On the Embodiment of Space and Time: Triadic Logic, Quantum Indeterminacy and the Metaphysics of Relativity
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Aristotle's Assertoric Syllogistic and Modern Relevance Logic*
Aristotle’s assertoric syllogistic and modern relevance logic* Abstract: This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises of a proof are actually used to derive the conclusion. Turning to Aristotle’s Prior Analytics, I argue that there is evidence that Aristotle’s Assertoric Syllogistic satisfies both conditions. Moreover, Aristotle at one point explicitly addresses the potential harmfulness of syllogisms with unused premises. Here, I argue that Aristotle’s analysis allows for a rejection of such syllogisms on formal grounds established in the foregoing parts of the Prior Analytics. In a final section I consider the view that Aristotle distinguished between validity on the one hand and syllogistic validity on the other. Following this line of reasoning, Aristotle’s logic might not be a relevance logic, since relevance is part of syllogistic validity and not, as modern relevance logic demands, of general validity. I argue that the reasons to reject this view are more compelling than the reasons to accept it and that we can, cautiously, uphold the result that Aristotle’s logic is a relevance logic. Keywords: Aristotle, Syllogism, Relevance Logic, History of Logic, Logic, Relevance 1. -
Why Do We Remember? the Communicative Function of Episodic Memory
BEHAVIORAL AND BRAIN SCIENCES (2018), Page 1 of 63 doi:10.1017/S0140525X17000012,e1 Why do we remember? The communicative function of episodic memory Johannes B. Mahr Department of Cognitive Science, Cognitive Development Center, Central European University, 1051 Budapest, Hungary [email protected] https://cognitivescience.ceu.edu/people/johannes-mahr Gergely Csibra Department of Cognitive Science, Cognitive Development Center, Central European University, 1051 Budapest, Hungary [email protected] https://cognitivescience.ceu.edu/people/gergely-csibra Abstract: Episodic memory has been analyzed in a number of different ways in both philosophy and psychology, and most controversy has centered on its self-referential, autonoetic character. Here, we offer a comprehensive characterization of episodic memory in representational terms and propose a novel functional account on this basis. We argue that episodic memory should be understood as a distinctive epistemic attitude taken toward an event simulation. In this view, episodic memory has a metarepresentational format and should not be equated with beliefs about the past. Instead, empirical findings suggest that the contents of human episodic memory are often constructed in the service of the explicit justification of such beliefs. Existing accounts of episodic memory function that have focused on explaining its constructive character through its role in future-oriented mental time travel do justice neither to its capacity to ground veridical beliefs about the past nor to its representational format. We provide an account of the metarepresentational structure of episodic memory in terms of its role in communicative interaction. The generative nature of recollection allows us to represent and communicate the reasons why we hold certain beliefs about the past. -
The Matter of Time
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 15 June 2021 doi:10.20944/preprints202106.0417.v1 Article The matter of time Arto Annila 1,* 1 Department of Physics, University of Helsinki; [email protected] * Correspondence: [email protected]; Tel.: (+358 44 204 7324) Abstract: About a century ago, in the spirit of ancient atomism, the quantum of light was renamed the photon to suggest its primacy as the fundamental element of everything. Since the photon carries energy in its period of time, a flux of photons inexorably embodies a flow of time. Time comprises periods as a trek comprises legs. The flows of quanta naturally select optimal paths, i.e., geodesics, to level out energy differences in the least time. While the flow equation can be written, it cannot be solved because the flows affect their driving forces, affecting the flows, and so on. As the forces, i.e., causes, and changes in motions, i.e., consequences, cannot be separated, the future remains unpre- dictable, however not all arbitrary but bounded by free energy. Eventually, when the system has attained a stationary state, where forces tally, there are no causes and no consequences. Then time does not advance as the quanta only orbit on and on. Keywords: arrow of time; causality; change; force; free energy; natural selection; nondeterminism; quantum; period; photon 1. Introduction We experience time passing, but the experience itself lacks a theoretical formulation. Thus, time is a big problem for physicists [1-3]. Although every process involves a passage of time, the laws of physics for particles, as we know them today, do not make a difference whether time flows from the past to the future or from the future to the past. -
The Peripatetic Program in Categorical Logic: Leibniz on Propositional Terms
THE REVIEW OF SYMBOLIC LOGIC, Page 1 of 65 THE PERIPATETIC PROGRAM IN CATEGORICAL LOGIC: LEIBNIZ ON PROPOSITIONAL TERMS MARKO MALINK Department of Philosophy, New York University and ANUBAV VASUDEVAN Department of Philosophy, University of Chicago Abstract. Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such as reductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titled Specimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule of reductio ad absurdum in a purely categor- ical calculus in which every proposition is of the form AisB. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule of reductio ad absurdum,but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic ¬ known as RMI→ . From its beginnings in antiquity up until the late 19th century, the study of formal logic was shaped by two distinct approaches to the subject. The first approach was primarily concerned with simple propositions expressing predicative relations between terms. -
Logic: a Brief Introduction Ronald L
Logic: A Brief Introduction Ronald L. Hall, Stetson University Chapter 1 - Basic Training 1.1 Introduction In this logic course, we are going to be relying on some “mental muscles” that may need some toning up. But don‟t worry, we recognize that it may take some time to get these muscles strengthened; so we are going to take it slow before we get up and start running. Are you ready? Well, let‟s begin our basic training with some preliminary conceptual stretching. Certainly all of us recognize that activities like riding a bicycle, balancing a checkbook, or playing chess are acquired skills. Further, we know that in order to acquire these skills, training and study are important, but practice is essential. It is also commonplace to acknowledge that these acquired skills can be exercised at various levels of mastery. Those who have studied the piano and who have practiced diligently certainly are able to play better than those of us who have not. The plain fact is that some people play the piano better than others. And the same is true of riding a bicycle, playing chess, and so forth. Now let‟s stretch this agreement about such skills a little further. Consider the activity of thinking. Obviously, we all think, but it is seldom that we think about thinking. So let's try to stretch our thinking to include thinking about thinking. As we do, and if this does not cause too much of a cramp, we will see that thinking is indeed an activity that has much in common with other acquired skills. -
Aristotle on Predication
DOI: 10.1111/ejop.12054 Aristotle on Predication Phil Corkum Abstract: A predicate logic typically has a heterogeneous semantic theory. Sub- jects and predicates have distinct semantic roles: subjects refer; predicates char- acterize. A sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homogeneous theory: both subjects and predicates refer; and a sentence is true if the subject and predicate name one and the same thing. In this paper, I will examine evidence for ascribing to Aristotle the view that subjects and predicates refer. If this is correct, then it seems that Aristotle, like the traditional term logician, problematically conflates predication and identity claims. I will argue that we can ascribe to Aristotle the view that both subjects and predicates refer, while holding that he would deny that a sentence is true just in case the subject and predicate name one and the same thing. In particular, I will argue that Aristotle’s core semantic notion is not identity but the weaker relation of consti- tution. For example, the predication ‘All men are mortal’ expresses a true thought, in Aristotle’s view, just in case the mereological sum of humans is a part of the mereological sum of mortals. A predicate logic typically has a heterogeneous semantic theory. Subjects and predicates have distinct semantic roles: subjects refer; predicates characterize. A sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homo- geneous theory: both subjects and predicates refer; and a sentence is true if the subject and predicate name one and the same thing. -
The History of Logic
c Peter King & Stewart Shapiro, The Oxford Companion to Philosophy (OUP 1995), 496–500. THE HISTORY OF LOGIC Aristotle was the first thinker to devise a logical system. He drew upon the emphasis on universal definition found in Socrates, the use of reductio ad absurdum in Zeno of Elea, claims about propositional structure and nega- tion in Parmenides and Plato, and the body of argumentative techniques found in legal reasoning and geometrical proof. Yet the theory presented in Aristotle’s five treatises known as the Organon—the Categories, the De interpretatione, the Prior Analytics, the Posterior Analytics, and the Sophistical Refutations—goes far beyond any of these. Aristotle holds that a proposition is a complex involving two terms, a subject and a predicate, each of which is represented grammatically with a noun. The logical form of a proposition is determined by its quantity (uni- versal or particular) and by its quality (affirmative or negative). Aristotle investigates the relation between two propositions containing the same terms in his theories of opposition and conversion. The former describes relations of contradictoriness and contrariety, the latter equipollences and entailments. The analysis of logical form, opposition, and conversion are combined in syllogistic, Aristotle’s greatest invention in logic. A syllogism consists of three propositions. The first two, the premisses, share exactly one term, and they logically entail the third proposition, the conclusion, which contains the two non-shared terms of the premisses. The term common to the two premisses may occur as subject in one and predicate in the other (called the ‘first figure’), predicate in both (‘second figure’), or subject in both (‘third figure’). -
Review of Philosophical Logic: an Introduction to Advanced Topics*
Teaching Philosophy 36 (4):420-423 (2013). Review of Philosophical Logic: An Introduction to Advanced Topics* CHAD CARMICHAEL Indiana University–Purdue University Indianapolis This book serves as a concise introduction to some main topics in modern formal logic for undergraduates who already have some familiarity with formal languages. There are chapters on sentential and quantificational logic, modal logic, elementary set theory, a brief introduction to the incompleteness theorem, and a modern development of traditional Aristotelian Logic: the “term logic” of Sommers (1982) and Englebretsen (1996). Most of the book provides compact introductions to the syntax and semantics of various familiar formal systems. Here and there, the authors briefly indicate how intuitionist logic diverges from the classical treatments that are more fully explored. The book is appropriate for an undergraduate-level second course in logic that will approach the topic from a philosophical (rather than primarily mathematical) perspective. Philosophical topics (sometimes very briefly) touched upon in the book include: intuitionist logic, substitutional quantification, the nature of logical consequence, deontic logic, the incompleteness theorem, and the interaction of quantification and modality. The book provides an effective jumping-off point for several of these topics. In particular, the presentation of the intuitive idea of the * George Englebretsen and Charles Sayward, Philosophical Logic: An Introduction to Advanced Topics (New York: Continuum International Publishing Group, 2013), 208 pages. 1 incompleteness theorem (chapter 7) is the right level of rigor for an undergraduate philosophy student, as it provides the basic idea of the proof without getting bogged down in technical details that would not have much philosophical interest. -
The Singular Universe and the Reality of Time: a Proposal in Natural Philosophy
philosophies Book Review The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy. By Roberto Mangabeira Unger and Lee Smolin. Cambridge University Press: Cambridge, UK, 2014; 566 pp.; ISBN-10: 1107074061, ISBN-13: 978-1107074064 Matt McManus ID Politics Science and International Relations, Tecnológico de Monterrey, Toronto, ON M6B 1T2, Canada; [email protected] Received: 14 July 2018; Accepted: 17 July 2018; Published: 18 July 2018 To do genuinely interdisciplinary and transdisciplinary work is the goal of many scholars. Some achieve it better than others. But to engage in truly systematic and all-encompassing scholarship almost seems anachronistic, not to mention a trifle arrogant. Given the complexities involved in mastering even a single discipline, who could have the audacity to claim expertise across them all. Such ambition and systematicity, not to mention the borderline audacity that underlies it, is part of the thrill that comes from reading any book Roberto Unger. Where others might painstakingly tie themselves into knots justifying their right to engage in interdisciplinary and transdisciplinary work, Unger simply steamrolls over all objections to think and write about whatever he wishes. In many, this might simply be intellectual over reach. But Unger is the rare exception. His seemingly encyclopediac capacity for philosophical systematization has moved from impressive to genuinely inspiring in his recent work. Unger began his career at Harvard Law in the 1970s, as a founding member of the critical legal theory movement in American jurisprudence. His youthful manuscript, Knowledge and Politics, remains a minor classic and develops a reasonably novel criticism of liberal legalism. -
Traditional Logic and Computational Thinking
philosophies Article Traditional Logic and Computational Thinking J.-Martín Castro-Manzano Faculty of Philosophy, UPAEP University, Puebla 72410, Mexico; [email protected] Abstract: In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve this objective, we argue in favor of two statements: (i) that traditional logic is not classical and (ii) that logic programming emanating from traditional logic is not classical logic programming. Keywords: syllogistic; aristotelian logic; logic programming 1. Introduction Computational thinking, like critical thinking [1], is a sort of general-purpose thinking that includes a set of logical skills. Hence logic, as a scientific enterprise, is an integral part of it. However, unlike critical thinking, when one checks what “logic” means in the computational context, one cannot help but be surprised to find out that it refers primarily, and sometimes even exclusively, to classical logic (cf. [2–7]). Classical logic is the logic of Boolean operators, the logic of digital circuits, the logic of Karnaugh maps, the logic of Prolog. It is the logic that results from discarding the traditional, Aristotelian logic in order to favor the Fregean–Tarskian paradigm. Classical logic is the logic that defines the standards we typically assume when we teach, research, or apply logic: it is the received view of logic. This state of affairs, of course, has an explanation: classical logic works wonders! However, this is not, by any means, enough warrant to justify the absence or the abandon of Citation: Castro-Manzano, J.-M. traditional logic within the computational thinking literature. -
What Does It Mean to Say That Logic Is Formal?
WHAT DOES IT MEAN TO SAY THAT LOGIC IS FORMAL? by John Gordon MacFarlane A.B., Philosophy, Harvard College, 1991 M.A., Philosophy, University of Pittsburgh, 1994 M.A., Classics, University of Pittsburgh, 1997 Submitted to the Graduate Faculty of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2000 i Robert Brandom, Distinguished Service Professor of Philosophy (Director) Nuel Belnap, Alan Ross Anderson Distinguished Professor of Philosophy (Second Reader) Joseph Camp, Professor of Philosophy Danielle Macbeth, Associate Professor of Philosophy, Haverford College (Outside Reader) Kenneth Manders, Associate Professor of Philosophy Gerald Massey, Distinguished Service Professor of Philosophy ii WHAT DOES IT MEAN TO SAY THAT LOGIC IS FORMAL? John Gordon MacFarlane, PhD University of Pittsburgh, 2000 Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a pri- ori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topic-neutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought. -
Conjectures on Spacetime
Conjectures on SpaceTime Alessandro Capurso – [email protected] – linkedin.com/in/capurso/ v190915 - Accepted as contribution at TM2019 INAF conference (Turin, Italy) Available online at indico.ict.inaf.it/event/751/contributions/5182/ Abstract Index The aim of this contribution is to propose new Abstract ................................................................................... 1 conjectures on SpaceTime variables and their description Index ........................................................................................ 1 through the concepts of network and coherent decoding (borrowed from Information Theory) and to offer a Variables and Geometry ....................................................... 2 possible wider perspective on SpaceTime fabric and Time, Memory and discreteness ..................................... 2 evolution. The model follows latest efforts to restore the Imaginary time and Information Space......................... 2 importance of Time in Physics (as Smolin in [1]). Perception of each Self ..................................................... 3 The critical step suggested is towards how we perceive AdS/CFT and Neural networks..................................... 4 SpaceTime dimensions: a 4D quantized expanding Living on the Surface ............................................................ 6 SpaceTime with 2 components for Information Space and Few bits of SpaceTime ....................................................... 6 2 orthogonal time-momentum components is considered. The time-dimensions