Logical Consequence Research Papers - Academia.edu (original) (raw)

The thesis is an investigation into the logical pluralism debate, aiming to understand how the philosophical commitments sustaining each side to the debate connects to more general issues connected to the foundations of logic. My investigation centers on the following three notions: (1) Epistemic justification, (2) The metaphysical "ground" for logical truth, and (3) Normativity. Chapter 1 traces the monistic and pluralistic conception of logic back to its philosophical/mathematical roots, which we find in the writings of Rudolf Carnap and Gottlob Frege. I argue that logical pluralism - in its more plausible, epistemic (rather than ontic) form - was enabled by the semantic shift which Carnap seems to have anticipated and that, from a conventionalist perspective, his 'Principle of Tolerance' follows as a consequence of that shift. Chapter 2 concerns the issues ensuing from Willard V. O Quine’s critique of Carnap's conventionalism, which had a devastating effect for his foundationalist project. The aim is in particular to address the issue of meaning-variance, a crucial assumption for the conventionalist approach to pluralism. In chapter 3, I present another framework for pluralism, due to Stewart Shapiro’s [2014] ‘modelling’ conception of logic, according which logic is conceived as a mathematical model of natural language. Shapiro argues that our concept of logical consequence is vague and in need of a sharpening to attain a fixed meaning. Pluralism follows from there being two or more equally "correct" such sharpenings; i.e., relative to our theoretical aims. I argue that the modelling-conception is the best way to approach a justification of basic logical laws. However, since that conception also grounds Timothy Williamson’s [2017] argument for monism, I argue that the conception ultimately fails to establish logical pluralism. Since both Williamson and Shapiro take a pragmatic approach to justification, I conclude that the question of pluralism does not turn on epistemological commitments (i.e., on (1)), and suggest instead that it is a matter of (2), i.e., of one's conception of the "ground" for logical truth.

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- Model Theory, Pragmatism, Philosophy Of Mathematics, Philosophy of Logic

► JOHN CORCORAN AND SRIRAM NAMBIAR, Five Goldfarb implications.
Expanding Corcoran’s “Meanings of implication” , we discuss five implication relations in Goldfarb’s Deductive logic , an important logic textbook that contains the latest articulation of approaches rooted in Quine’s 1940 masterpiece Mathematical logic, whose basic ideas were taught to generations of Harvard students, many now influential logicians, philosophers, and mathematicians.

- by John Corcoran and +1
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- Logic And Foundations Of Mathematics, Logic, Learning and Teaching, Fuzzy Logic

Indicates that everything standing on top of naive set theory is also proven.

In their book EVALUATING CRITICAL THINKING Stephen Norris and Robert Ennis say: “Although it is tempting to think that certain [unstated] assumptions are logically necessary for an argument or position, they are not. So do not ask for them.” Numerous writers of introductory logic texts as well as various highly visible standardized tests (e.g., the LSAT and GRE) presume that the Norris/Ennis view is wrong; the presumption is that many arguments have (unstated) necessary assumptions and that readers and test takers can reasonably be expected to identify such assumptions. This paper proposes and defends criteria for determining necessary assumptions of arguments. Both theoretical and empirical considerations are brought to bear.

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions, we argue that a proper account of conditional can be obtained by extending the logical notation of Frege's ideography. From a dialogical redefinition of truth-values as moves in a game, it becomes possible to characterize the logical meaning of " If " , and only " If ". That is: by getting rid of the paradoxes of material implication, whilst showing the bivalent roots of conditional as a speech-act based on affirmations and rejections. Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed in this algebraic and game-theoretical light.

- by Fabien Schang
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- Logical Constants, Logical Consequence, Gottlob Frege, Relevance Logic
- by Debbie Barry
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- Ethics, Culture, Logical Consequence, Morality

Logical pluralism is the view that there is more than one correct logic. This very general characterization gives rise to a whole family of positions. I argue that not all of them are stable. The main argument in the paper is inspired by considerations in Keefe (2014), Priest (2006a), Read (2006), and Williamson (1988), and it aims at the most popular form of logical pluralism advocated by Beall and Restall (2000, 2006). I argue that there is a more general argument available that challenges all variants of logical pluralism that meet the following three conditions: (i) that there are at least two correct logical systems characterized in terms of different consequence relations, (ii) that there is some sort of rivalry among the correct logics, and (iii) that logical consequence is normative. The hypothesis I argue for amounts to what Caret (2016) calls a ‘collapse problem’ in form the of a conditional claim: If a position satisfies all these conditions, then that position is unstable in the sense that it collapses into competing positions.

- by Erik Stei
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- Logical Consequence, Logical Pluralism

A survey of medieval logic games.

- by JT Paasch
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- Medieval logic, Logical Consequence, Scholastic Philosophy, Games

There is a profound, but frequently ignored relationship between logical consequence (formal implication) and material implication. The first repeats the patterns of the latter, but with a wider modal reach. It is argued that this kinship between formal and material implication simply means that they express the same kind of implication, but differ in scope. Formal implication is unrestricted material implication. This apparently innocuous observation has some significant corollaries: (1) conditionals are not connectives, but arguments; (2) the traditional examples of valid argumentative forms are metalogical principles that express the properties of logical consequence; (3) formal logic is not a useful guide to detect valid arguments in the real world; (4) it is incoherent to propose alternatives to the material implication while accepting the classical properties of formal implication; (5) some of the counter-examples to classical argumentative forms and known conditional puzzles are unsound.

- by Matheus Silva
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- Philosophy Of Language, Connectives, Conditionals, Philosophy of Logic

Resumo sobre Lógica Aristotélica e da Lógica Tradicional.

- by Ricardo P Tassinari
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- Computer Science, Formal Epistemology, Logical Consequence, Direito

In a recent article, "Logical Consequence and Natural Language", Michael Glanzberg claims that there is no relation of logical consequence in natural language (Glanzberg, 2015). The present paper counters that claim. I shall discuss Glanzberg's arguments and show why they don't hold. I further show how Glanzberg's claims may be used to rather support the existence of logical consequence in natural language.

- by Gil Sagi
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- Philosophy Of Language, Logic, Semantics, Philosophy of Logic
- by Gil Sagi
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- Philosophy of Logic, Logical Constants, Logical Consequence
- by Lenon Quadros
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- Logical Consequence, Direito, Direito Constitucional, Portugues
- by Matheus Silva
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- Set Theory, Philosophy Of Language, Conditionals, Philosophy of Logic

GABARDO, Emerson; SOUZA, Pablo Ademir de. O consequencialismo e a LINDB: a cientificidade das previsões quanto às consequências práticas das decisões. A&C – Revista de Direito Administrativo & Constitucional, Belo Horizonte, ano 20, n.... more

- by Emerson Gabardo and +1
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- Consequentialism, Logical Consequence, Direito Administrativo, Administração Pública

This article is focused on answering the question to what extent one can be a sceptic. Sextus Empiricus’s Outlines of Scepticism serves as a guide. In section 1, it is investigated whether three logical laws have a certain foundation or are subject to doubt. In section 2, Sextus’s way to deal with these laws is examined; the question arises how dogmatic his approach is. After that, a possible ‘reply’ by Sextus to the criticism receives attention. Section 3 is concentrated on a possible alternative to Sextus’s approach. Besides logical laws, some important methods are concerned.

- by Jasper Doomen
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- Logic And Foundations Of Mathematics, Calculus, Philosophy, Metaphysics

Resumen
Las paradojas muestran algo irracional pero de un modo perfectamente racional, mostrando que sólo contra el telón de fondo de una cierta definición de racionalidad algo resulta irracional. La paradoja no es pues un argumento a dilucidar o un problema a esclarecer, sino una perplejidad frente a la recursividad del lenguaje y al principio de información faltante, un agujero en el centro de nuestra lógica. Por ello la emancipación de la razón posmoderna requiere nuevas lógicas, polivalentes, de la vaguedad o paraconsistentes, para habérselas con los sistemas complejos y los desafíos a la que nos enfrentan la física cuántica, retos que exigen nuevas discursividades, así como cartografías lo suficientemente plásticas para desplazarse en medio de un universo de espejos, cuerdas y agujeros negros. Así las paradojas pueden ser pensadas como un inevitable "nudo gordiano cognitivo", imposible de desatar en las condiciones y con los modos de pensar con que lo creamos, pero que se desvanece en otro espacio conceptual.
Dr. Adolfo Vásquez Rocca

- by Adolfo Vasquez Rocca
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- Critical Theory, Semiotics, Neuroscience, Sociology

It is usually accepted that deductions are non-informative and monotonic, inductions are informative and nonmonotonic, abductions create hypotheses but are epistemically irrelevant, and both deductions and inductions can’t provide new insights. In this article, I attempt to provide a more cohesive view of the subject with the following hypotheses: (1) the paradigmatic examples of deductions, such as modus ponens and hypothetical syllogism, are not inferential forms, but coherence requirements for inferences; (2) since any reasoner aims to be coherent, any inference must be deductive; (3) a coherent inference is an intuitive process where the premises should be taken as sufficient evidence for the conclusion, which on its turn should be viewed as necessary evidence for the premises in some modal range; (4) inductions, properly understood, are abductions, but there are no abductions beyond the fact that in any inference the conclusion should be regarded as necessary evidence for the premises; (5) monotonicity is not only compatible with the retraction of past inferences given new information, but it is a requirement for it; (6) this explanation of inferences holds true for discovery processes, predictions and trivial inferences.

- by Matheus Silva
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- Epistemology, Philosophy of Science, Philosophy of Logic, Logical Consequence

This paper shows why the non-trivial zeros of the Riemann zeta function ζ must always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the... more

- by Bertrand Wong
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- Analytic Number Theory, Algebraic Number Theory, Algebra, Logic
- by Sebastiano Moruzzi
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- Logical Consequence

In 1898 C. S. Peirce declares that the medieval doctrine of consequences had been the starting point of his logical investigations in the 1860s. This paper shows that Peirce studied the scholastic theory of consequentiae as early as 1866–67, that he adopted the scholastics’ terminology, and that that theory constituted a source of logical doctrine that sustained Peirce for a lifetime of creative and original work.

- by Francesco Bellucci
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- Medieval Philosophy, Logic, History of Logic, Medieval logic

I argue against inferentialism about logic. First, I argue against an analogy between logic and chess, before considering a more basic objection to stipulating inference rules as a way of establishing the meaning of logical constants. The objection-the Mushroom Omelette Objection-is that stipulative acts are partly constituted by logical notions, and therefore cannot be used to explain logical thought. I then argue that the same problem also attaches to following existing conventional rules, since either those rules have logical contents, or following those conventional rules is done for logical reasons. Lastly, I compare this argument with other arguments found in Quine's early work, and consider two attempts to reply to Quine.

- by nick zangwill
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- Logic, Deductive reasoning, Philosophy of Logic, Logical Constants

Classical propositional logic can be characterized, indirectly , by means of a complementary formal system whose theorems are exactly those formulas that are not classical tautologies, i.e., contradictions and truth-functional contingencies. Since a formula is contingent if and only if its negation is also contingent, the system in question is paraconsistent. Hence classical propositional logic itself admits of a paraconsistent characterization, albeit "in the negative". More generally, any decidable logic with a syntactically incomplete proof theory allows for a paraconsistent characterization of its set of theorems. This, we note, has important bearing on the very nature of paraconsistency as standardly characterized.

- by Achille C . Varzi
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- Logical Consequence, Non-Classical Logic, Paraconsistent logic, Dialetheism
- by Seth Yalcin
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- Philosophy Of Language, Conditionals, Logical Consequence, Modus Tollens

Quantificational accounts of logical consequence account for it in terms of truth-preservation in all cases – be it admissible substitutional variants or interpretations with respect to non-logical terms. In this second of my three connected studies devoted to the quantificational tradition, I set out to reconstruct the seminal contributions of Russell, Carnap, Tarski and Quine and evaluate them vis-à-vis some of the most pressing objections. This study also prepares the ground for my discussion of the standard model-theoretic account of consequence to be found in the concluding study.

- by Ladislav Koren
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- Logic And Foundations Of Mathematics, Logic, Semantics, Bernard Bolzano

I study here the implications of Suszko-like reductive results for the common wisdom on the internal logic of a topos. My aim here is to question certain slogans about topos logic, and especially on its many-valuedness. The originality of this paper comes not from the observation that the internal logic of a topos is bivalent because it is in the scope of Suszko’s or any other reduction; that is easy. Rather, the originality comes from (1) recognizing the import of applying Suszko’s and similar results in a topos-theoretical setting, (2) the suggestions to give categorial content to the reduction, and (3) the extrapolation of the debate about Suszko’s thesis to the topos-theoretical framework, which gives us some insight about the scope of another theorem, namely that stating the intuitionistic character of the internal logic of a topos.

В статье рассматривается понятие факта, а также другие базовые понятия ситуационной семантики, как они даны в версии А. Кратцер. Выявляются преимущества способа их конструирования, используемого Кратцер, перед способом, который использовался Дж. Барвайсом и Дж. Перри. Особое внимание уделяется функциям понятия факта в версии Кратцер в семантике эпистемических установок, а также в теории особого вида следования («сильного» следования), выделяемого в ситуационной семантике.

- by Anna Moiseeva
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- Logical Consequence, Knowledge, Situation Semantics

This paper shows why the non-trivial zeros of the Riemann zeta function ζ will always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the... more

- by Bertrand Wong
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- Mathematics, Number Theory, Analytic Number Theory, Algebraic Number Theory
- by Fabien Schang
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- Aristotle, Subaltern, Logical Consequence, Formal Semantics

This is a survey paper in German covering a number of central themes in the philosophy of logic, including the debates surrounding the notion of logical consequence, the problem of demarcating logic, logical pluralism vs. logical monism... more

- by Florian Steinberger
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- Logic, Philosophy of Logic, Logical Constants, Logical Consequence
- by Massimiliano Carrara
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- Philosophy of Logic, Logical Consequence
- by Christian Wallmann
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- Logical Consequence

Oppositional geometry gives a mathematical model of oppositional phenomena through “oppositional structures” (logical squares, hexagons, cubes, …). Its so far known formal entities, the backbone of which are the “oppositional bi-simplexes (and poly-simplexes) of dimension m”, are distributed into three families (the alpha-, beta- and gamma-structures). However, some recent studies by different authors exhibit strange structures, notably strange variations of the notion of “oppositional hexagon” (or “logical hexagon”). In this paper we show that inside the oppositional tetrahexahedron, i.e. the beta3-structure (discovered in 1968 and rediscovered in 2008) – a 3D solid made of a logical cube and six logical “strong hexagons”, containing 14 vertices and 36 implication arrows – there are in fact C(6|14) = 30030 strange hexagons, which we call “hybrid hexagons”. In this paper, through a systematic study of those among them which have as invariant property a regular perimeter made of alternated arrows (henceforth “arrow-hexagons”), we show that they divide into a much smaller number of families, nine, each containing several isomorphic instances of the same oppositional pattern. An interesting result seems to be that when seen from the viewpoint of their mutual transformations (i.e. moving from one to another kind of arrow-hexagon, just by exchanging one of its 6 vertices with one among the remaining 14-6=8 vertices of the tetrahexahedron), these arrow-hexagonal patterns taken as points can be displayed into a new kind of 3D structure. The latter, by putting into order these points (each representing a family of arrow-hexagons), gives some kind of morphogenetic cartography of the arrow-hexagons of the beta3-structure. As we will argue, since several arrow-hexagons play the role of “attractors”, there are reasons for thinking that such a cartography could be very meaningful in the future for modelling “oppositional dynamics”, that is the systematic formal study of the situations where a given complex oppositional structure sees its shape change within time.

- by Alessio Moretti
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- Modal Logic, Logic, Graph Theory, Complexity
- by Gerhard Preyer
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- Languages, Buddhism, Mathematics, Philosophy

In standard model-theoretic semantics, the meaning of logical terms is said to be fixed in the system while that of nonlogical terms remains variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing their meaning precisely amounts to. My proposal is that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension. I provide a rigorous way of spelling out this idea, and show that it leads to a graded account of logicality: the less structure a term requires in order for its intension to be fixed, the more logical it is. Finally, I focus on the class of terms that are invariant under isomorphisms, as they render themselves more easily to mathematical treatment. I propose a mathematical measure for the logicality of such terms based on their associated Löwenheim numbers.

- by Gil Sagi
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- Logic And Foundations Of Mathematics, Logic, Philosophy of Logic, Logical Constants

In this paper I argue against the view that logical consequence is a truth-preserving relation and, in general, that it is a reﬂexive and transitive relation. I expound a number of non-reﬂexive or non-transitive notions of logical consequence and argue that they satisfy the requirements to be considered part of the so-called “core tradition” of logic, and that they thus give rise to logics bona ﬁde.

- by Michael P Lynch
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- Philosophy Of Language, Truth, Logical Consequence, Theories Of Truth