Epistemic logic: All knowledge is based on our experience, and epistemic logic is the cognitive representation of our experiential confrontation in reality

Semiotica ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dan Nesher

AbstractEpistemic Logic is our basic universal science, the method of our cognitive confrontation in reality to prove the truth of our basic cognitions and theories. Hence, by proving their true representation of reality we can self-control ourselves in it, and thus refuting the Berkeleyian solipsism and Kantian a priorism. The conception of epistemic logic is that only by proving our true representation of reality we achieve our knowledge of it, and thus we can prove our cognitions to be either true or rather false, and otherwise they are doubtful. Therefore, truth cannot be separated from being proved and we cannot hold anymore the principle of excluded middle, as it is with formal semantics of metaphysical realism. In distinction, the intuitionistic logic is based on subjective intellectual feeling of correctness in constructing proofs, and thus it is epistemologically encapsulated in the metaphysical subject. However, epistemic logic is our basic science which enable us to prove the truth of our cognitions, including the epistemic logic itself.

Semiotica ◽  
2018 ◽  
Vol 2018 (221) ◽  
pp. 29-52
Author(s):  
Dan Nesher

AbstractCharles S. Peirce attempted to develop his semiotic theory of cognitive signs interpretation, which are originated in our basic perceptual operations that quasi-prove the truth of perceptual judgment representing reality. The essential problem was to explain how, by a cognitive interpretation of the sequence of perceptual signs, we can represent external physical reality and reflectively represent our cognitive mind’s operations of signs. With his phaneroscopy introspection, Peirce shows how, without going outside our cognitions, we can represent external reality. Hence Peirce can avoid the Berkeleyian, Humean, and Kantian phenomenologies, as well as the modern analytic philosophy and hermeneutic phenomenology. Peirce showed that with the trio of semiotic interpretation – abductive logic of discovery of hypotheses, deductive logic of necessary inference, and inductive logic of evaluation – we can reach a complete proof of the true representation of reality. This semiotic logic of reasoning is the epistemic logic representing human confrontation in reality, with which we can achieve knowledge and conduct our behavior. However, Peirce did not complete his realistic revolution to eliminate previously accepted nominalistic and idealistic epistemologies of formal logic and pure mathematics. Here, I inquire why Peirce did not complete his historical realist epistemological revolution and following that inquiry I attempt to reconstruct it.


Author(s):  
Walter Carnielli ◽  
Abilio Rodrigues

Abstract From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic (for example intuitionistic logic) lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle, this duality can be interpreted either ontologically or epistemically. An ontological interpretation of intuitionistic logic is Brouwer’s idealism; of paraconsistency is dialetheism. The epistemic interpretation of intuitionistic logic is in terms of preservation of constructive proof; of paraconsistency is in terms of preservation of evidence. In this paper, we explain and defend the epistemic approach to paraconsistency. We argue that it is more plausible than dialetheism and allows a peaceful and fruitful coexistence with classical logic.


Author(s):  
Christopher Hookway

Peirce was an American philosopher, probably best known as the founder of pragmatism and for his influence upon later pragmatists such as William James and John Dewey. Personal and professional difficulties interfered with his attempts to publish a statement of his overall philosophical position, but, as the texts have become more accessible, it has become clear that he was a much more wide-ranging and important thinker than his popular reputation suggests. He claimed that his pragmatism was the philosophical outlook of an experimentalist, of someone with experience of laboratory work. His account of science was vigorously anti-Cartesian: Descartes was criticized for requiring an unreal ‘pretend’ doubt, and for adopting an individualist approach to knowledge which was at odds with scientific practice. ‘Inquiry’ is a cooperative activity, whereby fallible investigators progress towards the truth, replacing real doubts by settled beliefs which may subsequently be revised. In ‘The Fixation of Belief’ (1877), he compared different methods for carrying out inquiries, arguing that only the ‘method of science’ can be self-consciously adopted. This method makes the ‘realist’ assumption that there are real objects, existing independently of us, whose nature will be discovered if we investigate them for long enough and well enough. Peirce’s ‘pragmatist principle’ was a rule for clarifying concepts and hypotheses that guide scientific investigations. In the spirit of laboratory practice, we can completely clarify the content of a hypothesis by listing the experiential consequences we would expect our actions to have if it were true: if an object is fragile, and we were to drop it, we would probably see it break. If this is correct, propositions of a priori metaphysics are meaningless. Peirce applied his principle to explain truth in terms of the eventual agreement of responsible inquirers: a proposition is true if it would be accepted eventually by anyone who inquired into it. His detailed investigations of inductive reasoning and statistical inference attempted to explain how this convergence of opinion was achieved. Taken together with his important contributions to formal logic and the foundations of mathematics, this verificationism encouraged early readers to interpret Peirce’s work as an anticipation of twentieth-century logical positivism. The interpretation is supported by the fact that he tried to ground his logic in a systematic account of meaning and reference. Much of his most original work concerned semiotic, the general theory of signs, which provided a novel framework for understanding of language, thought and all other kinds of representation. Peirce hoped to show that his views about science, truth and pragmatism were all consequences of his semiotic. Doubts about the positivistic reading emerge, however, when we note his insistence that pragmatism could be plausible only to someone who accepted a distinctive form of metaphysical realism. And his later attempts to defend his views of science and meaning bring to the surface views which would be unacceptable to an anti-metaphysical empiricist. From the beginning, Peirce was a systematic philosopher whose work on logic was an attempt to correct and develop Kant’s philosophical vision. When his views were set out in systematic order, positions came to the surface which, he held, were required by his work on logic. These include the theory of categories which had long provided the foundations for his work on signs: all elements of reality, thought and experience can be classified into simple monadic phenomena, dyadic relations and triadic relations. Peirce called these Firstness, Secondness and Thirdness. He also spoke of them as quality, reaction and mediation, and he insisted that the error of various forms of empiricism and nominalism was the denial that mediation (or Thirdness) was an irreducible element of our experience. Peirce’s ‘synechism’ insisted on the importance for philosophy and science of hypotheses involving continuity, which he identified as ‘ultimate mediation’. This emphasis upon continuities in thought and nature was supposed to ground his realism. Furthermore, his epistemological work came to focus increasingly upon the requirements for rational self-control, for our ability to control our inquiries in accordance with norms whose validity we can acknowledge. This required a theory of norms which would explain our attachment to the search for truth and fill out the details of that concept. After 1900, Peirce began to develop such an account, claiming that logic must be grounded in ethics and aesthetics. Although pragmatism eliminated a priori speculation about the nature of reality, it need not rule out metaphysics that uses the scientific method. From the 1880s, Peirce looked for a system of scientific metaphysics that would fill important gaps in his defence of the method of science. This led to the development of an evolutionary cosmology, an account of how the world of existent objects and scientific laws evolved out of a chaos of possibilities through an evolutionary process. His ‘tychism’ insisted that chance was an ineliminable component of reality, but he argued that the universe was becoming more governed by laws or habits through time. Rejecting both physicalism and dualism, he defended what he called a form of ‘Objective Idealism’: matter was said to be a form of ‘effete mind’.


Author(s):  
Peter Pagin

The law of excluded middle (LEM) says that every sentence of the form A∨¬A (‘A or not A’) is logically true. This law is accepted in classical logic, but not in intuitionistic logic. The reason for this difference over logical validity is a deeper difference about truth and meaning. In classical logic, the meanings of the logical connectives are explained by means of the truth tables, and these explanations justify LEM. However, the truth table explanations involve acceptance of the principle of bivalence, that is, the principle that every sentence is either true or false. The intuitionist does not accept bivalence, at least not in mathematics. The reason is the view that mathematical sentences are made true and false by proofs which mathematicians construct. On this view, bivalence can be assumed only if we have a guarantee that for each mathematical sentence, either there is a proof of the truth of the sentence, or a proof of its falsity. But we have no such guarantee. Therefore bivalence is not intuitionistically acceptable, and then neither is LEM. A realist about mathematics thinks that if a mathematical sentence is true, then it is rendered true by the obtaining of some particular state of affairs, whether or not we can know about it, and if that state of affairs does not obtain, then the sentence is false. The realist further thinks that mathematical reality is fully determinate, in that every mathematical state of affairs determinately either obtains or does not obtain. As a result, the principle of bivalence is taken to hold for mathematical sentences. The intuitionist is usually an antirealist about mathematics, rejecting the idea of a fully determinate, mind-independent mathematical reality. The intuitionist’s view about the truth-conditions of mathematical sentences is not obviously incompatible with realism about mathematical states of affairs. According to Michael Dummett, however, the view about truth-conditions implies antirealism. In Dummett’s view, a conflict over realism is fundamentally a conflict about what makes sentences true, and therefore about semantics, for there is no further question about, for example, the existence of a mathematical reality than as a truth ground for mathematical sentences. In this vein Dummett has proposed to take acceptance of bivalence as actually defining a realist position. If this is right, then both the choice between classical and intuitionistic logic and questions of realism are fundamentally questions of semantics, for whether or not bivalence holds depends on the proper semantics. The question of the proper semantics, in turn, belongs to the theory of meaning. Within the theory of meaning Dummett has laid down general principles, from which he argues that meaning cannot in general consist in bivalent truth-conditions. The principles concern the need for, and the possibility of, manifesting one’s knowledge of meaning to other speakers, and the nature of such manifestations. If Dummett’s argument is sound, then bivalence cannot be justified directly from semantics, and may not be justifiable at all.


2019 ◽  
Vol 16 (7) ◽  
pp. 319 ◽  
Author(s):  
Woods Jack

I distinguish two ways of developing anti-exceptionalist approaches to logical revision. The first emphasizes comparing the theoretical virtuousness of developed bodies of logical theories, such as classical and intuitionistic logic. I'll call this whole theory comparison. The second attempts local repairs to problematic bits of our logical theories, such as dropping excluded middle (and modifying elsewhere accordingly) to deal with intuitions about vagueness. I'll call this the piecemeal approach. I then briefly discuss a problem I've developed elsewhere for comparisons of logical theories. Essentially, the problem is that a pair of logics may each evaluate the alternative as superior to themselves, resulting in oscillation between logical options. The piecemeal approach offers a way out of this problem andthereby might seem a preferable to whole theory comparisons. I go on to show that reflective equilibrium, the best known piecemeal method, has deep problems of its own when applied to logic.


2021 ◽  
pp. 209-260
Author(s):  
Crispin Wright

This chapter addresses three problems: the problem of formulating a coherent relativism, the Sorites paradox, and a seldom noticed difficulty in the best intuitionistic case for the revision of classical logic. A response to the latter is proposed which, generalized, contributes towards the solution of the other two. The key to this response is a generalized conception of indeterminacy as a specific kind of intellectual bafflement—Quandary. Intuitionistic revisions of classical logic are merited wherever a subject matter is conceived both as liable to generate Quandary and as subject to a broad form of evidential constraint. So motivated, the distinctions enshrined in intuitionistic logic provide both for a satisfying resolution of the Sorites paradox and a coherent outlet for relativistic views about, for example, matters of taste and morals. An important corollary of the discussion is that an epistemic conception of vagueness can be prised apart from the strong metaphysical realism with which its principal supporters have associated it, and acknowledged to harbour an independent insight.


2015 ◽  
Vol 30 (4) ◽  
pp. 953-989 ◽  
Author(s):  
Patrick Kahl ◽  
Richard Watson ◽  
Evgenii Balai ◽  
Michael Gelfond ◽  
Yuanlin Zhang

Abstract In this article, we present a new version of the language of Epistemic Specifications. The goal is to simplify and improve the intuitive and formal semantics of the language. We describe an algorithm for computing solutions of programs written in this new version of the language. The new semantics is illustrated by a number of examples, including an Epistemic Specifications-based framework for conformant planning. In addition, we introduce the notion of an epistemic logic program with sorts . This extends recent efforts to define a logic programming language that includes the means for explicitly specifying the domains of predicate parameters. An algorithm and its implementation as a solver for epistemic logic programs with sorts is also discussed.


2020 ◽  
Vol 30 (1) ◽  
pp. 381-402
Author(s):  
Tudor Protopopescu

Abstract Intuitionistic epistemic logic introduces an epistemic operator to intuitionistic logic, which reflects the intended Brouwer–Heyting–Kolmogorov (BHK) semantics of intuitionism. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the product of verification. The BHK interpretation of intuitionistic logic has a precise formulation in the logic of proofs and its arithmetical semantics. We show here that this interpretation can be extended to the notion of verification upon which intuitionistic knowledge is based, providing the systems of intuitionistic epistemic logic based on verification with an arithmetical semantics too. This confirms that the conception of verification incorporated in these systems reflects the BHK interpretation.


1982 ◽  
Vol 46 (6) ◽  
pp. 314-322
Author(s):  
GI Roth ◽  
RB Bridges ◽  
AT Brown ◽  
R Calmes ◽  
TT Lillich ◽  
...  

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