Basic Laws Of Logic Research Articles

Do Logical Aliens Think? Frege’s Agent-Relative View of Logic’s Constitutive Role for Thinking

Abstract Must you respect basic logical laws (BLL) – such as the law of non-contradiction – in order to think? Frege wrote that one must “acknowledge” BLL in order not to “abandon judgement altogether”. Some have argued that Frege therefore thought of logic as somehow ‘constitutive’ of thinking. However, some interpreters contend, due to his strong commitment to logic’s normative status, that Frege held the opposite view, namely the non-constitutivist view that (systematic) ‘illogical’ thinking is possible and that one need not accept or follow BLL in order to think as such, although one must do so in order to think correctly. The aim of this paper is to investigate the interpretative landscape regarding Frege’s view on logic’s constitutive role for thinking and suggest, against the non-constitutivist readings, that he indeed was committed to some version of the constitutivity thesis, but that this commitment is not, as some constitutivist interpretations suggest, inconsistent with the idea that logic is normative for thinking. I will, instead, propose to read his view in a soft and agent-relative sense, according to which it is a necessary condition for the possibility of thinking that the agent in question is sensitive to and acknowledges BLL.

Logical exceptionalism: Development and predicaments

AbstractThis paper examines the conceptions of logic from Leibniz, Hume, Kant, Frege, Wittgenstein and Ayer, and regards the six philosophers as the representatives of logical exceptionalism. From their standpoints, this paper refines the tenets of logical exceptionalism as follows: logic is exceptional to all other sciences because of four reasons: (i) logic is formal, neutral to any domain and any entities, and general; (ii) logical truths are made true by the meanings of logical constants they contain or by logicians' rational insight to consequence relations; (iii) logical truths are analytical, a prior and necessary, so not‐revisable; and (iv) logical laws are normative for how to correctly think. However, logical exceptionalism has encountered difficult open problems: What are logical constants? How to justify basic laws of logic? How are logical laws accessible to us? How to explain the reasonability of rival logics and select from them? How to explain the universal applicability of logical laws? How to explain the normativity of logical laws for correct thinking? This paper concludes that logical anti‐exceptionalism is more hopeful to successfully answer these questions than logical exceptionalism.

Mülahizələr hesabında deduksiya metodunun tətbiqinin elmi-nəzəri metodoloji problemləri

The issue of the emergence of formal axiomatic logical systems due to the emergence of logical antinomies in formal axiomatic systems, specifically the issue of developing formal logical axiomatics in the calculus of considerations was investigated in the considered research. At the same time, in order to determine the characteristics of the implementation of the logical-methodological principles and provisions of the deductive reasoning obviously, conceptual-logical foundations of the calculus of considerations was studied and the main propositions of the calculus of considerations and the analysis of the initial logical operations on them were given in the study. The basic laws of logic and the expression of one logical act with another one were also explained in the research work by giving the concepst of proportional form and tautology in the calculus of considerations. At the same time, main properties and the procedure of setting of the formal deductive theory in the calculus of considerations were studied in the article. In order to provide an adequate characterization of the conceptual and methodological bases of the calculus of considerations in the research work, the basic logical laws of the calculus of considerations developed by the German mathematician and thinker P. Hilbert were also given. In addition, the main principles and methodological provisions of the deductive method were investigated, and the rules of deriving new conclusions from the axioms were interpreted. At the end of the reviewed article, the main principles and methods of the formal axiomatic mathematical systems built on a deductive basis, specifically the calculus of considerations, were studied and a logical-methodological analysis of the calculus of considerations was carried out on this basis. In this framework, the syntactic and semantic analysis of formalized language in formal axiomatic logical systems was carried out separately, the constituent parts of those systems, including the construction scheme, were given.

AMBIGUITY AS A LOGICAL FALLACY: THE PROJECTION OF ARISTOTLE'S REASONING TOPS ONTO CONTEMPORARY MEDIA DISCOURSE

The article considers ambiguity as an error resulting from the violation of the basic laws of logic. Its relevance is conditioned by poorly expressed interdisciplinarity in existing linguistic studies, which inevitably entails the lack of a well-established approach. Aristotle’s works devoted to logic and specifically to logical errors are an inexhaustible source of knowledge for the modern scientist. In the process of their study, the connection between logic and linguistics becomes more obvious, allowing a deeper and more detailed consideration of the nature of ambiguity as a paralogism or sophism. The article deals with the reasons for the emergence of ambiguity in speech as a violation of speech accuracy, builds a subsequent typology of ambiguity, and suggests potential ways of its neutralization. The material for the study was microtexts taken from the news website The Mirror.

Laws of Logical Thinking and the Gospel

The article aims to clarify the basic laws of logic and show their application in the Gospel. The content of selected fragments of the Gospel proves that it contains fundamental laws of rational thinking in the form of: the law of identity, the law of non-contradiction, the law of the excluded middle, the law of sufficient reason, the law of finality. The statements and teachings of Jesus Christ are not without logical principles, which man already applies in everyday thinking. The source of this kind of laws is real existence. The so-called the first principles that govern the existence of being, in the order of knowledge, become the laws of thinking. For the message of revelation to be understood and accepted by the person to whom it is addressed, the laws of thought must exist in the Gospel.

The Justification of the Basic Laws of Logic

Take a correct sequent of formal logic, perhaps a simple logical truth, like the law of excluded middle, or something with premises, like disjunctive syllogism, but basically a claim of the form φ.1 Such a sequent attributes the properties of logical truth or logical consequence to a schematic sentence or argument. This paper aims to answer the question of how beliefs in such attributions are justified, on both its descriptive and normative interpretations; I aim to say when we generally take ourselves to be justified in forming such beliefs, and to make it plausible that beliefs formed this way really are justified. We can ask such questions about many domains (e.g. unobserved matters of fact Hume [9]) but there are special difficulties for answering them in logic. Some of the difficulties stem from the fact that logic is thought to be necessary and a priori; it is difficult to account for both a priori justification, and justification for thinking that something couldn’t have been otherwise. Moreover, it is often thought that logic is epistemically basic; we normally think that it is permissible to presuppose logic in the justification of our beliefs in other domains—engineering and arithmetic, for example, and even in justifying everyday common sense beliefs— yet we are not supposed to presuppose claims from these other domains when justifying our beliefs about logic. Logical beliefs come first, epistemologically speaking.

On A Neglected Path to Intuitionism

According to Quine, in any disagreement over basic logical laws the contesting parties must mean different things by the connectives or quantifiers implicated in those laws; when a deviant logician ‘tries to deny the doctrine he only changes the subject’. The standard (Heyting) semantics for intuitionism offers some confirmation for this thesis, for it represents an intuitionist as attaching quite different senses to the connectives than does a classical logician. All the same, I think Quine was wrong, even about the dispute between classicists and intuitionists. I argue for this by presenting an account of consequence, and a cognate semantic theory for the language of the propositional calculus, which (a) respects the meanings of the connectives as embodied in the familiar classical truth-tables, (b) does not presuppose Bivalence, and with respect to which (c) the rules of the intuitionist propositional calculus are sound and complete. Thus the disagreement between classicists and intuitionists, at least, need not stem from their attaching different senses to the connectives; one may deny the doctrine without changing the subject. The basic notion of my semantic theory is truth at a possibility, where a possibility is a way that (some) things might be, but which differs from a possible world in that the way in question need not be fully specific or determinate. I compare my approach with a previous theory of truth at a possibility due to Lloyd Humberstone, and with a previous attempt to refute Quine’s thesis due to John McDowell.

Design of fuzzy rule-based classifiers with semantic cointension

In computing with words (CWW), knowledge is linguistically represented and has an explicit semantics defined through fuzzy information granules. The linguistic representation, in turn, naturally bears an implicit semantics that belongs to users reading the knowledge base; hence a necessary condition for achieving interpretability requires that implicit and explicit semantics are cointensive. Interpretability is definitely stringent when knowledge must be acquired from data through inductive learning. Therefore, in this paper we propose a methodology for designing interpretable fuzzy models through semantic cointension. We focus our analysis on fuzzy rule-based classifiers (FRBCs), where we observe that rules resemble logical propositions, thus semantic cointension can be partially regarded as the fulfillment of the “logical view”, i.e. the set of basic logical laws that are required in any logical system. The proposed approach is grounded on the employment of a couple of tools: DC f, which extracts interpretable classification rules from data, and Espresso, that is capable of fast minimization of Boolean propositions. Our research demonstrates that it is possible to design models that exhibit good classification accuracy combined with high interpretability in the sense of semantic cointension. Also, structural parameters that quantify model complexity show that the derived models are also simple enough to be read and understood.

Logical deviance and semantic competence

Among the topics to whose discussion Diego Marconi has contributed outstandingly over the years, two of the most notable are the nature of lexical competence and the status of the law of non-contradiction. The topics are linked by the popular idea that adherence to basic logical laws is a necessary condition of understanding logical words, in particular that adherence to the law of non-contradiction is a necessary condition of understanding words for negation. For example, it may be proposed ...

Frege, Kant, and the Logic in Logicism

1. The Problem Let me start with a well-known story. Kant held that logic and conceptual analysis alone cannot account for our knowledge of arithmetic: “however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what is the sum [7+5]” (KrV, B16). Frege took himself to have shown that Kant was wrong about this. According to Frege’s logicist thesis, every arithmetical concept can be defined in purely logical terms, and every theorem of arithmetic can be proved using only the basic laws of logic. Hence, Kant was wrong to think that our grasp of arithmetical concepts and our knowledge of arithmetical truth depend on an extralogical source—the pure intuition of time (Frege 1884, §89, §109). Arithmetic, properly understood, is just a part of logic. Never mind whether Frege was right about this. I want to address a different question: Does Frege’s position on arithmetic really contradict Kant’s? I do not deny that Frege endorsed (F) Arithmetic is reducible to logic

On Proof for the Existence of God, and Other Reflective Inquiries.

The book takes a fresh look at fundamental philosophical and scientific issues, like the nature of reality, how it becomes known, how abstractions like mathematics become known, etc. In the process, our concepts of things and language for them is examined, as are such as free will, the mind, and the way laws of nature are formulated. Later, basic laws of logic are explored together with the well-known paradoxes found in it, and the foundations of mathematics and some of its basic truths, as in geometry, are reviewed. Lastly, the parts played by spiritual matters, including questions concerning the existence of God, as indicated in the title, are turned to.

Frege, Informative Identities, and Logicism

Frege's Grundgesetze der Arithmetik are inconsistent, as Russell first caused to be observed. My purpose here is to demonstrate that what Frege has to say about them is also inconsistent. Specifically, there is no Fregean way to reconcile the claims that arithmetical identity statements can be informative because they contain singular terms possessing co-referential but distinct senses, and that arithmetical truth is logical truth. Gregory Currie (Currie [1982]) has noticed this incompatibility and presumably regards it as a fairly obvious one, for he offers little in the way of detailed argument. Christian Thiel (Thiel [1968]) also realized that there is a problem here. Unfortunately his main supporting evidence has been dismissed by Michael Dummett. Since the incompatibility is not widely acknowledged and is therefore not so obvious to others it seems worthwhile filling in the details. The laws of logic are for Frege analytic by the definition of that term. More importantly for present concerns, they are always and everywhere true. Yet a simple arithmetical truth such as '2 + 2 =4' is conceivably false: the senses of the terms on either side of the equality-sign differ and hence the thought expressed by the whole equation is not true in virtue of the identity of the senses of its part.' Frege would have us believe that all arithmetical truths are derivable by truth-preserving rules of inference from his basic laws of logic. Evidently matters are less than transparently clear and a likely source of disquiet is the claim that the senses of '2 + 2' and of '4' are different: we shall see that it proves incompatible with the thesis that arithmetic is derivable from logic. For Frege logic has truth for its subject matter:

Predication versus membership in the distinction between logic as language and logic as calculus

This is a post-peer-review, pre-copyedit version of an article published in Synthese. The final authenticated version is available online at: https://doi.org/10.1007/BF00869546