna zatvorenost nije neizbježno svojstvo. Slijedeći von Wrightovu pretpostavku da aksiomi standardne deontične logike opisuju svojstva savršenoga normativnog sustava, uvodi se algoritam za prevođenje iz modalnoga u skupovnoteorijski jezik. Prijevod nam otkriva da plauzibilnost pojedinih metanormativnih načela leži na različitim osnovama. Koristeći se metodološkim pristupom koji prepoznaje različite aktere u normama upravljanome međudjelovanju, pokazuje se da su metanormativna načela obveze drugoga reda upućene različitim ulogama. Poseban slučaj jest zahtjev (...) koji se odnosi na deduktivnu zatvorenost jer se pokazuje da je upućen ulozi koja primjenjuje, a ne onoj koja izdaje norme. Pristup je primijenjen i na slučaj čiste derogacije, što dovodi do novoga rezultata; svojstvo neovisnosti biva svojstvom savršenoga normativnog sustava u odnosu na moguću derogaciju. Ovaj članak na polemički način dodiruje nekoliko točaka iznesenih u Kristanovome nedavnom članku. (shrink)

F. H. Bradley was the foremost philosopher of the British Idealist school, which came to prominence in the second half of the nineteenth century and remained influential into the first half of the twentieth. Bradley, who was educated at Oxford, and spent his life as a fellow of Merton College, was influenced by Hegel, and also reacted against utilitarianism. He was recognised during his lifetime as one of the greatest intellectuals of his generation and was the first philosopher to receive (...) the Order of Merit, in 1924. In this major work, originally published in 1883, Bradley discusses the basic principles of logic: judgment and inference. He rejects the idea of a separation between mind and body, arguing that human thought cannot be separated from its worldly context. In the second edition, published in 1922 and reissued here, Bradley added a commentary and essays, but left the text largely unaltered. (shrink)

Clear focus on its application of formal logic to ordinary English is the most distinctive feature of this textbook for the introductory course in deductive logic. Great care is taken with the appropriate translation into logical languages of ordinary English sentences. Evaluation of these translations promotes a more effective use of ordinary language. The Principles of Deductive Logic presents symbolic logic in a fuller and more leisurely fashion than other introductory textbooks. Early chapters cover informal material, including definition (...) and informal fallacies. The remainder of the text is devoted to the treatment of four distinct artificial languages. The Categorical language is the language of syllogistic logic. The Extended Categorical language enriches this first language with the symbolic connectives for conjunction and negation. The Propositional Connective language and the First-Order language are the two basic languages of modern logic. Each language is accompanied by a deductive system, and is used as an instrument for exploring ordinary language, including ordinary arguments The book contains a large number of exercises whose answers are supplied in the back of the book, and many more that can be assigned as homework. A solution’s manual is available to instructors upon their request. The request must be written on college or university letterhead. (shrink)

Doubts concerning the validity of logic are as old as the empirical criticism of science. In the last two decades the idea that truth is relative to given sets of basic assumptions has been prominent; and the controversy about the principle of excluded middle has focussed renewed attention upon the nature of logic and its fundamental principles.Recent investigations in formal logic have contributed greatly to the understanding of the principles of logic. It is simply a misunderstanding to (...) conclude from them that the logical principles have been suspended, despite the various formal structures which are called “logics.” The purely formal treatment of problems concerning the foundations of logic, while necessarily undertaken as far as it can go, has essential limitations. (shrink)

This paper presents new constructions of models of Hume's Principle and Basic Law V with restricted amounts of comprehension. The techniques used in these constructions are drawn from hyperarithmetic theory and the model theory of fields, and formalizing these techniques within various subsystems of second-order Peano arithmetic allows one to put upper and lower bounds on the interpretability strength of these theories and hence to compare these theories to the canonical subsystems of second-order arithmetic. The main results of this (...) paper are: (i) there is a consistent extension of the hyperarithmetic fragment of Basic Law V which interprets the hyperarithmetic fragment of second-order Peano arithmetic, and (ii) the hyperarithmetic fragment of Hume's Principle does not interpret the hyperarithmetic fragment of second-order Peano arithmetic, so that in this specific sense there is no predicative version of Frege's Theorem. (shrink)

This article proposes a basic logic for application in physics dispensing with the Principle of Excluded Middle. It is based on the article “Matrix Based Logics for Application in Physics (RMQ) which appeared 2009. In his article with Stachow on the Principle of Excluded Middle in Quantum Logic (QL), Peter Mittelstaedt showed that for some suitable QLs, including their own, the Principle of Excluded Middle can be added without any harm for QL; where ‘without any harm for QL’ means (...) that the basic desiderata and the basic results (theorems) of those QLs remain satised in the sense that they avoid the well known difficulties with commensurability and distributivity.In the following article I want to show that the basic desiderata and results (theorems) of RMQ (of avoiding the well-known difficulties with commensurability, distributivity, fusion and Bell’s inequalities) remain satised if by introducing a strong negation (or strong negation and disjunction) the resulting weak intuitionist system RMQI dispenses with the Principle of Excluded Middle; it becomes either invalid or not strictly valid. (shrink)

As anyone who is familiar with the literature knows, there is a great deal of controversy concerning which, if any, of the extant theories of propositional modal logic correctly formalizes the logic of certain logical concepts such as analyticity and logical necessity. Most of the controversy concerns certain principles that involve iterated modalities (where one modal operator occurs within the scope of another). For example, there is considerable disagreement about whether the principle(□p⊃□□p)should be considered valid. However, when (...) philosophers and logiciansapplymodal logic to concrete problems, they rarely need principles which involve iterated modalities. For most practical purposes, principles involving only one layer of modalities are all that are needed. This suggests that if we try to construct a theory of modal logic in which there are no iterated modalities, we can avoid most of the controversy and still have a theory that is strong enough for all of the normal uses to which modal logic is put. (shrink)

I address a type of circularity threat that arises for the view that we employ general basic logical principles in deductive reasoning. This type of threat has been used to argue that whatever knowing such principles is, it cannot be a fully cognitive or propositional state, otherwise deductive reasoning would not be possible. I look at two versions of the circularity threat and answer them in a way that both challenges the view that we need to (...) apply general logical principles in deductive reasoning and defuses the threat to a cognitivist account of knowing basic logical principles. (shrink)

Epistemic Logic is our basic universal science, the method of our cognitive confrontation in reality to prove the truth of our basic cognitions and theories. Hence, by proving their true representation of reality we can self-control ourselves in it, and thus refuting the Berkeleyian solipsism and Kantian a priorism. The conception of epistemic logic is that only by proving our true representation of reality we achieve our knowledge of it, and thus we can prove our cognitions to be (...) either true or rather false, and otherwise they are doubtful. Therefore, truth cannot be separated from being proved and we cannot hold anymore the principle of excluded middle, as it is with formal semantics of metaphysical realism. In distinction, the intuitionistic logic is based on subjective intellectual feeling of correctness in constructing proofs, and thus it is epistemologically encapsulated in the metaphysical subject. However, epistemic logic is our basic science which enable us to prove the truth of our cognitions, including the epistemic logic itself. (shrink)

A lean hylomorphism stands as a metaphysical holy grail. An embarrassing feature of traditional hylomorphic ontologies is prime matter. Prime matter is both so basic that it cannot be examined (in principle) and its engagement with the other hylomorphic elements is far from clear. One particular problem posed by prime matter is how it is to be understood both as a principle of individuation for material substances and as pure potency. I present Thomas Aquinas’s way of squeezing some intelligibility (...) out of prime matter by modeling it on the idea of logical genus. Such a modeling provides insight into understanding prime matter as substratum, as maximally indeterminate, and as ontologically vague. One of the unusual but exciting things that fall out from this analysis of prime matter is the Entirety Thesis: “For any substance x, if x has prime matter then the prime matter of x is the same* as x,” where ‘same*’ is understood as “indeterminately identical.”. (shrink)

What is the proper role of logic in analytic theology? This question is thrown into sharp relief when a basic logical principle is questioned, as in Beall’s ‘Christ – A Contradiction.’ Analytic philosophers of logic have debated between exceptionalism and anti-exceptionalism, with the tide shifting towards anti-exceptionalism in recent years. By contrast, analytic theologians have largely been exceptionalists. The aim of this paper is to argue for an anti-exceptionalist view, specifically treating logic as a modelling tool. Along the (...) way I critically engage with Beall on the role of logic in theology, maintaining that theological inquiry is in some ways disanalogous with other theoretical enterprises. (shrink)

In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid (...) class='Hi'>principles that relate the various notions of proving to each other and to notions of justified knowledge, implicit knowledge, and possibility. We also point out and comment upon certain principles our semantics fails to validate. (shrink)

This lively introductory text exposes the student in the humanities to the world of discrete mathematics. A problem-solving based approach grounded in the ideas of George Pólya are at the heart of this book. Students learn to handle and solve new problems on their own. A straightforward, clear writing style and well-crafted examples with diagrams invite the students to develop into precise and critical thinkers. Particular attention has been given to the material that some students find challenging, such as proofs. (...) This book illustrates how to spot invalid arguments, to enumerate possibilities, and to construct probabilities. It also presents case studies to students about the possible detrimental effects of ignoring these basic principles. The book is invaluable for a discrete and finite mathematics course at the freshman undergraduate level or for self-study since there are full solutions to the exercises in an appendix. (shrink)

Let S be a set, P the class of all subsets of S and F the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P into a fuzzy closure operator J* defined in F. This enables us to give the notion of canonical extension of a deduction system and to (...) give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory. (shrink)

The purpose of this article was to comprehensively explore the phenomenon of the narrative of the Decalogue in its fundamental principles in the context of the theological understanding of Jewish law. For this purpose abstract-logical methods, historical-legal, phenomenological, axiological, epistemological methods, method of critical and systematic analysis and method of comparative theology were used. The result is a theological understanding of the basic moral and legal principles and reducing to a single, systematic; a study of the (...) correlation between the normative and the moral side of such a narrative was conducted. Of particular importance is the establishment and isolation of the basic initial principle in the defined context that underlies both Sinai law and all the biblical law. Because with the change of historical realities, which coincided with the destruction of the Temple and the termination of sacrifices, the law has also changed. However, the biblical law was of particular ideological importance, it set the tone and revealed and formed the basic principles for the further development of all Jewish law. Therefore, in our study we have drawn attention to the main ideological features of the biblical laws, because in our opinion, the basic formative essence is hidden in them and only by understanding it − will we be able to understand Jewish law itself. However, the phenomenon of law and even more so of Jewish law, is one of the best regulators and exponents of the educational principle that is designed to raise a person in love. Of course, morality is called for it and it should take precedence over everything else, but the legal part should not be ignored. Law should serve as a socially just, integrative, fundamental, binding, most effective, most respected regulator. Therefore, the problem of combining legal principles and moral precepts for biblical law did not stand basically. The significant part of the adopted legal norms initially was characterized by moral prescriptions, confirmed and expressed by law. Such a transition, the shift from morality to law, and the close relationship between them are one inseparable whole. And apart from Halacha, which was responsible for the legal aspect, there were also the writings of the prophets whose task was to illuminate the transition from law to morality, because precisely morality is the essence of everything. Here is the true meaning of the existence of a legal expression of such an educational principle. Thus, the basic educational principle of the Decalogue, in particular, and of biblical law in general, was to educate a high-moral person who had restrictive precepts that would not allow him to fall into lawlessness, and the formative commandments that would allow a person to be educated in the search for God, and to stabilize himself in the godlike state commanded by God through Moses. That is the essence of the Decalogue and Jewish law. The educational principle, both basic and effective, though not so familiar to the modern understanding of the nature of law, is precisely the principle that laid down both the basis of the Decalogue and the foundation of all Jewish law at least in its biblical part. (shrink)

Abstractionism in the philosophy of mathematics aims at deriving large fragments of mathematics by combining abstraction principles (i.e. the abstract objects $\S e_1, \S e_2$, are identical if, and only if, an equivalence relation $Eq_\S$ holds between the entities $e_1, e_2$) with logic. Still, as highlighted in work on the semantics for relevant logics, there are different ways theories might be combined. In exactly what ways must logic and abstraction be combined in order to get interesting mathematics? In this (...) paper, we investigate the matter by deriving the axioms of second-order Peano Arithmetic from Frege's Basic Law V (the extension of $F$ is identical with the extension of $G$ if, and only if, $F$ and $G$ are extensionally equivalent) in the presence of a relevant higher-order logic. The results are interesting. Not only must we take on logic as true, and not only must we apply our logic to abstraction principles, but also we have to apply our theory of abstraction back to the logic in order to arrive at arithmetic. Thus, what Abstractionism gives us is not simply what we get from abstraction via logic, but also what we get from logic via abstraction. (shrink)

Metaphysics and language: Quine, W. V. O. On the individuation of attributes. Körner, S. On some relations between logic and metaphysics. Marcus, R. B. Does the principle of substitutivity rest on a mistake? Van Fraassen, B. C. Platonism's pyrrhic victory. Martin, R. M. On some prepositional relations. Kearns, J. T. Sentences and propositions.--Basic and combinatorial logic: Orgass, R. J. Extended basic logic and ordinal numbers. Curry, H. B. Representation of Markov algorithms by combinators.--Implication and consistency: Anderson, A. R. (...) Fitch on consistency. Belnap, N. D., Jr. Grammatical propaedeutic. Thomason, R. H. Decidability in the logic of conditionals. Myhill, J. Levels of implication.--Deontic, epistemic, and erotetic logic: Bacon, J. Belief as relative knowledge. Wu, K. J. Believing and disbelieving. Kordig, C. R. Relativized deontic modalities. Harrah, D. A system for erotetic sentences. (shrink)

This book is devoted to the problems of the growth of science. These prob lems, neglected for a long time by the philosophers of science, have become in the 60's and 70's a subject of vivid discussion. There are philosophers who stress only the dependence of science upon various sociological, psycho logical and other factors and deny any internal laws of the development of knowledge, like approaching the truth. The majority rejects such nihilism and searches for the laws of (...) the growth of science. However, they often overlook the role of the Correspondence Principle which connects the suc cessive scientific theories. On the other hand, some authors, while stressing the role of this principle, overlook logical difficulties connected with it, e. g. the problem of the incompatibility of successive theories, of the falsity of some of their assumptions, etc. I believe the Correspondence Principle to be a basic principle of the pro gress of contemporary physics and, probably, of every advanced science. How ever, this principle must be properly interpreted and the above-mentioned logical difficulties must be solved. Their solution requires, as it seems, revealing the idealizational nature of the basic laws of science, in any case of the quantitative laws of advanced sciences. This point has been recently emphasized by some Polish philosophers, especially in Poznan. (shrink)

F. H. Bradley was the foremost philosopher of the British Idealist school, which came to prominence in the second half of the nineteenth century and remained influential into the first half of the twentieth. Bradley, who was influenced by Hegel and also reacted against utilitarianism, was recognised during his lifetime as one of the greatest intellectuals of his generation, and was the first philosopher to receive the Order of Merit, in 1924. In this major work, originally published in 1883, Bradley (...) discusses the basic principles of logic: judgment and inference. He rejects the idea of a separation between mind and body, arguing that human thought cannot be separated from its worldly context. In the second edition, published in 1922 and reissued here, Bradley added a commentary and essays, but left the text largely unaltered. Volume 1 contains Book 1 on judgment and Book 2 on inference. (shrink)

This article is divided into five parts. After a brief example in the first part, the second explains what historical sense-generation is about. The third characterizes tradition as a pregiven condition of all historical thinking. With respect to this condition, the constructivist theory of history is criticized as one-sided. The fourth part presents tradition as one of the four basic sense criteria of historical narration. The article concludes with a discussion of the role of tradition in the historical culture (...) of modern societies.Historical sense-generation is a mental procedure by which the past is interpreted for the sake of understanding the present and anticipating the future. This mental procedure is an anthropological universal in the cultural orientation of human practical life and will lead to a concept of the course of time as a necessary factor in the cultural orientation of human life.Today the dominant opinion in metahistory conceives of historical sense-generation in a constructivist way. The sense of the past is understood as an ascription of meaning onto the past; the past itself has no impact on this meaning. But I hold that the past is already present in the circumstances and conditions under which historical thinking is performed and is obviously influenced by it. This presence can be called tradition. Before historians construct the past they themselves are already constructed by the present outcome of past developments in the world. Thus tradition is always at work in historical thinking before the past is thematized as history.Historical sense-generation needs basic principles of sense and meaning. Using these principles transforms the experience of the past into a meaningful history for the present. Despite cultural differences, four sense criteria can be identified as basic for making historical sense of the past. One of the four principles is tradition. It is the most fundamental one upon which all other modes of making sense of the past are grounded. It presents temporal change in the human world such that the world’s order is maintained despite all its changes. Since the emergence of the so-called advanced civilizations, other types of historical narration have overshadowed the constitutive role of tradition. Historical narration has been supplemented by exemplary, genetic, and critical approaches to the past. Yet the traditional one has remained the most frequently used and is the most basic and popular. (shrink)

Critical discussion of Alan Code's paper "Aristotle's Investigation of a Basic Logical Principle: Which Science Investigates the Principle of Non-Contradiction?".

After introducing the adoption problem (AP) as the claim that certain basic logical principles cannot be adopted, I offer a characterization of this notion as a two-phase process consisting in (1) the acceptance of a basic logical principle, and (2) the development, in virtue of Phase 1, of a practice of inferring in accordance with that principle. The case of a subject who does not infer in accordance with universal instantiation is considered in detail. I (...) argue that the AP has deep and wide implications for the epistemology of logic, extending well beyond Kripke’s original target, viz. Putnam’s proposal for the empirical revision of logic and its background Quinean epistemology. In particular, the AP questions whether basic logical principles could have a fundamental role in our inferential practices, drawing our attention to the nature of basic inferences and the need to have a clearer conception of them before taking a stand on the matter of the epistemic justification of the logical principles. (shrink)

We present a unified approach for investigating rational reasoning about basic argument forms involving indicative conditionals, counterfactuals, and basic quantified statements within coherence-based probability logic. After introducing the rationality framework, we present an interactive view on the relation between normative and empirical work. Then, we report a new experiment which shows that people interpret indicative conditionals and counterfactuals by coherent conditional probability assertions and negate conditionals by negating their consequents. The data support the conditional probability interpretation of conditionals (...) and the narrow-scope reading of the negation of conditionals. Finally, we argue that coherent conditional probabilities are important for probabilistic analyses of conditionals, nonmonotonic reasoning, quantified statements, and paradoxes. (shrink)

Recently, there has been a significant upsurge of interest in what has come to be known as the 'Adoption Problem', first developed by Saul Kripke in 1974. The problem purports to raise a difficulty for Quine’s anti-exceptionalist conception of logic. In what follows, we first offer a statement of the problem and argue that, so understood, it depends upon natural but resistible assumptions. We then use that discussion as a springboard for developing a different adoption problem, arguing that, for a (...) significant class of basic logical principles, there is indeed a difficulty in seeing how they might be ‘freely adopted,’ thereby vindicating something close to the spirit of Kripke’s original claim. This first part of our argument will enforce a significant qualification of Quine’s claim that basic logical principles can be empirically confirmed. In the concluding sections of the paper, we turn to the question, specifically, of the empirical revisability of logic, arguing that when proper attention is paid to the role of reasoning in theory revision, it does indeed emerge that anti-exceptionalism, in full generality, is untenable. (shrink)

We present an axiomatization for Basic Propositional Calculus BPC and give a completeness theorem for the class of transitive Kripke structures. We present several refinements, including a completeness theorem for irreflexive trees. The class of intermediate logics includes two maximal nodes, one being Classical Propositional Calculus CPC, the other being E1, a theory axiomatized by T → ⊥. The intersection CPC ∩ E1 is axiomatizable by the Principle of the Excluded Middle A V ∨ ⌝A. If B is a (...) formula such that → B is not derivable, then the lattice of formulas built from one propositional variable p using only the binary connectives, is isomorphically preserved if B is substituted for p. A formula → B is derivable exactly when B is provably equivalent to a formula of the form → A) →. (shrink)

The nature of measurement is a topic of central concern in the philosophy of science and, indeed, measurement is the essential link between science and mathematics. Professor Ellis's book, originally published in 1966, is the first general exposition of the philosophical and logical principles involved in measurement since N. R. Campbell's Principles of Measurement and Calculation, and P. W. Bridgman's Dimensional Analysis. Professor Ellis writes from an empiricist standpoint. His object is to distinguish and define the (...) class='Hi'>basic concepts in measurement, for example: scale, quantity, unit. dimension, number and probability. He discusses the problem of classifying scales of measurement and the special logical problems associated with each kind of scale. A translation of mach's Critique on the Concept of Temperature, which gives his views on the nature of measurement more fully than in any of his other works, is given as an appendix. (shrink)

The question motivating my investigation is: Are the basic philosophical principles underlying the "core" system of contemporary logic exhausted by the standard version? In particular, is the accepted narrow construal of the notion "logical term" justified? ;As a point of comparison I refer to systems of 1st-order logic with generalized quantifiers developed by mathematicians and linguists . Based on an analysis of the Tarskian conception of the role of logic I show that the standard division of terms (...) into logical and extra-logical is partly arbitrary. I argue that the semantic principles of Tarskian logic allow any higher order mathematical predicate or relation to function as a logical term in a 1st-order system, provided it is introduced in the right way into the syntactic-semantic apparatus. ;Formally, I propose a new, "constructive", semantic characterization of logical terms. A logical term is defined by a function which, given a model, "shows" how to construct relations, sets, or n-tuples of individuals which satisfy it. I discuss the linguistic applicability of the extended logic and bring numerous examples. ;One chapter is devoted to branching quantification--a non-standard logico-linguistic construction obtained by affixing a non-linear, partially-ordered quantifier-prefix to a well-formed formula. Although standard branching quantifiers were given a complete account by Henkin and Walkoe, it is not altogether clear what the meaning of branching generalized quantifiers is. I propose a new analysis of the generalized branching prefix which extends the existent, partial, definitions due to Barwise, and I develop a generalization leading to a "family" of branching structures. ;In conclusion I discuss the philosophical impact of the generalized conception of logic on such issues as the logicist thesis, the interaction between mathematics and logic, ontological commitment via logic, metaphysics and logical semantics. (shrink)

This volume consists of two lecture series given by Heidegger in the 1940s and 1950s. The lectures given in Bremen constitute the first public lectures Heidegger delivered after World War II, when he was officially banned from teaching. Here, Heidegger openly resumes thinking that deeply engaged him with Hölderlin's poetry and themes developed in his earlier works. In the Freiburg lectures Heidegger ponders thought itself and freely engages with the German idealists and Greek thinkers who had provoked him in the (...) past. Andrew J. Mitchell's translation allows English-speaking readers to explore important connections with Heidegger's earlier works on language, logic, and reality. (shrink)

We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic, aims to present logical analysis of Talmudic reasoning (...) using modern logical tools. We investigate principles of Talmudic Logic and publish a series of books, one book or more for each principle. The series begins with the systematic analysis of Talmudic inference rules. The first book shows that we can present Talmudic reasoning intuitions as a systematic logical system basic to modern non-deductive reasoning, such as Argumentum A Fortiori, Abduction and Analogy. The second book offers a systematic common sense method for intuitively defining sets and claims that this method adequately models the Talmudic use of the rules Klal uPrat. These books also criticize modern Talmudic research methodology. Later books deal with additional topics like Deontic logic, and Temporal logic, Agency and processes in the Talmud and more. The aims of the project are two fold: 1. To import into the Talmudic study modern logical methods with a view to help understand complicated Talmudic passages, which otherwise cannot be addressed. 2. To export from the Talmud new logical principles which are innovative and useful to modern contemporary logic. (shrink)

This volume consists of two lecture series given by Heidegger in the 1940s and 1950s. The lectures given in Bremen constitute the first public lectures Heidegger delivered after World War II, when he was officially banned from teaching. Here, Heidegger openly resumes thinking that deeply engaged him with Hölderlin's poetry and themes developed in his earlier works. In the Freiburg lectures Heidegger ponders thought itself and freely engages with the German idealists and Greek thinkers who had provoked him in the (...) past. Andrew J. Mitchell's translation allows English-speaking readers to explore important connections with Heidegger's earlier works on language, logic, and reality. (shrink)

In this paper the language of first-order modal logic is enriched with an operator @ ('actually') such that, in any model, the evaluation of a formula @A at a possible world depends on the evaluation of A at the actual world. The models have world-variable domains. All the logics that are discussed extend the classical predicate calculus, with or without identity, and conform to the philosophical principle known as serious actualism. The basic logic relies on the system K, whereas (...) others correspond to various properties that the actual world may have. All the logics are axiomatized. (shrink)

Kolmogorov established the principle of the double negation translation by which to embed Classical Predicate Logic |${\operatorname {CQC}}$| into Intuitionistic Predicate Logic |${\operatorname {IQC}}$|⁠. We show that the obvious generalizations to the Basic Predicate Logic of [3] and to |${\operatorname {BQC}}$| of [12], a proper subsystem of |${\operatorname {IQC}}$|⁠, go through as well. The obvious generalizations of Kuroda’s embedding are shown to be equivalent to the Kolmogorov variant. In our proofs novel nontrivial techniques are needed to overcome the absence (...) of full modus ponens in Basic Predicate Logic. In [3] we argued that |${\operatorname {IQC}}$| is not the logic of constructive mathematics. Our doubts were far from new. New was that we put forward an alternative, |${\operatorname {BQC}}$|⁠. One concern is that |${\operatorname {BQC}}$| is too weak for serious mathematics, or even trivial. This paper is one step to alleviate such concerns. (shrink)

General historical introduction (concerning the law of historical development) -- Concerning the three types of philosophy -- Principles of organic logic : characterization -- Of integral knowledge point of departure and method of organic logic -- Principles of organic logic (continuation) : concept of the absolute : basic definitions according to the categories of the existent, essence, and being -- Principles of organic logic (continuation) : relative categories that define idea as an entity.

In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest (...) existing logical formalism. I start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory of the concept of God. I focus exclusively on the monotheistic concept of God. (shrink)

This is an introductory guide to the basic principles of constructing good arguments and criticizing bad ones. It is nontechnical in its approach, and is based on 150 key examples, each discussed and evaluated in clear, illustrative detail. The author explains how errors, fallacies, and other key failures of argument occur. He shows how correct uses of argument are based on sound argument strategies for reasoned persuasion and critical questions for responding. Among the many subjects covered are: techniques (...) of posing, replying to, and criticizing questions, forms of valid argument, relevance, appeals to emotion, personal attack, uses and abuses of expert opinion, problems in deploying statistics, loaded terms, equivocation, and arguments from analogy. (shrink)

According to the Adoption Problem certain basic logical principles cannot be adopted. Drawing on the AP, Suki Finn presents an argument against logical pluralism: Modus Ponens and Universal Instantiation both govern a general structure shared by every logical rule. As such, analogues of these two rules must be present in every meta-logic for any logical system L, effectively imposing a restriction to logical pluralism at the meta-level through their presence constituting a “meta-logical (...) monism”. We find a tension in the dual role that the “unadoptable rules” must play in Finn’s “meta-logical monism” rendering it ineffective to restrict logical theories and systems. Consequently, we argue they cannot be both analogues of MP and UI and inferentially productive. We conclude with a series of suggestions regarding where a more satisfying and robust interpretation of the AP could lie. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:176 Reviews c:\users\ken\documents\type3402\rj 3402 050 red.docx 2015-02-04 9:19 PM THE GRUNDGESETZE Nicholas Griffin Russell Research Centre / McMaster U. Hamilton, on, Canada l8s 4l6 [email protected] Gottlob Frege. Basic Laws of Arithmetic. Derived Using Concept-script. Volumes i and ii. Translated and edited by Philip A. Ebert and Marcus Rossberg with Crispin Wright. Oxford: Oxford U. P., 2013. Pp. xxxix + xxxii + 253 + xv + 285 + A–42 (...) + i–11. isbn 978-0-19-928174-9. £60; us$110. iven the steadily rising interest in Frege’s work since the 1950s, it is surprising that his Grundgesetze der Arithmetik, the work he thought would be the crowning achievement of his career, has not previously been fully translated into English. Other Frege works have long been available in English. The earlier Grundlagen der Arithmetik was nicely, if not always entirely accurately, translated by J. L. Austin and published in 1950.1 Translations of Frege’s other philosophical writings began to appear in influential editions about the same time,2 initially a small corpus that has been gradually added to over the years to include works from his Nachlass and letters from his correspondence.3 Somewhat later, the Begriffsschrift, Frege’s momentous first 1 The Foundations of Arithmetic (Oxford: Blackwell, 1950; 2nd edn. 1953). The later translation under the same title by Dale Jacquette (London: Longman, 2007) is much less satisfactory. 2 The first importance source for these was Peter Geach and Max Black’s Translations from the Philosophical Writing of Gottlob Frege (1952; 2nd edn. 1960; 3rd edn. 1980), though it included reprints of some much earlier translations. 3 The two most comprehensive English sources for the shorter writings are now Brian d= Reviews 177 c:\users\ken\documents\type3402\rj 3402 050 red.docx 2015-02-04 9:19 PM contribution to modern logic, the work which Quine 4 said had made logic a great subject, was translated in full despite the difficulties of Fregean notation.5 But through all this the Grundgesetze remained largely (though not entirely ) untranslated. The view seems, for a long time, to have been that Frege’s contributions to logic were to be found in the Begriffsschrift and his contributions to philosophy in the Grundlagen and a small number of seminal articles. The Grundgesetze, on the other hand, was widely thought not to have added much to these magni ficent achievements, but to have employed them in a project that was doomed by the discovery of Russell’s paradox; namely, the attempt to show that arithmetic could be rigorously derived from purely logical principles. In the bleak aftermath of Russell’s paradox it came to seem as if whatever was of value in the Grundgesetze had already been published elsewhere, while what was new in it was mistaken.6 That assessment of the book’s value, combined with the huge difficulties of typesetting Frege’s idiosyncratic two-dimensional notation, and the sheer scale of the work (even without the anticipated third volume, which was abandoned in the face of Russell’s paradox, it was, by far, Frege’s largest work) made it seem as though a translation of the whole Grundgesetze was not only a prohibitively large undertaking, but also one which was not really necessary. And so, through much of the twentieth century, the Grundgesetze vied with Principia Mathematica as the world’s bestknown but least-read philosophical book. But this understanding of the Grundgesetze’s importance could not withstand the development of neo-logicism, brought to prominence by Crispin Wright’s Frege’s Conception of Numbers as Objects.7 The key insight of neoMcGuinness, ed., Frege, Collected Papers on Mathematics, Logic, and Philosophy (1984); and Michael Beaney, ed., The Frege Reader (1997). 4 At least in early editions of Mathematical Logic. The remark was removed in later ones in deference to Boole. 5 By Stefan Bauer-Mengelberg in Jean van Heijenoort, ed., From Frege to Gödel (1967), pp. 5–82. 6 Not surprisingly the one part of the Grundgesetze which has appeared most frequently in translation is the “Nachwort” responding to Russell’s paradox which Frege added as the book was in press. Geach... (shrink)

An introduction to the basic principles of logic, including chapters on different kinds of fallacies, deductive and inductive reasoning, and syllogisms.