Van Fraassen and a Defense of Inference to the Best
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Reliability of Mathematical Inference
Reliability of mathematical inference Jeremy Avigad Department of Philosophy and Department of Mathematical Sciences Carnegie Mellon University January 2020 Formal logic and mathematical proof An important mathematical goal is to get the answers right: • Our calculations are supposed to be correct. • Our proofs are supposed to be correct. Mathematical logic offers an idealized account of correctness, namely, formal derivability. Informal proof is viewed as an approximation to the ideal. • A mathematician can be called on to expand definitions and inferences. • The process has to terminate with fundamental notions, assumptions, and inferences. Formal logic and mathematical proof Two objections: • Few mathematicians can state formal axioms. • There are various formal foundations on offer. Slight elaboration: • Ordinary mathematics relies on an informal foundation: numbers, tuples, sets, functions, relations, structures, . • Formal logic accounts for those (and any of a number of systems suffice). Formal logic and mathematical proof What about intuitionstic logic, or large cardinal axioms? Most mathematics today is classical, and does not require strong assumptions. But even in those cases, the assumptions can be make explicit and formal. Formal logic and mathematical proof So formal derivability provides a standard of correctness. Azzouni writes: The first point to observe is that formalized proofs have become the norms of mathematical practice. And that is to say: should it become clear that the implications (of assumptions to conclusion) of an informal proof cannot be replicated by a formal analogue, the status of that informal proof as a successful proof will be rejected. Formal verification, a branch of computer science, provides corroboration: computational proof assistants make formalization routine (though still tedious). -
Misconceived Relationships Between Logical Positivism and Quantitative Research: an Analysis in the Framework of Ian Hacking
DOCUMENT RESUME ED 452 266 TM 032 553 AUTHOR Yu, Chong Ho TITLE Misconceived Relationships between Logical Positivism and Quantitative Research: An Analysis in the Framework of Ian Hacking. PUB DATE 2001-04-07 NOTE 26p. PUB TYPE Opinion Papers (120) ED 2S PRICE MF01/PCO2 Plus Postage. 'DESCRIPTORS *Educational Research; *Research Methodology IDENTIFIERS *Logical Positivism ABSTRACT Although quantitative research methodology is widely applied by psychological researchers, there is a common misconception that quantitative research is based on logical positivism. This paper examines the relationship between quantitative research and eight major notions of logical positivism:(1) verification;(2) pro-observation;(3) anti-cause; (4) downplaying explanation;(5) anti-theoretical entities;(6) anti-metaphysics; (7) logical analysis; and (8) frequentist probability. It is argued that the underlying philosophy of modern quantitative research in psychology is in sharp contrast to logical positivism. Putting the labor of an out-dated philosophy into quantitative research may discourage psychological researchers from applying this research approach and may also lead to misguided dispute between quantitative and qualitative researchers. What is needed is to encourage researchers and students to keep an open mind to different methodologies and apply skepticism to examine the philosophical assumptions instead of accepting them unquestioningly. (Contains 1 figure and 75 references.)(Author/SLD) Reproductions supplied by EDRS are the best that can be made from the original document. Misconceived relationships between logical positivism and quantitative research: An analysis in the framework of Ian Hacking Chong Ho Yu, Ph.D. Arizona State University April 7, 2001 N N In 4-1 PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIALHAS BEEN GRANTED BY Correspondence: TO THE EDUCATIONAL RESOURCES Chong Ho Yu, Ph.D. -
Applying Logic to Philosophical Theology: a Formal Deductive Inference of Affirming God's Existence from Assuming the A-Priori
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Tomsk State University Repository Вестник Томского государственного университета Философия. Социология. Политология. 2020. № 55 ОНТОЛОГИЯ, ЭПИСТЕМОЛОГИЯ, ЛОГИКА УДК 16 + 17 + 2 + 51-7 DOI: 10.17223/1998863Х/55/1 V.O. Lobovikov1 APPLYING LOGIC TO PHILOSOPHICAL THEOLOGY: A FORMAL DEDUCTIVE INFERENCE OF AFFIRMING GOD’S EXISTENCE FROM ASSUMING THE A-PRIORI-NESS OF KNOWLEDGE IN THE SIGMA FORMAL AXIOMATIC THEORY For the first time a precise definition is given to the Sigma formal axiomatic theory, which is a result of logical formalization of philosophical epistemology; and an interpretation of this formal theory is offered. Also, for the first time, a formal deductive proof is constructed in Sigma for a formula, which represents (in the offered interpretation) the statement of God’s Existence under the condition that knowledge is a priori. Keywords: formal axiomatic epistemology theory; two-valued algebra of formal axiology; formal-axiological equivalence; a-priori knowledge; existence of God. 1. Introduction Since Socrates, Plato, Aristotle, Stoics, Cicero, and especially since the very beginning of Christianity philosophy, the possibility or impossibility of logical proving God’s existence has been a nontrivial problem of philosophical theology. Today the literature on this topic is immense. However, even in our days, the knot- ty problem remains unsolved as all the suggested options of solving it are contro- versial from some point of view. Some respectable researchers (let us call them “pessimists”) believed that the logical proving of God’s existence in theoretical philosophy was impossible on principle, for instance, Occam, Hume [1], and Kant [2] believed that any rational theoretic-philosophy proof of His existence was a mistake (illusion), consequently, a search for the logical proving of His existence was wasting resources and, hence, harmful; only faith in God was relevant and useful; reason was irrelevant and use- less. -
The Routledge Companion to Islamic Philosophy Reasoning in the Qurn
This article was downloaded by: 10.3.98.104 On: 25 Sep 2021 Access details: subscription number Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: 5 Howick Place, London SW1P 1WG, UK The Routledge Companion to Islamic Philosophy Richard C. Taylor, Luis Xavier López-Farjeat Reasoning in the Qurn Publication details https://www.routledgehandbooks.com/doi/10.4324/9781315708928.ch2 Rosalind Ward Gwynne Published online on: 03 Sep 2015 How to cite :- Rosalind Ward Gwynne. 03 Sep 2015, Reasoning in the Qurn from: The Routledge Companion to Islamic Philosophy Routledge Accessed on: 25 Sep 2021 https://www.routledgehandbooks.com/doi/10.4324/9781315708928.ch2 PLEASE SCROLL DOWN FOR DOCUMENT Full terms and conditions of use: https://www.routledgehandbooks.com/legal-notices/terms This Document PDF may be used for research, teaching and private study purposes. Any substantial or systematic reproductions, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 2 REASONING- IN THE QURʾAN Rosalind Ward Gwynne Introduction Muslims consider the Qurʾa-n to be the revealed speech of God—sublime, inimitable and containing information that only God knows. It has been analyzed in every pos- sible way—theologically, linguistically, legally, metaphorically—and some of these analyses have presented their results as the conclusions of reasoning in the Qurʾa-n itself, whether explicit or implicit. -
Logical Inference and Its Dynamics
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by PhilPapers Logical Inference and Its Dynamics Carlotta Pavese 1 Duke University Philosophy Department Abstract This essay advances and develops a dynamic conception of inference rules and uses it to reexamine a long-standing problem about logical inference raised by Lewis Carroll's regress. Keywords: Inference, inference rules, dynamic semantics. 1 Introduction Inferences are linguistic acts with a certain dynamics. In the process of making an inference, we add premises incrementally, and revise contextual assump- tions, often even just provisionally, to make them compatible with the premises. Making an inference is, in this sense, moving from one set of assumptions to another. The goal of an inference is to reach a set of assumptions that supports the conclusion of the inference. This essay argues from such a dynamic conception of inference to a dynamic conception of inference rules (section x2). According to such a dynamic con- ception, inference rules are special sorts of dynamic semantic values. Section x3 develops this general idea into a detailed proposal and section x4 defends it against an outstanding objection. Some of the virtues of the dynamic con- ception of inference rules developed here are then illustrated by showing how it helps us re-think a long-standing puzzle about logical inference, raised by Lewis Carroll [3]'s regress (section x5). 2 From The Dynamics of Inference to A Dynamic Conception of Inference Rules Following a long tradition in philosophy, I will take inferences to be linguistic acts. 2 Inferences are acts in that they are conscious, at person-level, and 1 I'd like to thank Guillermo Del Pinal, Simon Goldstein, Diego Marconi, Ram Neta, Jim Pryor, Alex Rosenberg, Daniel Rothschild, David Sanford, Philippe Schlenker, Walter Sinnott-Armstrong, Seth Yalcin, Jack Woods, and three anonymous referees for helpful suggestions on earlier drafts. -
The Epistemology of Testimony
Pergamon Stud. His. Phil. Sci., Vol. 29, No. 1, pp. 1-31, 1998 0 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0039-3681/98 $19.004-0.00 The Epistemology of Testimony Peter Lipton * 1. Introduction Is there anything you know entirely off your own bat? Your knowledge depends pervasively on the word of others. Knowledge of events before you were born or outside your immediate neighborhood are the obvious cases, but your epistemic dependence on testimony goes far deeper that this. Mundane beliefs-such as that the earth is round or that you think with your brain-almost invariably depend on testimony, and even quite personal facts-such as your birthday or the identity of your biological parents--can only be known with the help of others. Science is no refuge from the ubiquity of testimony. At least most of the theories that a scientist accepts, she accepts because of what others say. The same goes for almost all the data, since she didn’t perform those experiments herself. Even in those experiments she did perform, she relied on testimony hand over fist: just think of all those labels on the chemicals. Even her personal observations may have depended on testimony, if observation is theory-laden, since those theories with which it is laden were themselves accepted on testimony. Even if observation were not theory-laden, the testimony-ladenness of knowledge should be beyond dispute. We live in a sea of assertions and little if any of our knowledge would exist without it. If the role of testimony in knowledge is so vast, why is its role in the history of epistemology so slight? Why doesn’t the philosophical canon sparkle with titles such as Meditations on Testimony, A Treatise Concerning Human Testimony, and Language, Truth and Testimony? The answer is unclear. -
Truth, Existence, and the Best Explanation Formulate an Inductive, Argujnent for Scientific Realism on the Basis of Empirical Facts
Anthony A. Derksen ism has already been successfully defended.] HarrB's essential and almost disrespectful insight is to have tried to Truth, existence, and the best explanation formulate an inductive, argujnent for scientific realism on the basis of empirical facts. My conclusion was that we do need these empirical facts, and we do need an induqtive argument, but not the direct one HarrB relied on, but the inverse one !based on epistemic relevance of the Normal Thing Peter Lipton and the Rare Event. As long as this style of arguing is used in every-day life, science and philosophy I do not feel too worried that I have not pres- ented a defence of this style of arguing in this paper. 1 Introduction References When Oxford offered me a place to read for the B.Phil. in Philosophy some twenty years ago, the decision to accept seemed obvious. It was only Harre, R. (1961). Thebrie~,and Things. London/New York: Sheed and some time after arrival that I realised what a chance I had taken. Unlike Ward. the other universities to which I had applied, instruction at Oxford is based Had, R. (1970). ~h;Principles of Scientific Thinking. London: almost exclusively on individual supervisions. The tutorial system has Macmillan. obvious advantages, but it is also risky. Unlucky students with supervisors Harr6, R. (1985). 'Theories Families, Plausibility, and the Defense of who were uninterested, uncooperative, or just uninspiring faced fortnight- Modest realism'. In: N. Rescher (ed.), Reason and Rationality in Natu- long stints of solitary work, punctuated by unremunerative tutorials. Many ral Science. -
Passmore, J. (1967). Logical Positivism. in P. Edwards (Ed.). the Encyclopedia of Philosophy (Vol. 5, 52- 57). New York: Macmillan
Passmore, J. (1967). Logical Positivism. In P. Edwards (Ed.). The Encyclopedia of Philosophy (Vol. 5, 52- 57). New York: Macmillan. LOGICAL POSITIVISM is the name given in 1931 by A. E. Blumberg and Herbert Feigl to a set of philosophical ideas put forward by the Vienna circle. Synonymous expressions include "consistent empiricism," "logical empiricism," "scientific empiricism," and "logical neo-positivism." The name logical positivism is often, but misleadingly, used more broadly to include the "analytical" or "ordinary language philosophies developed at Cambridge and Oxford. HISTORICAL BACKGROUND The logical positivists thought of themselves as continuing a nineteenth-century Viennese empirical tradition, closely linked with British empiricism and culminating in the antimetaphysical, scientifically oriented teaching of Ernst Mach. In 1907 the mathematician Hans Hahn, the economist Otto Neurath, and the physicist Philipp Frank, all of whom were later to be prominent members of the Vienna circle, came together as an informal group to discuss the philosophy of science. They hoped to give an account of science which would do justice -as, they thought, Mach did not- to the central importance of mathematics, logic, and theoretical physics, without abandoning Mach's general doctrine that science is, fundamentally, the description of experience. As a solution to their problems, they looked to the "new positivism" of Poincare; in attempting to reconcile Mach and Poincare; they anticipated the main themes of logical positivism. In 1922, at the instigation of members of the "Vienna group," Moritz Schlick was invited to Vienna as professor, like Mach before him (1895-1901), in the philosophy of the inductive sciences. Schlick had been trained as a scientist under Max Planck and had won a name for himself as an interpreter of Einstein's theory of relativity. -
What Is Inference? Penalty
WHAT IS INFERENCE? OR THE FORCE OF REASONING by Ulf Hlobil Dipl.-Psych., University of Trier, 2008 Magister Artium in Philosophy, University of Trier, 2009 M.A. in Philosophy, University of Pittsburgh, 2012 Submitted to the Graduate Faculty of the Kenneth P. Dietrich School of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2016 UNIVERSITY OF PITTSBURGH KENNETH P. DIETRICH SCHOOL OF ARTS AND SCIENCES This dissertation was presented by Ulf Hlobil It was defended on May 31, 2016 and approved by Robert Brandom, Distinguished Professor of Philosophy John McDowell, Distinguished University Professor of Philosophy Kieran Setiya, Professor of Philosophy James Shaw, Associate Professor of Philosophy Dissertation Director: Robert Brandom, Distinguished Professor of Philosophy ii Copyright © by Ulf Hlobil 2016 iii WHAT IS INFERENCE? OR THE FORCE OF REASONING Ulf Hlobil, PhD University of Pittsburgh, 2016 What are we doing when we make inferences? I argue that to make an inference is to attach inferential force to an argument. Inferential force must be understood in analogy to assertoric force, and an argument is a structure of contents. I call this the “Force Account of inference.” I develop this account by first establishing two criteria of adequacy for accounts of inference. First, such accounts must explain why it is absurd to make an inference one believes to be bad. The upshot is that if someone makes an inference, she must take her inference to be good. Second, accounts of inference must explain why we cannot take our inferences to be good—in the sense that matters for inference—by merely accepting testimony to the effect that they are good. -
The “Positive Argument” for Constructive Empiricism and Inference to the Best Explanation Moti Mizrahi Florida Institute Of
The “Positive Argument” for Constructive Empiricism and Inference to the Best Explanation Moti Mizrahi Florida Institute of Technology [email protected] Abstract: In this paper, I argue that the “positive argument” for Constructive Empiricism (CE), according to which CE “makes better sense of science, and of scientific activity, than realism does” (van Fraassen 1980, 73), is an Inference to the Best Explanation (IBE). But constructive empiricists are critical of IBE, and thus they have to be critical of their own “positive argument” for CE. If my argument is sound, then constructive empiricists are in the awkward position of having to reject their own “positive argument” for CE by their own lights. Keywords: Constructive Empiricism; Inference to the Best Explanation; Positive Argument; Scientific Realism According to Bas van Fraassen (1980, 73), the “positive argument” for Constructive Empiricism (CE), is that “it makes better sense of science, and of scientific activity, than realism does and does so without inflationary metaphysics.” Although van Fraassen would not characterize it as such, this “positive argument” for CE looks like an Inference to the Best Explanation (IBE), for in IBE, “a hypothesis is accepted on the basis of a judgment that it best explains the available evidence” (Psillos 2007, 442). And a “good explanation makes sense out of that which it is intended to explain” (Sinnott-Armstrong and Fogelin 2015, 198; emphasis added). In van Fraassen’s “positive argument,” CE is said to be supported by the premise that it “makes better 1 sense of,” or provides a better explanation for, scientific activity than Scientific Realism (SR) does. -
Scholasticism, the Medieval Synthesis CVSP 202 General Lecture Monday, March 23, 2015 Encountering Aristotle in the Middle-Ages Hani Hassan [email protected]
Scholasticism, The Medieval Synthesis CVSP 202 General Lecture Monday, March 23, 2015 Encountering Aristotle in the middle-ages Hani Hassan [email protected] PART I – SCHOLASTIC PHILOSOPHY SCHOLASTIC: “from Middle French scholastique, from Latin scholasticus "learned," from Greek skholastikos "studious, learned"” 1 Came to be associated with the ‘teachers’ and churchmen in European Universities whose work was generally rooted in Aristotle and the Church Fathers. A. Re-discovering Aristotle & Co – c. 12th Century The Toledo school: translating Arabic & Hebrew philosophy and science as well as Arabic & Hebrew translations of Aristotle and commentaries on Aristotle (notably works of Ibn Rushd and Maimonides) Faith and Reason united From Toledo, through Provence, to… th by German painter Ludwig Seitz Palermo, Sicily – 13 Century – Under the rule of Roger of Sicily (Norman (1844–1908) ruler) th William of Moerbeke (Dutch cleric): greatest translator of the 13 century, and (possibly) ‘colleague’ of Thomas Aquinas. B. Greek Philosophy in the Christian monotheistic world: Boethius to scholasticism Boethius: (c. 475 – c. 526) philosopher, poet, politician – best known for his work Consolation of Philosophy, written as a dialogue between Boethius and 'Lady Philosophy', addressing issues ranging from the nature and essence of God, to evil, and ethics; translated Aristotle’s works on logic into Latin, and wrote commentaries on said works. John Scotus Eriugena (c. 815 – c. 877) Irish philosopher of the early monastic period; translated into Latin the works of pseudo-Dionysius, developed a Christian Neoplatonic world view. Anselm (c. 1033 – 1109) Archbishop of Canterbury from 1093 to 1109; best known for his “ontological argument” for the existence of God in chapter two of the Proslogion (translated into English: Discourse on the Existence of God); referred to by many as one of the founders of scholasticism. -
Wittgenstein Vs. Frege and Russell
teorema Vol. XL/2, 2021, pp. 45-61 ISNN 0210-1602 [BIBLID 0210-1602 (2021) 40:2; pp. 45-61] Are Rules of Inference Superfluous? Wittgenstein vs. Frege and Russell Gilad Nir RESUMEN En el Tractatus 5.132 Wittgenstein argumenta que la justificación inferencial depen- de solo de la comprensión de las premisas y la conclusión y no está mediada por ningún otro acto adicional. Tomando lo anterior como base, Wittgenstein defiende que las reglas de inferencia de Frege y Russell “carecen de sentido” y son “superfluas”. Esta línea de argumento es problemática, puesto que no está claro que pueda haber una explicación viable de la inferencia de acuerdo con la cual no haya tal mediación. Muestro que el re- chazo por parte de Wittgenstein de las reglas de inferencia puede estar motivado si se tie- ne en cuenta su interpretación holista de la relación entre inferencia y comprensión. PALABRAS CLAVE: Wittgenstein, Frege, Russell, inferencia, holismo. ABSTRACT In Tractatus 5.132 Wittgenstein argues that inferential justification depends solely on the understanding of the premises and conclusion, and is not mediated by any further act. On this basis he argues that Frege’s and Russell’s rules of inference are “senseless” and “superfluous”. This line of argument is puzzling, since it is unclear that there could be any viable account of inference according to which no such mediation takes place. I show that Wittgenstein’s rejection of rules of inference can be motivated by taking ac- count of his holistic construal of the relation between inference and understanding. KEYWORDS: Wittgenstein, Frege, Russell, Inference, Holism.