This book provides a detailed commentary on the classic monograph by Alfred Tarski, and offers a reinterpretation and retranslation of the work using the original Polish text and the English and German translations. In the original work, Tarski presents a method for constructing definitions of truth for classical, quantificational formal languages. Furthermore, using the defined notion of truth, he demonstrates that it is possible to provide intuitively adequate definitions of the semantic notions of definability and denotation and that the notion (...) in a structure can be defined in a way that is analogous to that used to define truth. Tarski’s piece is considered to be one of the major contributions to logic, semantics, and epistemology in the 20th century. However, the author points out that some mistakes were introduced into the text when it was translated into German in 1935. As the 1956 English version of the work was translated from the German text, those discrepancies were carried over in addition to new mistakes. The author has painstakingly compared the three texts, sentence-by-sentence, highlighting the inaccurate translations, offering explanations as to how they came about, and commenting on how they have influenced the content and suggesting a correct interpretation of certain passages. Furthermore, the author thoroughly examines Tarski’s article, offering interpretations and comments on the work. (shrink)

In 1902 there arrived in Jena a letter from Russell laying out a proof that shattered Frege’s confidence in logicism, which is widely taken to be the doctrine according to which every truth of arithmetic is re-expressible without relevant loss as a provable truth about a purely logical object. Frege was persuaded that Russell had exposed a pathology in logicism, which faced him with the task of examining its symptoms, diagnosing its cause, assessing its seriousness, arriving at a treatment option, (...) and making an estimate of future prospects. The symptom was the contradiction that had crept into naïve set theory in the form of the set that provably is and is not its own member. The diagnosis was that it is caused by Basic Law V of the Grundgesetze (Frege, In: Grundgesetze der Arithmetik: Begrifsschriftlich abgeleitet, Jena: Herman Pohle, 1893/1903. Translated into English as Basic Laws of Arithmetic, also edited by Philip A. Ebert and Marcus Rossberg, with Crispin Wright, Oxford: Oxford University Press, 2013). Triage answers the question, “How bad is it?” The answer was that the contradiction irreparably destroys the logicist project. The treatment option was nil. The disease was untreatable. In due course, the prognosis turned out to be that a scaled-down Fregean logic could have an honourable life as a theory inference for various domains of mathematical discourse, but not for domains containing the logical objects required for logicism. Since there aren’t such objects, there aren’t such domains. On the face of it, Frege’s logicist collapse is astonishing. Why wouldn’t he have repaired the fault in Law V and gone back to the business of bringing logicism to an assured realization? In the course of our reflections, we will have nice occasion to consider the good it might have done Frege to have booked some time with Aristotle had he been able to. By the time we’re finished, we’ll have cause to think that in the end the Russell might well have begged the question against Frege. (shrink)

A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Leśniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Leśniewski's published or unpublished work is known where the standard conditions are discussed. Second, Leśniewski's own logical theories allow for creative definitions. Third, Leśniewski's celebrated ‘rules of definition’ lay (...) merely syntactical restrictions on the form of definitions: they do not provide definitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 1930s, a study of these meta-theoretical conditions is more readily found in the works of Łukasiewicz and Ajdukiewicz. (shrink)

The concept of quantity (Größe) plays a key role in Frege's theory of real numbers. Typically enough, he refers to this theory as ?theory of quantity? (?Größenlehre?) in the second volume of his opus magnum Grundgesetze der Arithmetik (Frege 1903). In this essay, I deal, in a critical way, with Frege's treatment of the concept of quantity and his approach to analysis from the beginning of his academic career until Frege 1903. I begin with a few introductory remarks. In Section (...) 2, I first analyze Frege's use of the term ?source of knowledge? (?Erkenntnisquelle?) with particular emphasis on the logical source of knowledge. The analysis includes a brief comparison between Frege and Kant's conceptions of logic and the logical source of knowledge. In a second step, I examine Frege's theory of quantity in Rechnungsmethoden, die sich auf eine Erweiterung des Größenbegriffes gründen (Frege 1874). Section 3 contains a couple of critical observations on Frege's comments on Hankel's theory of real numbers in Die Grundlagen der Arithmetik (Frege 1884). In Section 4, I consider Frege's discussion of the concept of quantity in Frege 1903. Section 5 is devoted to Cantor's theory of irrational numbers and the critique deployed by Frege. In Section 6, I return to Frege's own constructive treatment of analysis in Frege 1903 and succinctly describe what I take to be the quintessence of his account. (shrink)

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...) We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference. (shrink)

The Constitution is considered as an informal axiomatic system. The strategy proposed by the authors rests on the following propositions: axioms are considered as contextual definitions of those concepts by means of which they are formulated; and the main requirement for this type of system is internal consistency. The first proposition is necessary for considering the Constitution as an informal axiomatic system, while the second is sufficient, because the approach proposed, apart from consistency, must certainly consider the requirements for formal (...) axiomatic systems, such as independence and completeness. The authors argue that the Constitution can be compared to axiomatic constructions in modern science in the sense that is given in the research on the logic and methodology of deductive sciences. This analogy is appropriate to the extent to which constitutional provisions are interpreted as the basic elements of the legal system, just as in the formal sciences axioms are regarded as basic principles that define the main features of the formal system. This means that the Constitution itself is seen as coherent, consistent discourse that contextually defines the meaning of the basic terms of the legal system. (shrink)

Jay Newhard (2021) proposes a novel solution to the Liar Paradox, which he calls the alethic indeterminacy solution to the Liar Paradox. Bradley Armour-Garb (2021) raises a pair of objections to the alethic indeterminacy solution. Both objections are based upon the alethic indeterminacy solution’s alleged commitment that the truth conditions for a Liar Sentence are indeterminate, and therefore not true. In this paper, this alleged commitment is shown to be mistaken. The alethic indeterminacy solution is compatible with maintaining that the (...) truth conditions for a Liar Sentence are a non-truth-functional biconditional which is true, and not indeterminate. Logically complex sentences are typically and standardly treated as truth-functional, and the philosophical literature on non-truth-functionality is diffuse. Two independent accounts of non-truth-functional biconditionals are defended. The first account is based on the claim that indicative conditionals express a non-truth-functional dependency relation between consequent and antecedent. The second account is based upon connected sentences having interdependent truth conditions, which can occur with any polyadic connective. These accounts are fully general, not ad hoc measures. Each account solves both of Armour-Garb’s objections. With both objections met, the alethic indeterminacy solution is shown to be a viable solution to the Liar Paradox worth further development. (shrink)

The present paper analyses the topic of scientific discovery and the problem of the existence of a logical framework involved in such endeavour. We inquire how several non-monotonic logic frameworks and other formalisms can account for such a task. In the same vein, we analyse some key aspects of the historical and theoretical debate surrounding scientific discovery, in particular, the context of discovery and context of justification context distinction. We present an argument concerning the weakening of the discovery/justification context dichotomy (...) based on the descriptive accent contained in the non-monotonic logic perspective together with its epistemological concerns. (shrink)

According to most contemporary philosophers, the Indiscernibility of Identicals is obviously true. We might therefore expect earlier philosophers to endorse it. But I will use a puzzle about identity over time to argue that Descartes would reject it.

Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus, many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate modal logics of all cardinalities. Thus ways of exploring model-theoretic logics (...) can be transferred to modal logics. (shrink)

This article outlines the work of a group of US mathematicians called the American Postulate Theorists and their influence on Tarski's work in the 1930s that was to be foundational for model theory. The American Postulate Theorists were influenced by the European foundational work of the period around 1900, such as that of Peano and Hilbert. In the period roughly from 1900???1940, they developed an indigenous American approach to foundational investigations. This made use of interpretations of precisely formulated axiomatic theories (...) to prove such metatheoretic properties as independence, consistency, categoricity and, in some cases, completeness of axiom sets. This approach to foundations was in many respects similar to that later taken by Tarski, who frequently cites the work of American Postulate Theorists. Their work served as paradigm examples of the theories and concepts investigated in model theory. The article also examines the possibility of a more specific impetus to Tarski's model theoretic investigation, arising from his having studied in 1927???1929 a paper by C. H. Langford proving completeness for various axiom sets for linear orders. This used the method of elimination of quantifiers. The article concludes with an examination of one example of Langford's methods to indicate how their correct formulation seems to call for model-theoretic concepts. (shrink)

Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus, many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate modal logics of all cardinalities. Thus ways of exploring model-theoretic logics (...) can be transferred to modal logics. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

H. Post's conception of quantal particles as non-individuals is set in a formal logico-mathematical framework. By means of this approach certain metaphysical implications of quantum mechanics can be further explored.

The thesis of the paper holds that some future developments of argumentation theory may be inspired by the rich logico-methodological legacy of the Lvov–Warsaw School (LWS), the Polish research movement that was most active from 1895 to 1939. As a selection of ideas of the LWS which exploit both formal and pragmatic aspects of the force of argument, we present: Ajdukiewicz’s account of reasoning and inference, Bocheński’s analyses of superstitions or dogmas, and Frydman’s constructive approach to legal interpretation. This paper (...) does not aim at exhaustive elaboration of any of these topics or their usefulness in current discussions within argumentation theory. Rather, we intend to indicate chosen directions of a potentially fruitful research program for the emerging Polish School of Argumentation which would consist in application of methods and conceptions elaborated by the LWS to selected open problems of contemporary research on argumentation. (shrink)

We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ?sortal terms?, two theories that will feature prominently. Second, we propose that logic comprises four ?momental sectors?: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (...) (in)valid deduction, inference or substitution. Third, we elaborate on two neglected features of logic: the various modes of negating some part(s) of a proposition R, not only its ?external? negation not-R; and the assertion of R in the pair of propositions ?it is (un)true that R? belonging to the neglected logic of asserted propositions, which is usually left unstated. We also address the overlooked task of testing the asserted truth-value of R. Fourth, we locate logic among other foundational studies: set theory and other theories of collections, metamathematics, axiomatisation, definitions, model theory, and abstract and operator algebras. Fifth, we test this characterisation in two important contexts: the formulation of some logical paradoxes, especially the propositional ones; and indirect proof-methods, especially that by contradiction. The outcomes differ for asserted propositions from those for unasserted ones. Finally, we reflect upon self-referring self-reference, and on the relationships between logical and mathematical knowledge. A subject index is appended. (shrink)

Logical pluralists are committed to the idea of a neutral metalanguage, which serves as a framework for debates in logic. Two versions of this neutrality can be found in the literature: an agreed upon collection of inferences, and a metalanguage that is neutral as such. I discuss both versions and show that they are not immune to Quinean criticism, which builds on the notion of meaning. In particular, I show that the first version of neutrality is sub-optimal, and hard to (...) reconcile with the theories of meaning for logical constants, and the second version collapses mathematically, if rival logics, as object languages, are treated with charity in the metalanguage. I substantiate by proving a collapse theorem that generalizes familiar results. Thus, the existence of a neutral metalanguage cannot be taken for granted, and meaning-invariant logical pluralism might turn out to be dubious. (shrink)

Tarski's theory of truth brings out the question of whether he intended his theory to be a correspondence theory of truth and whether, whatever his intentions, his theory is in fact a correspondence theory. The aim of this paper is to answer both questions. The answer to the first question depends on Tarski's relevant assertions on semantics and his conception of truth. In order to answer the second question Popper's and Davidson's interpretations of Tarski's truth theory are examined; to this (...) end both Tarski's definition of truth in terms of satisfaction and the T-sentences are taken into account. (shrink)

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal result (...) to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

In Writing the Book of the World, Ted Sider argues that David Lewis’s distinction between those predicates which are ‘perfectly natural’ and those which are not can be extended so that it applies to words of all semantic types. Just as there are perfectly natural predicates, there may be perfectly natural connectives, operators, singular terms and so on. According to Sider, one of our goals as metaphysicians should be to identify the perfectly natural words. Sider claims that there is a (...) perfectly natural first-order quantifier. I argue that this claim is not justified. Quine has shown that we can dispense with first-order quantifiers, by using a family of ‘predicate functors’ instead. I argue that we have no reason to think that it is the first-order quantifiers, rather than Quine’s predicate functors, which are perfectly natural. The discussion of quantification is used to provide some motivation for a general scepticism about Sider’s project. Shamik Dasgupta’s ‘generalism’ and Jason Turner’s critique of ‘ontological nihilism’ are also discussed. (shrink)

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...) universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects (...) of Boole's book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole's contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology.… using mathematical methods … has led to more knowledge about logic in one century than had been obtained from the death of Aristotle up to … when Boole's masterpiece was published.Paul Rosenbloom 1950. (shrink)

The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the (...) effectiveness of mathematics in natural science. (shrink)

The concept of truth arises from puzzling over distinctions between the real and the apparent, while the origin of these distinctions lies in the neurobiology of mammalian cerebral lateralization, that is, in the evolution of brains that can address the world both indicatively and subjunctively; brains that represent the world both categorically and hypothetically. After some 2,500 years of thinking about it, the Western philosophical tradition has come up with three major theories of truth: correspondence, coherence, and pragmatist. Traditional philosophy (...) has nevertheless failed to arbitrate much among these views; certainly no clear winner has emerged. I argue, however, that contemporary neuroscience provides adequate theoretical grounds for a unified theory of truth. More specifically, I contend that the correspondence, the coherence, and the pragmatic utility of symbols are each biological features of our neurophysiological information processing systems—that is to say, our brains. On my view, the traditional trifurcation of philosophical accounts of the predicate, “is true”, stems from a trifurcation of focus on the information latent in sensory, motor, and somatosensory cortices of the human brain. (shrink)

Logic is about reasoning, or so the story goes. This thesis looks at the concept of logic, what it is, and what claims of correctness of logics amount to. The concept of logic is not a settled matter, and has not been throughout the history of it as a notion. Tools from conceptual analysis aid in this historical venture. Once the unsettledness of logic is established we see the repercussions in current debates in the philosophy of logic. Much of the (...) battle over the ‘one true logic’ is conceptually talking past each other. The theory of logics-as-formalizations is presented as a conceptually open theory of logic which is Carnapian in flavour and grounding. Rudolf Carnap’s notions surrounding ‘external’ and ‘pseudo-questions’ about linguistic frameworks apply to formalizations, thus logics, as well. An account of what formalizations are, a more structured sub-set of modelling, is given to ground the claim that logics are formalizations. Finally, a novel account of correctness, the COFE framework, is developed which allows the notions of logical monism, pluralism and nihilism to be more precisely formulated than they currently are in the discourse. (shrink)

Scientific discourse leaves implicit a vast amount of knowledge, assumes that this background knowledge is taken into account – even taken for granted – and treated as undisputed. In particular, the terminology in the empirical sciences is treated as antecedently understood. The background knowledge surrounding a theory is usually assumed to be true or approximately true. This is in sharp contrast with logic, which explicitly ignores underlying presuppositions and assumes uninterpreted languages. We discuss the problems that background knowledge may cause (...) for the formalization of scientific theories. In particular, we will show how some of these problems can be addressed in the context of the computational representation of scientific theories. (shrink)

Translated from: W.V.O.Quine, W. H. O. (1986): Philosophy of Logic. Second Edition. Harvard University Press. Cambridge, Massachusetts and London, England, 47-61.

Purpose – The purpose of the research reported here is to improve comprehension of the socially-negotiated identity of concepts in the domain of knowledge organization. Because knowledge organization as a domain has as its focus the order of concepts, both from a theoretical perspective and from an applied perspective, it is important to understand how the domain itself understands the meaning of a concept. Design/methodology/approach – The paper provides an empirical demonstration of how the domain itself understands the meaning of (...) a concept. The paper employs content analysis to demonstrate the ways in which concepts are portrayed in KO concept maps as signs, and they are subjected to evaluative semiotic analysis as a way to understand their meaning. The frame was the entire population of formal proceedings in knowledge organization – all proceedings of the International Society for Knowledge Organization’s international conferences (1990-2010) and those of the annual classification workshops of the Special Interest Group for Classification Research of the American Society for Information Science and Technology (SIG/CR). Findings – A total of 344 concept maps were analyzed. There was no discernible chronological pattern. Most concept maps were created by authors who were professors from the USA, Germany, France, or Canada. Roughly half were judged to contain semiotic content. Peirceian semiotics predominated, and tended to convey greater granularity and complexity in conceptual terminology. Nodes could be identified as anchors of conceptual clusters in the domain; the arcs were identifiable as verbal relationship indicators. Saussurian concept maps were more applied than theoretical; Peirceian concept maps had more theoretical content. Originality/value – The paper demonstrates important empirical evidence about the coherence of the domain of knowledge organization. Core values are conveyed across time through the concept maps in this population of conference papers. (shrink)

Provides a certain conception of the target of a theory of intentionality in terms of five properties (aboutness, non-existence, aspectuality, generality, and semantic normativity) and provides a guided tour of how different styles of theories of intentionality can meet up these requirements.

Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...) be crucial, and show how one may provide responses to Maddy's concerns based on a careful analysis of 'multiverse practice'. (shrink)

The main thrust of the argument of this thesis is to show the possibility of articulating a method of construction or of synthesis--as against the most common method of analysis or division--which has always been (so we shall argue) a necessary component of scientific theorization. This method will be shown to be based on a fundamental synthetic logical relation of thought, that we shall call inversion--to be understood as a species of logical opposition, and as one of the basic monadic (...) logical operators. Thus the major objective of this thesis is to This thesis can be viewed as a response to Larry Laudan's challenge, which is based on the claim that ``the case has yet to be made that the rules governing the techniques whereby theories are invented (if any such rules there be) are the sorts of things that philosophers should claim any interest in or competence at.'' The challenge itself would be to show that the logic of discovery (if at all formulatable) performs the epistemological role of the justification of scientific theories. We propose to meet this challenge head on: a) by suggesting precisely how such a logic would be formulated; b) by demonstrating its epistemological relevance (in the context of justification) and c) by showing that a) and b) can be carried out without sacrificing the fallibilist view of scientific knowledge. OBJECTIVES: We have set three successive objectives: one general, one specific, and one sub-specific, each one related to the other in that very order. (A) The general objective is to indicate the clear possibility of renovating the traditional analytico-synthetic epistemology. By realizing this objective, we attempt to widen the scope of scientific reason or rationality, which for some time now has perniciously been dominated by pure analytic reason alone. In order to achieve this end we need to show specifically that there exists the possibility of articulating a synthetic (constructive) logic/reason, which has been considered by most mainstream thinkers either as not articulatable, or simply non-existent. (B) The second (specific) task is to respond to the challenge of Larry Laudan by demonstrating the possibility of an epistemologically significant generativism. In this context we will argue that this generativism, which is our suggested alternative, and the simplified structuralist and semantic view of scientific theories, mutually reinforce each other to form a single coherent foundation for the renovated analytico-synthetic methodological framework. (C) The third (sub-specific) objective, accordingly, is to show the possibility of articulating a synthetic logic that could guide us in understanding the process of theorization. This is realized by proposing the foundations for developing a logic of inversion, which represents the pattern of synthetic reason in the process of constructing scientific definitions. (shrink)

Talking about objects requires talking with objects, presenting objects in speech to identify a term's referent. I say This figure is a circle while handing you a ring. The ring is a prop, a perceptual object referenced by an extra-sentential event to identify the extension of a term, its director ('This figure'). Props operate in speech acts and their products, not in sentences. Intra-sentential objects we talk with are displays. Displayed objects needn't be words but must be like words, perceptually, (...) reproductively, and syntactically. Displays are presented by their syntactical position, as terms, with a term-like function. Semantically they are props. The O in FOD (This figure O is a circle) is a prop-like referent, not a term. The O in OD (O is a circle) may be that of FOD, but that display may have semantically and syntactically diverse directors, and without a specific one OD has no determinate sense Describing the display of quotations demands distinguishing displays from quotations. Quotations are repetitions of something said. Displays are perceptual objects, linguistic and non-linguistic, reproductions and originals, presented in sentences to identify a referent. Display markers are disambiguators that say: Read this as a prop. They may mark direct speech from indirect speech. Markers of quotation say: Someone said this. That historical claim is outside a sentence's propositional content. Those marks don't say: This is a display. They do make it true. Calling displays quotations muddies the study of speaking with speech. Calling both displays and intranyms quotations muddies the study of meaning and truth. Intranyms are terms, consisting of an expression flanked by lines, that denote that interior expression. Intranyms are created by stipulation to formalize a metalanguage. Formalization of a metalanguage replaces displays with intranyms. Formalized metalanguages lack the logical form and subject matter of our natural metalanguage. (shrink)

The paper emphasizes significant resemblances between the Informal Logic Initiative and the Lvov-Warsaw School – the Polish philosophical movement, the rise of which is associated with “the Golden Age of Science and Letters”. The correspondence between informal logic and the logical studies of the LWS will be explored by discussing their subject-matter, goals, and methods. The project focused on applying logical studies of the LWS in analyzing and assessing arguments will be proposed.

Is identity fundamental to formal systems? Even if a system have no the identity relation, is that concept is not assumed in any way – whether in a metalinguistic or intuitive level? In this paper we shall discuss this issue. Otávio Bueno (2014, 2016) argues against the elimination of identity, holding that this concept is fundamental and non-eliminable (even in does systems that claim to do so). Décio Arenhart Krause and Jonas (2015), by the other hand, have a number of (...) objections to Bueno’s thesis. Firstly, we look at how the concept of identity was accounted in the philosophical tradition, as well as part of its formal account. We will also examine the notion of indiscernibility that, according to the traditional approach to identity, is equivalent to the notion of identity, but (arguably) is not it logically equivalent. Thus, we shall state Krause and Arenhart’s strategy, according to, in a formal system we can eliminate identity in favor of the indiscernibility notion. Finally, we shall expose Bueno’s criticism to such strategy, and then to put forward some objections against it. (shrink)