According to the fitting-attitude analysis of value (FA-analysis), to be valuable is to be a fitting object of a pro-attitude. In earlier publications, setting off from this format of analysis, I proposed a modelling of value relations which makes room for incommensurability in value. In this paper, I first recapitulate the value modelling and then move on to suggest adopting a structurally similar analysis of probability. Indeed, many probability theorists from Poisson onwards did adopt an analysis of this kind. This (...) move allows to formally model probability and probability relations in essentially the same way as value and value relations. One of the advantages of the model is that we get a new account of Keynesian incommensurable probabilities, which goes beyond Keynes in distinguishing between different types of incommensurability. It also becomes possible to draw a clear distinction between incommensurability and vagueness (indeterminacy) in probability comparisons. (shrink)

The traditional definition per genus et differentiam is argued to be cognitively grounded in perception and in order to avoid needless argument, definitions are stipulated to assert boundaries. An analysis of the notion of perspective shows that a boundary is a composite of two distinctions: similarity that includes and difference that excludes. The concept is applied to the type-token distinction and percepts are shown to be the result of a comparison between a token as representing some phenomenon and a type (...) as representing the kind of object the phenomenon might be. The Principle of Connection is proposed as the mental architecture that gives rise to percepts. The value of a percept is shown to be one of Identical, Similar, Different or Contrary and its perceptual aspects represent the cognitive schema of Essence, Quality, Quantity and Relation. The two notions of similarity and difference are claimed to constitute the necessary and sufficient conditions for definitions. Accordingly, the qualitative elements of a definition signify the genus as representing the similarity of the defined entity in terms of others of its kind and the quantitative elements signify the differentia as representing the difference it has from everything else. Paying proper attention to both qualitative and quantitative aspects will enable formulation of definitions that are ‘good’. (shrink)

In this paper two concepts of psychologism in logic are outlined: the one which Frege and Husserl fought against and the new psychologism, or cognitivism, which underlies a cognitive turn in contemporary logic. Four issues such cognitively oriented logic should be interested in are indicated. They concern: new fields opened for logical analysis, new methods and tools needed to address these fields, neural basis of logical reasoning, and an educational problem: how to teach such logic? Several challenging questions, which arise (...) in the context of these issues, are listed. (shrink)

The introduction has a brief statement, sufficient for the purpose of this paper, which describes in general terms the notion of probability logic on which the paper is based. Contributions made in the eighteenth century by Leibniz, Jacob Bernoulli and Lambert, and in the nineteenth century by Bolzano, De Morgan, Boole, Peirce and MacColl are critically examined from a contemporary point of view. Historicity is maintained by liberal quotations from the original sources accompanied by interpretive explanation. Concluding the paper is (...) a summary. (shrink)

Contrary to received opinion, the Aristotelian Square of Opposition (square) is logically sound, differing from standard modern predicate logic (SMPL) only in that it restricts the universe U of cognitively constructible situations by banning null predicates, making it less unnatural than SMPL. U-restriction strengthens the logic without making it unsound. It also invites a cognitive approach to logic. Humans are endowed with a cognitive predicate logic (CPL), which checks the process of cognitive modelling (world construal) for consistency. The square is (...) considered a first approximation to CPL, with a cognitive set-theoretic semantics. Not being cognitively real, the null set Ø is eliminated from the semantics of CPL. Still rudimentary in Aristotle’s On Interpretation (Int), the square was implicitly completed in his Prior Analytics (PrAn), thereby introducing U-restriction. Abelard’s reconstruction of the logic of Int is logically and historically correct; the loca (Leaking O-Corner Analysis) interpretation of the square, defended by some modern logicians, is logically faulty and historically untenable. Generally, U-restriction, not redefining the universal quantifier, as in Abelard and loca, is the correct path to a reconstruction of CPL. Valuation Space modelling is used to compute the effects of U-restriction. (shrink)

Most recent discussions of John Stuart Mill’s System of Logic (1843) neglect the fifth book concerned with logical fallacies. Mill not only follows the revival of interest in the traditional Aristotelian doctrine of fallacies in Richard Whately and Augustus De Morgan, but he also develops new categories and an original analysis which enhance the study of fallacies within the context of what he calls ‘the philosophy of error’. After an exploration of this approach, the essay relates the philosophy of error (...) to the discussion of truth and error in chapter two of On Liberty (1859) concerned with freedom of thought and discussion. Drawing on Socratic and Baconian perspectives, Mill defends both the traditional study of logic against Jevons, Boole, De Morgan, and others, as well as the study of fallacies as the key to maintaining truth and its dissemination in numerous fields, such as science, morality, politics, and religion. In Mill’s view the study of fallacies also liberates ordinary people to explore the truth and falsity of ideas and, as such, to participate in society and politics and develop themselves as progressive beings. (shrink)

In this essay, I discuss some observations by Peirce which suggest he had some idea of the substantive metalogical differences between logics which permit both quantifiers and relations, and those which do not. Peirce thus seems to have had arguments?which even De Morgan and Frege lacked?that show the superior expressiveness of relational logics.

This paper shows how Peirce's semeiotic could be turned into a powerful science. The New Science of Semiotics provides not only a new paradigm and an empirical justification for all these applications, but also a rational and systematic procedure for carrying them out as well. Thus the New Science of Semiotics transforms the philosophy of law into the science of legal scholarship, the discipline that I call jurisology.

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a (...) corresponding reading of such De Morgan style syllogistics in the previously referred to fragment of linear logic. (shrink)

This paper objects to treating begging the question as circular reasoning. It argues that what is at issue in the argument is not to be confused with the claim or position that the arguer is adopting, and that logicians from Aristotle on give the wrong definition and have difficulty making sense of the fallacy because they try to define it in terms of how an argument is defined by logical theory - as a sequence consisting of premises followed by a (...) conclusion. That the problematic about begging the question depends on treating an argument as a context-less sequence of statements seems to be anticipated by the pragma-dialectical approach. The paper offers a critique of this dialogical approach, as exemplified by Douglas Walton in his recent book on begging the question, on the grounds that it raises more problems than it solves. It concludes with the suggestion that what is really at issue in discussions of begging the question is the need for a theory of fallacy. (shrink)

One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...) the focal point is the categorical syllogism. (shrink)

Despite its basically syllogistic character, Richard Whately's Elements of logic presents the subject in a modern theoretical setting. Whately, for instance, regarded logic as an abstract science, and defined the syllogism as a purely formal device to be used as a means of determining the validity of all arguments. In this paper, I argue that such instances of abstractive ascent place Whately's theory in closer proximity to later 19th-century developments than to the work of his 17th-century predecessors. In addition to (...) discussing the theory itself, other sections deal with its historical setting, and various reactions to it. (shrink)

Lepore and Stone seek to replace the rationality-based Gricean picture of coordination between speaker and hearer with one leaning more strongly on the roles of convention and speaker knowledge while doing away with conversational implicature. Focusing on the phenomena of indirect speech acts, asymmetric conjunction, and scalar inferencing, I argue that the case for abandoning implicature as an analytical tool is not ultimately compelling. I seek further to demonstrate the utility of the classical Gricean distinction between what is said and (...) what is implicated in the construction of an intuitively appealing approach to the perennial question of how to distinguish lying from misleading inside and outside the legal domain. (shrink)

Following a brief preface, the second section of this paper discusses Mill's early reflections on the problem of how deductive inference can be illuminating. In the third section it is suggested that in his Logic Mill misconstrued the feature that the premises of a logically valid argument contain the conclusion as the ground of a charge that deductive proof is question-begging. The fourth section discusses the nature of the traditional petitio objection to syllogism, and the fifth shows that Mill had (...) a theory capable of answering it. The final section cites the confusion described in section 3 to explain why Mill nevertheless continued to think that syllogistic proofs beg the question. (shrink)

Three distinctly different interpretations of Aristotle’s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle’s remarkable degree of metalogical (...) sophistication to distinguish logical syntax from semantics and, thus, also from not grasping him to refine the deduction system of his underlying logic. While it is obvious that Aristotle most often uses ‘sullogimos’ to denote a valid argument of a certain kind, we show that at Prior Analytics A4-6, 7, 45 Aristotle specifically treats a sullogismos as an elemental argument pattern having only valid instances and that such a pattern then serves as a rule of deduction in his syllogistic logic. By extracting Aristotle’s understanding of three proof-theoretic processes, this paper provides new insight into what Aristotle thinks reasoning syllogistically is and, moreover, it resolves three problems in the most recent interpretation that takes a sullogismos to be a deduction. (shrink)

John Venn and Charles L. Dodgson (Lewis Carroll) created systems of logic diagrams capable of representing classes (sets) and their relations in the form of propositions. Each is a proof method for syllogisms, and Carroll's is a sound and complete system. For a large number of sets, Carroll diagrams are easier to draw because of their self-similarity and algorithmic construction. This regularity makes it easier to locate and thereby to erase cells corresponding with classes destroyed by the premises of an (...) argument, a particularly difficult task in Venn diagrams for more than four sets. Carroll diagrams can represent existential propositions easily, so they are capable of clearly representing more complex problems than Venn's system can. Finally, both Carroll and Venn diagrams are maximal, in the sense that no additional logic information like inclusive disjunctions is able to be represented by them. Carroll's logic diagrams and logic trees constitute his visual logic system. (shrink)

In this essay, my aim is twofold: to clarify how the late Mill conceived of the certainty of inductive generalizations and to offer a systematic clarification of the limited domain of application of the Mill’s Canons of Induction. I shall argue that Mill’s views on the certainty of knowledge changed overtime and that this change was accompanied by a new view on the certainty of the inductive results yielded by the Canons of Induction. The key message of the later editions (...) of The System of Logic as conceived by the late Mill was no longer that by the Canons of Induction we can establish scientific certainty and true causes, but rather that the Canons are useful in establishing causal laws in a provisional way. (shrink)

Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...) Q is one whose existentialization, ∃ x Q, is logically true; otherwise, Q is existential-import-free or simply import-free.How abundant or widespread is existential import? How abundant or widespread are existential-import predicates in themselves or in comparison to import-free predicates? We show that existential-import predicates are quite abundant, and no less so than import-free predicates. Existential.. (shrink)

In 1866, the young John Venn published The Logic of Chance, motivated largely by the desire to correct what he saw as deep fallacies in the reasoning of historical determinists such as Henry Buckle and in the optimistic heralding of a true social science by Adolphe Quetelet. Venn accepted the inevitable determinism implied by the physical sciences, but denied that the stable social statistics cited by Buckle and Quetelet implied a similar determinism in human actions. Venn maintained that probability statements (...) were intelligible solely as projections of the ultimate frequency of an outcome in an unlimited series of trials and therefore led to no inferences about free will. An issue here was Venn's claim that although the aggregate probability may be stable, the individual events were completely irregular and, in fact, displayed randomness. Venn's concept of randomness was really apparent, or pseudo-, randomness, which could be totally determined. Ironically, Venn's frequentist position was very useful to the growing field of statistics, which could develop correlations and predictive models empirically without having to address implications for personal freedom or fatalism. (shrink)

The language of the propositional calculus is extended by two families of propositional probability operators, inductively applicable to the formulae, and the set of all formulae provable in an arbitrary superintuitionistic propositional logic is extended by the probability measure axioms concerning those probability operators. A logical system obtained in such a way, similar to a kind of polymodal logic, makes possible to express a probability measure of truthfulness of any formula. The paper contains a description of the Kripke-type possible worlds (...) semantics covering the considered logical systems, being followed by the corresponding completeness results. (shrink)

For Ivor Grattan-Guinness on the occasion of his retirement. The work of Augustus De Morgan on symbolic logic in the mid-nineteenth century is familiar to historians of logic and mathematics alike. What is less well known is his work on probability and, more specifically, the use of probabilistic ideas and methods in his logic. The majority of De Morgan's work on probability was undertaken around 1837???1838, with his earliest publications on logic appearing from 1839, a period which culminated with the (...) publication of his Formal Logic in 1847. This article examines the overlap between his work on probability theory and logic during the earliest period of his interest in both. (shrink)

Hypotheticals, conditionals, and their connecting relation, implication, dramatically changed their meanings during the nineteenth and early part of the twentieth century. Modern logicians ordinarily do not distinguish between the terms hypothetical and conditional. Yet in the late nineteenth century their meanings were quite different, their ties to the implication relation either were unclear, or the implication relation was used exclusively as a logical operator. I will trace the development of implication as an inference operator from these earlier notions into the (...) first third of the twentieth century using as the starting point the ideas primarily of R. Whately and W. Hamilton before discussing the work of the transitional logicians, A. De Morgan and G. Boole on these topics. Then we discuss the relevant views of four prominent but relatively unknown nineteenth century British logicians, W.E. Johnson, J.N. Keynes, E.E.C. Jones, and H. MacColl, as well as those of the more influential logicians, W.S. Jevons and J. Venn, closing with a section on ‘implication as inference’ where we explore some key ideas of B. Russell and sketch the work of D. Hilbert, P. Hertz, and G. Gentzen who together are responsible for the development of the modern ideas related to the subjects of this paper. (shrink)

This entry traces the historical development of the Square of Opposition, a collection of logical relationships traditionally embodied in a square diagram. This body of doctrine provided a foundation for work in logic for over two millenia. For most of this history, logicians assumed that negative particular propositions ("Some S is not P") are vacuously true if their subjects are empty. This validates the logical laws embodied in the diagram, and preserves the doctrine against modern criticisms. Certain additional principles ("contraposition" (...) and "obversion") were sometimes adopted along with the Square, and they genuinely yielded inconsistency. By the nineteenth century an inconsistent set of doctrines was widely adopted. Strawson's 1952 attempt to rehabilitate the Square does not apply to the traditional doctrine; it does salvage the nineteenth century version but at the cost of yielding inferences that lead from truth to falsity when strung together. (shrink)

In October 2009 I decided to stop doing philosophy. This meant, in particular, stopping work on the book that I was writing on the nature of probability. At that time, I had no intention of making my unfinished draft available to others. However, I recently noticed how many people are reading the lecture notes and articles on my web site. Since this draft book contains some important improvements on those materials, I decided to make it available to anyone who wants (...) to read it. That is what you have in front of you. The account of Laplace’s theory of probability in Chapter 4 is very different to what I said in my seminar lectures, and also very different to any other account I have seen; it is based on a reading of important texts by Laplace that appear not to have been read by other commentators. The discussion of von Mises’ theory in Chapter 7 is also new, though perhaps less revolutionary. And the final chapter is a new attempt to come to grips with the popular, but amorphous, subjective theory of probability. The material in the other chapters has mostly appeared in previous articles of mine but things are sometimes expressed differently here. I would like to say again that this is an incomplete draft of a book, not the book I would have written if I had decided to finish it. It no doubt contains poor expressions, it may contain some errors or inconsistencies, and it doesn’t cover all the theories that I originally intended to discuss. Apart from this preface, I have done no work on the book since October 2009. (shrink)

“Formal logic”, an expression created by Kant to characterize Aristotelian logic, has also been used as a name for modern logic, originated by Boole and Frege, which in many aspects differs radically from traditional logic. We shed light on this paradox by distinguishing in this paper five different meanings of the expression “formal logic”: (1) Formal reasoning according to the Aristotelian dichotomy of form and content, (2) Formal logic as a formal science by opposition to an empirical science, (3) Formal (...) systems in the sense of Hilbert, Curry and the formalist school, (4) Symbolic logic, a science using symbols, such as Venn diagrams, (5) Mathematical logic, a mathematical approach to reasoning. We argue that these five meanings are independent and that the meaning (5) is the one which better characterized modern logic, which should therefore not be called “formal logic”. (shrink)

The central problem of the dissertation concerns the possibility of a distinction between truth-evaluable and non-truth-evaluable utterances of a natural language. The class of truth-evaluable utterances includes assertions, con. ectures and other kinds of speech act susceptible of truth evaluation. The class of non-truth-evaluable utterances includes commands, exhortations, wishes i.e. utterances not evaluated as being true or false. The problem is placed in the context of radical interpretation theory and it shown that it is a substantial problem of Davidson‘s early (...) theory of radical interpret at ion. I consider the possibility of distinguishing between locutionary and illocutionary act in uttering a sentence and its significance in the present project. I discuss the suggestion that the mood of the verb of the sentence signifies the required distinction between truth-evaluable utterances and non-truth-evaluable ones. I argue that no criterion for the distinction based on the mood of the verb is adequate. The solution that I propose to the problem of classifylng truth-evaluable utterances appeals to mental states. The view that grounds this line of inquiry is that the truth-evaluability of an utterance is a characteristic of it exclusively relevant to the doxastic dimension of the speaker’s mind. I discuss the constraints that the nature of radical interpretation puts upon the way we construe the notion of belief. I propose that a possible classification of mental states into doxastic and non-doxastic that would result in a classification of utterances into truth-evaluable and non-truthevaluable ones can be given by an elaborated version of a decision theoretic scheme. I suggest that a decision theoretic scheme based on a decision theory that, like Savage’s theory, grants independence axioms is a better candidate to offer a solution to the central problem of the dissertation than a scheme based on a non- standard decision theory such as Richard Jeffrey’s. I conclude by showing that the proposal I make satisfies the constraints I have considered and that it can be accommodated by a radical interpretation theory. (shrink)

We present a coherence-based probability semantics for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation rules of argument forms (...) of the syllogistic Figures I, II, and III, respectively. These results allow to show, for all three Figures, that each traditionally valid syllogism is also valid in our coherence-based probability semantics. Moreover, we interpret the basic syllogistic sentence types by suitable defaults and negated defaults. Thereby, we build a knowledge bridge from our probability semantics of Aristotelian syllogisms to nonmonotonic reasoning. Finally, we show how the proposed semantics can be used to analyze syllogisms involving generalized quantifiers. (shrink)

The translation into French of the English word “fallacy” opens a discussion on the difference between fallacy and sophism in English. The two words are sometimes synonyms, but a difference is sometimes made on the ground that a sophism is deliberate and a fallacy is non-deliberate. In a second part of the paper this distinctive criterion is taken seriously to discuss the relative frequency of sophisms and of fallacies for a typical kind of fallacious argument. I claim that this aspect (...) should be taken into account by a theory of fallacious argument. (shrink)