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  1. Command and Consequence.Josh Parsons - 2013 - Philosophical Studies 164 (1):61-92.
    An argument is usually said to be valid iff it is truth-preserving—iff it cannot be that all its premises are true and its conclusion false. But imperatives (it is normally thought) are not truth-apt. They are not in the business of saying how the world is, and therefore cannot either succeed or fail in doing so. To solve this problem, we need to find a new criterion of validity, and I aim to propose such a criterion.
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  2. Model of Intelligence.Miro Brada - manuscript
    Model of intelligence and new methods to assess IQ. MA thesis in 1998 (Comenius University). Art exhibitions "From Animation" London 2013, "Fading Memory" Weißenohe 2015, TAIF Tokyo 2017. Conferences in Santorini, Daejon 2016, Geneva 2017.
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  3. Maximization of Originality.Miro Brada - manuscript
    The richer you are, the less equally rich or richer people. The richest is only one (=unique). Maximization of richness or leisure (=classic utility), maximizes the uniqueness (=improbability) that can be maximized also by: extreme sport, suicide, tattoo, count of views... The richest seem unique as the poorest, but the rich can easily become poor, while the poor can hardly get rich. So the aim of maximization reflects IQ and options. Few options increase irrationality, regardless of IQ. I also present (...)
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  4. Aristotle on Logical Consequence.Phil Corkum - manuscript
    Compare two conceptions of validity: under an example of a modal conception, an argument is valid just in case it is impossible for the premises to be true and the conclusion false; under an example of a topic-neutral conception, an argument is valid just in case there are no arguments of the same logical form with true premises and a false conclusion. This taxonomy of positions suggests a project in the philosophy of logic: the reductive analysis of the modal conception (...)
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  5. What is Logical in First-Order Logic?Boris Čulina - manuscript
    In this article, logical concepts are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language.
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  6. Introduction to Mathematical Logic, Edition 2021.Vilnis Detlovs & Karlis Podnieks - manuscript
    Textbook for students in mathematical logic. Part 1. Total formalization is possible! Formal theories. First order languages. Axioms of constructive and classical logic. Proving formulas in propositional and predicate logic. Glivenko's theorem and constructive embedding. Axiom independence. Interpretations, models and completeness theorems. Normal forms. Tableaux method. Resolution method. Herbrand's theorem.
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  7. Is Every Deductively Valid Argument Circular?Danny Frederick - manuscript
    David Miller claims that every valid deductive argument begs the question. Other philosophers and logicians have made similar claims. I show that the claim is false. Its appeal depends on the existence of logical terminology, particularly concerning what a proposition 'contains' or its 'logical content,' that is best understood as metaphoric and that, given its aptness to mislead, would be better eschewed. I show how the terminology appears to derive from early modern theories of the nature of mind, ideas and (...)
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  8. Knowledge and Content: Critique of David Miller.Danny Frederick - manuscript
    David Miller propounds a theory of objective knowledge from which he mistakenly derives some consequences about question-begging and persuasion that appear to be false. He makes a further claim about persuasion that also seems false. I argue that Miller’s account of objective knowledge is explanatorily weak unless supplemented with an account of subjective knowledge and that the latter enables us to extricate Miller’s theory from the falsehoods he associates with it.
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  9. Are There Any Good Reasons?Danny Frederick - manuscript
    David Miller argues that there are no good reasons, either sufficient or insufficient. I show that most of his arguments are invalid or unsound. Several of his arguments depend upon the false claim that every deductively valid argument is circular. I accept one of Miller's arguments for the conclusion that there are no good reasons which are less-than-sufficient. I accept one of his arguments to the conclusion that there are no probative sufficient reasons. But I explain how there are epistemic (...)
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  10. Proof Terms for Classical Derivations.Restall Greg - manuscript
    I give an account of proof terms for derivations in a sequent calculus for classical propositional logic. The term for a derivation δ of a sequent Σ≻Δ encodes how the premises Σ and conclusions Δ are related in δ. This encoding is many–to–one in the sense that different derivations can have the same proof term, since different derivations may be different ways of representing the same underlying connection between premises and conclusions. However, not all proof terms for a sequent Σ≻Δ (...)
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  11. A Puzzle About Inferential Strength and Probability.Alexander Hughes - manuscript
    Inductive logic would be the logic of arguments that are not valid, but nevertheless justify belief in something like the way in which valid arguments would. Maybe we could describe it as the logic of “almost valid” arguments. There is a sort of transitivity to valid arguments. Valid arguments can be chained together to form arguments and such arguments are themselves valid. One wants to distinguish the “almost valid” arguments by noting that chains of “almost valid” arguments are weaker than (...)
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  12. Harmony, Normality and Stability.Nils Kurbis - manuscript
    The paper begins with a conceptual discussion of Michael Dummett's proof-theoretic justification of deduction or proof-theoretic semantics, which is based on what we might call Gentzen's thesis: 'the introductions constitute, so to speak, the "definitions" of the symbols concerned, and the eliminations are in the end only consequences thereof, which could be expressed thus: In the elimination of a symbol, the formula in question, whose outer symbol it concerns, may only "be used as that which it means on the basis (...)
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  13. A Decision Procedure for Herbrand Formulas Without Skolemization.Timm Lampert - manuscript
    This paper describes a decision procedure for disjunctions of conjunctions of anti-prenex normal forms of pure first-order logic (FOLDNFs) that do not contain V within the scope of quantifiers. The disjuncts of these FOLDNFs are equivalent to prenex normal forms whose quantifier-free parts are conjunctions of atomic and negated atomic formulae (= Herbrand formulae). In contrast to the usual algorithms for Herbrand formulae, neither skolemization nor unification algorithms with function symbols are applied. Instead, a procedure is described that rests on (...)
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  14. The Dream of Recapture.Carlo Nicolai - manuscript
    As a response to the semantic and logical paradoxes, theorists often reject some principles of classical logic. However, classical logic is entangled with mathematics, and giving up mathematics is too high a price to pay, even for nonclassical theorists. The so-called recapture theorems come to the rescue. When reasoning with concepts such as truth/class membership/property instantiation, if ones is interested in consequences of the theory that only contain mathematical vocabulary, nothing is lost by reasoning in the nonclassical framework. It is (...)
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  15. Systems for Non-Reflexive Consequence.Carlo Nicolai & Lorenzo Rossi - manuscript
    Substructural logics and their application to logical and semantic paradoxes have been extensively studied, but non-reflexive systems have been somewhat neglected. Here, we aim to fill this lacuna, at least in part, by presenting a non-reflexive logic and theory of naive consequence (and truth). We also investigate the semantics and the proof-theory of the system. Finally, we develop a compositional theory of truth (and consequence) in our non-reflexive framework.
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  16. Tarski Undefinability Theorem Terse Refutation.P. Olcott - manuscript
    Both Tarski and Gödel “prove” that provability can diverge from Truth. When we boil their claim down to its simplest possible essence it is really claiming that valid inference from true premises might not always derive a true consequence. This is obviously impossible.
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  17. Prolog Detects Pathological Self Reference in the Gödel Sentence.P. Olcott - manuscript
    This sentence G ↔ ¬(F ⊢ G) and its negation G ↔ ~(F ⊢ ¬G) are shown to meet the conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)). They meet conventional definition of incompleteness because neither the sentence nor its negation is provable in F (or any other formal system). -- .
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  18. Defining Gödel Incompleteness Away.P. Olcott - manuscript
    We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable (...)
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  19. Refuting Tarski and Gödel with a Sound Deductive Formalism.P. Olcott - manuscript
    The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive conclusions are the result of these finite string transformation rules.
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  20. Defining a Decidability Decider.Pete Olcott - manuscript
    By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be semantically (...)
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  21. Provability with Minimal Type Theory.Pete Olcott - manuscript
    Minimal Type Theory (MTT) shows exactly how all of the constituent parts of an expression relate to each other (in 2D space) when this expression is formalized using a directed acyclic graph (DAG). This provides substantially greater expressiveness than the 1D space of FOPL syntax. -/- The increase in expressiveness over other formal systems of logic shows the Pathological Self-Reference Error of expressions previously considered to be sentences of formal systems. MTT shows that these expressions were never truth bearers, thus (...)
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  22. Minimal Type Theory (MTT).Pete Olcott - manuscript
    Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.
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  23. Probability of Immortality and God’s Existence. A Mathematical Perspective.Jesús Sánchez - manuscript
    What are the probabilities that this universe is repeated exactly the same with you in it again? Is God invented by human imagination or is the result of human intuition? The intuition that the same laws/mechanisms (evolution, stability winning probability) that have created something like the human being capable of self-awareness and controlling its surroundings, could create a being capable of controlling all what it exists? Will be the characteristics of the next universes random or tend to something? All these (...)
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  24. Credence for Epistemic Discourse.Paolo Santorio - manuscript
    Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...)
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  25. Making Conditional Speech Acts in the Material Way.Matheus Silva - manuscript
    The conventional wisdom about conditionals claims that (1) conditionals that have non-assertive acts in their consequents, such as commands and promises, cannot be plausibly interpreted as assertions of material implication; (2) the most promising hypothesis about those sentences is conditional-assertion theory, which explains a conditional as a conditional speech act, i.e., a performance of a speech act given the assumption of the antecedent. This hypothesis has far-reaching and revisionist consequences, because conditional speech acts are not synonymous with a proposition with (...)
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  26. A Contextualist Defence of the Material Account of Indicative Conditionals.Matheus Silva - manuscript
    The material account of indicative conditionals faces a legion of counterexamples that are the bread and butter in any entry about the subject. For this reason, the material account is widely unpopular among conditional experts. I will argue that this consensus was not built on solid foundations, since these counterexamples are contextual fallacies. They ignore a basic tenet of semantics according to which when evaluating arguments for validity we need to maintain the context constant, otherwise any argumentative form can be (...)
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  27. Subjunctive Conditionals Are Material.Matheus Silva - manuscript
    The material account claims that indicative conditionals are material. However, the conventional wisdom even among material account enthusiasts is that the material account cannot be extended to subjunctive conditionals. There are mainly three reasons that motivate this consensus: (1) the belief that if subjunctives were material, most subjunctive conditionals would be vacuously true, which is implausible; (2) its inconsistency with Adams pair, which suggest that indicative and subjunctive conditionals have different truth conditions; and (3) the belief that it is an (...)
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  28. Conditionals All the Way Down.Matheus Silva - manuscript
    It is usually accepted that unconditional statements are clearer and less problematic than conditional ones. This article goes against this popular belief by advancing the contrarian hypothesis that all unconditional statements can be reduced to conditional ones due to the way our assumptions support our assertions. In fact, considering the coherentist process by which most of our different beliefs mutually support themselves, the only genuine example of unconditional statements are cases of self-justified beliefs, but these examples are controversial and few (...)
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  29. The Big Four - Their Interdependence and Limitations.Matheus Silva - manuscript
    Four intuitions are recurrent and influential in theories about conditionals: the Ramsey’s test, the Adams’ Thesis, the Equation, and the robustness requirement. For simplicity’s sake, I call these intuitions ‘the big four’. My aim is to show that: (1) the big four are interdependent; (2) they express our inferential dispositions to employ a conditional on a modus ponens; (3) the disposition to employ conditionals on a modus ponens doesn’t have the epistemic significance that is usually attributed to it, since the (...)
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  30. Directional Bias.Matheus Silva - manuscript
    There is almost a consensus among conditional experts that indicative conditionals are not material. Their thought hinges on the idea that if indicative conditionals were material, A → B could be vacuously true when A is false, even if B would be false in a context where A is true. But since this consequence is implausible, the material account is usually regarded as false. It is argued that this point of view is motivated by the grammatical form of conditional sentences (...)
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  31. The Inextricable Link Between Conditionals and Logical Consequence.Matheus Silva - manuscript
    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 variety 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 (...)
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  32. "If-Then" as a Version of "Implies".Matheus Silva - manuscript
    Russell’s role in the controversy about the paradoxes of material implication is usually presented as a tale of how even the greatest minds can fall prey of basic conceptual confusions. Quine accused him of making a silly mistake in Principia Mathematica. He interpreted “if-then” as a version of “implies” and called it material implication. Quine’s accusation is that this decision involved a use-mention fallacy because the antecedent and consequent of “if-then” are used instead of being mentioned as the premise and (...)
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  33. The Logical Web.Matheus Silva - manuscript
    Different logic systems are motivated by attempts to fix the counter-intuitive instances of classical argumentative forms, e.g., strengthening of the antecedent, contraposition and conditional negation. These counter-examples are regarded as evidence that classical logic should be rejected in favour of a new logic system in which these argumentative forms are considered invalid. It is argued that these logical revisions are ad hoc, because those controversial argumentative forms are implied by other argumentative forms we want to keep. It is impossible to (...)
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  34. In Defence of Extensional Evidence.Matheus Silva - manuscript
    Intensional evidence is any reason to accept a proposition that is not the truth values of the proposition accepted or, if it is a complex proposition, is not the truth values of its propositional contents. Extensional evidence is non-intensional evidence. Someone can accept a complex proposition, but deny its logical consequences when her acceptance is based on intensional evidence, while the logical consequences of the proposition presuppose the acceptance of extensional evidence, e.g., she can refuse the logical consequence of a (...)
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  35. Indicative Conditionals Are Material - Expanding the Survey.Matheus Martins Silva - manuscript
    Adam Rieger (2013) has carried out a survey of arguments in favour of the material account of indicative conditionals. These arguments involve simple and direct demonstrations of the material account. I extend the survey with new arguments and clarify the logical connections among them. I also show that the main counter-examples against these arguments are not successful either because their premises are just as counter-intuitive as the conclusions, or because they depend on contextual fallacies. The conclusion is that the unpopularity (...)
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  36. Logical Consequence — C. Model-Theoretic Conceptions.Author unknown - manuscript
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  37. Relation Of Correspondence And Logical Consequence.Jan Such - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 79:185-215.
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  38. The Significance of Evidence-Based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences.Bhupinder Singh Anand - forthcoming
    In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...)
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  39. Logical Argumentation by Dynamic Proof Systems.Ofer Arieli & Christian Straßer - forthcoming - Theoretical Computer Science.
    In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered ‘derived’ or ‘not derived’ according (...)
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  40. On Stalnaker's "Indicative Conditionals".Fabrizio Cariani - forthcoming - In Louise McNally & Zoltan Szabo (eds.), Studies in Linguistics and Philosophy, Vol 100. Springer.
    This paper is a guide to the main ideas and innovations in Robert Stalnaker's "Indicative Conditionals". The paper is for a volume of essays on twenty-one classics of formal semantics edited by Louise McNally and Zoltàn Gendler Szabò.
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  41. On the Overlap Between Everything and Nothing.Massimiliano Carrara, Filippo Mancini & Jeroen Smid - forthcoming - Logic and Logical Philosophy.
    Graham Priest has recently proposed a solution to the problem of the One and the Many which involves inconsistent objects and a non-transitive identity relation. We show that his solution entails either that the object everything is identical with the object nothing or that they are mutual parts; depending on whether Priest goes for an extensional or a non-extensional mereology.
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  42. Ramsey’s Coheir.Eugenio Colla & Domenico Zambella - forthcoming - Journal of Symbolic Logic:1-13.
    We use the model theoretic notion of coheir to give short proofs of old and new theorems in Ramsey Theory. As an illustration we start from Ramsey's theorem itself. Then we prove Hindman's theorem and the Hales-Jewett theorem. Finally, we prove the two Ramsey theoretic principles that have among their consequences partition theorems due to Carlson and to Gowers.
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  43. Calculizing Classical Inferential Erotetic Logic.Moritz Cordes - forthcoming - Review of Symbolic Logic:1-22.
    This paper contributes to the calculization of evocation and erotetic implication as defined by Inferential Erotetic Logic (IEL). There is a straightforward approach to calculizing (propositional) erotetic implication which cannot be applied to evocation. First-order evocation is proven to be uncalculizable, i.e. there is no proof system, say FOE, such that for all X, Q: X evokes Q iff there is an FOE-proof for the evocation of Q by X. These results suggest a critique of the represented approaches to calculizing (...)
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  44. Sequent-Calculi for Metainferential Logics.Bruno Da Ré & Federico Pailos - forthcoming - Studia Logica:1-35.
    In recent years, some theorists have argued that the clogics are not only defined by their inferences, but also by their metainferences. In this sense, logics that coincide in their inferences, but not in their metainferences were considered to be different. In this vein, some metainferential logics have been developed, as logics with metainferences of any level, built as hierarchies over known logics, such as \, and \. What is distinctive of these metainferential logics is that they are mixed, i.e. (...)
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  45. Aristotelian Diagrams for Semantic and Syntactic Consequence.Lorenz Demey - forthcoming - Synthese:1-21.
    Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the well-known square of opposition for the categorical statements from (...)
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  46. ST, LP and Tolerant Metainferences.Bogdan Dicher & Francesco Paoli - forthcoming - In C. Bașkent & Thomas Ferguson (eds.), Graham Priest on dialetheism and paraconsistency. Springer.
  47. Logical Nihilism and the Logic of ‘Prem’.Andreas Fjellstad - forthcoming - Logic and Logical Philosophy:1.
    As the final component of a chain of reasoning intended to take us all the way to logical nihilism, Russell (2018) presents the atomic sentence ‘prem’ which is supposed to be true when featuring as premise in an argument and false when featuring as conclusion in an argument. Such a sentence requires a non-reflexive logic and an endnote by Russell (2018) could easily leave the reader with the impression that going non-reflexive suffices for logical nihilism. This paper shows how one (...)
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  48. Overgeneration in the Higher Infinite.Salvatore Florio & Luca Incurvati - forthcoming - In Gil Sagi & Jack Woods (eds.), The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning. Cambridge: Cambridge University Press.
    The Overgeneration Argument is a prominent objection against the model-theoretic account of logical consequence for second-order languages. In previous work we have offered a reconstruction of this argument which locates its source in the conflict between the neutrality of second-order logic and its alleged entanglement with mathematics. Some cases of this conflict concern small large cardinals. In this article, we show that in these cases the conflict can be resolved by moving from a set-theoretic implementation of the model-theoretic account to (...)
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  49. Reversing Logical Nihilism.Tristan Grøtvedt Haze - forthcoming - Synthese.
    Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction (e.g. ‘Snow is white. Grass is green. Therefore, snow is white and grass is green’) and Identity (e.g. ‘Snow is white. Therefore, snow is white’). These purported counterexamples involve expressions that are sensitive to linguistic context—for example, a sentence which is true when it appears alone but false when embedded in a larger sentence. If they are genuine counterexamples, it looks as though logical nihilism—the view that (...)
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  50. Validity as (Material!) Truth-Preservation in Virtue of Form.Tristan Grøtvedt Haze - forthcoming - Analytic Philosophy.
    According to a standard story, part of what we have in mind when we say that an argument is valid is that it is necessarily truth preserving: if the premises are true, the conclusion must also be true. But—the story continues—that’s not enough, since ‘Roses are red, therefore roses are coloured’ for example, while it may be necessarily truth-preserving, is not so in virtue of form. Thus we arrive at a standard contemporary characterisation of validity: an argument is valid when (...)
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