# Predicate logic. Miguel Palomino Dpto. Sistemas Informáticos y Computación (UCM) Madrid Spain

Size: px
Start display at page:

Download "Predicate logic. Miguel Palomino Dpto. Sistemas Informáticos y Computación (UCM) Madrid Spain"

## Transcription

1 Predicate logic Miguel Palomino Dpto. Sistemas Informáticos y Computación (UCM) Madrid Spain Synonyms. First-order logic. Question 1. Describe this discipline/sub-discipline, and some of its more recent developments. Predicate logic is a sub-discipline of logic that had its roots in the last quarter of the nineteenth century, though it had to wait until the second decade of the twentieth century for a solid foundation. Like any other logic, it is concerned with the validity of arguments, though not of any kind: its interest lies in reasoning about what is universally true. As such, predicate logic is especially suited to reason about mathematical statements and can be considered a generalization of Aristotelian syllogisms. Predicate logic goes beyond syllogisms by introducing predicates with arbitrary numbers of arguments, and quantifiers that allow to refer either to all or to some of the elements in the universe that is under consideration. It has a proof theory, which consists of a set of rules that describe how to mechanically derive sentences from a given set of premises (and such derivations are called proofs ), as well as a model theory that assigns meaning to the sentences with respect to structures so that a given sentence is either true or false in a given structure. Predicate logic is sound, meaning that every sentence that can be derived using the rules in its proof theory holds in every possible structure. More importantly, a fundamental result by Gödel in 1929 shows that predicate logic is also complete in the sense that if a sentence is true in every structure then it can be derived from the empty set of premises. Question 2 (a) To what extent does this discipline/sub-discipline self-identify as a science? How so? In what way, or why not at all? Logic, and in particular predicate logic, is a formal science. As opposed to natural sciences, knowledge in predicate logic is not obtained through observations and empirical study but from the analysis and processing of certain symbols and rules. It is also formal in the sense that it provides a framework in which reasoning can take place, the form of the argumentation being the only element that determines whether it is valid or not (disregarding any purported meaning). 1

2 (b) To what extent does this discipline/sub-discipline self-identify as a religion? How so? In what way, or why not at all? This discipline does not identify itself as a religion. It lacks a liturgy, rites, divine entities, a moral, or any of the elements pertaining to a religion. Question 3. What makes this discipline/sub-discipline distinctive among the other disciplines/sub-disciplines? Predicate logic, with its focus on universally true statements, has proved to be sufficient in principle to formalize and reason about the main bulk of mathematics. In addition, predicate logic satisfies many good properties (such as completeness), that not all variants of logic posses, and it has been shown in a precise manner that a logic more expressive than predicate logic must give up some of these properties in exchange of its additional power. However, different disciplines (like computer science) require other kinds of reasoning, such as probabilistic, subjunctive, temporal, or fuzzy, to name a few. Dealing with that kind of arguments in predicate logic is convoluted at best, while other branches of logic are more appropriate and should be used instead: probabilistic logic, temporal logic, fuzzy logic,.... Question 4. To what extent does this discipline/sub-discipline see itself as relevant to, interested in the scholarly area called Science and Religion? If interested, in what way? If not interested, why not? Predicate logic is not interested in the area Science and Religion. It is relevant to it, though, in the same broad sense that logic in general is: it is a useful tool which provides a universal language with which to reason about any subject matter. Question 5. What are the sources of authority for this discipline/subdiscipline? What makes these sources authoritative? The sources of authority in predicate logic are the peer-reviewed papers published in journals and conferences, where new results are proved in a rigorous mathematical manner. Among the many prominent logicians, Kurt Gödel ( ) and Alfred Tarski ( ) can be singled out as two of the most influential and important of all time: neither created this sub-discipline, but they both changed it profoundly and set forth research in new and unexpected directions. Question 6. What are the ethical principles that guide this discipline/subdiscipline? Since predicate logic has no direct effect and is not affected by the physical world, ethical or moral considerations have no especial application here. Being honest, as in any scientific discipline, would be the main guiding principle. 2

3 Question 7. What are the key values of this discipline/sub-discipline? Providing an abstract framework in which to reason in a precise manner about any subject and, especially, about mathematics, for which it offers a way of attacking many interesting problems. It is a potent tool to avoid ambiguities when posing an argument as well as when solving it. Question 8. How does this discipline/sub-discipline define/conceptualize the following? Nature / world The empirical world is of no concern to predicate logic due to its formal character. Thus, there is no explicit treatment of these terms within this sub-discipline. Human being Again, this concept is not part of the field of study of predicate logic and thus the human being is not defined within this sub-discipline. Life (and origins of) / death By the same reason, questions about life and death do not apply to this subdiscipline. Reality As a formal science predicate logic is not directly concerned with reality. At most, it can be said that predicate logic s principles of inference are not arbitrary but inspired on what happens in reality, as in the case of the principle of identity (A is A) or non-contradiction (it cannot be the case that both A and not A). Knowledge Reasoning about knowledge is more suited for other sub-disciplines of logic such as modal logic. Though not concerned with knowledge, the renowned Gödel s (first) incompleteness theorem has been widely put to philosophical uses with regard the limitations of what can be known. Roughly, this theorem states that given a set of axioms for a sufficiently strong (mathematical) system, there is always a sentence such that neither it nor its negation can be derived from the axioms using the proof theory; this implies that there are truths in the system for which no proof can be found. Truth Truth as an absolute notion was abandoned by logicians during the first thirty years of the twentieth century. A predicate logic sentence on its own is, in general, neither true nor false, but requires a context, a given structure with respect to which it does have a truth value. Moreover, the completeness of predicate logic allows to deal with this semantic notion in a mechanical way: logically valid sentences, those which are true with respect to every structure, are exactly those that can be derived by means of the rules in the proof theory. (Different logics may use different classes of structures, so that logically valid sentences may vary from 3

4 one to another.) Note that this is in sharp contrast with truth in concrete mathematical systems where, by the incompleteness theorem, there are true sentences which are not provable. Perception Predicate logic is not concerned with perception since it does not have to deal with sensorial experiences. Time Time is not treated explicitly within this sub-discipline. Even though time could be formalized so as to reason about facts that take it into account, there are many variants of temporal logic more suited for this purpose. Consciousness Consciousness is not treated within this sub-discipline. Rationality / reason Predicate logic does not define what reason is nor treats it. However, as a formal science it is driven by rationality alone, with complete disregard of the physical world. Mystery Mystery has no place in this sub-discipline. On the contrary, predicate logic has played an enlightening role in the clarification of the nature of many semantic paradoxes in the natural language through their rephrasing as logical sentences. What (additional) issues/themes/concepts are especially relevant for this discipline/sub-discipline as regards Science and Religion engagement? In what way are these issues/themes/concepts critical? A critical issue, already sketched in the answers to the previous questions, is the notion of proof and the distinction between true and provable sentences. In particular, the results by Gödel and Tarski show that the notion of provability in a given system is definable within the system itself (assuming minimum requirements about its expressive power), whereas the corresponding notion of truth can only be defined in another system that adequately extends the original. Glossary - Axiom. An axiom is simply a sentence in the logic which, in combination with others, is used as a premise to derive new sentences. Intuitively, it expresses an evident proposition about some concrete system that is taken for granted when reasoning about it. - Empirical study. Study based on experience and the observation of natural phenomena. 4

5 - Expressive. A logic L is said to be at least as expressive as another logic L if, for every sentence in L, there exists a sentence in L such that the structures that make the first sentence true are exactly the same as the structures that make the second true. - Structure. A structure in predicate logic is a model in which to interpret sentences. It consists of a universe of elements, together with operations over these elements associated to the symbols in the language. - Syllogism. A logical argument which reaches a conclusion from two given premises of a certain form. Syllogisms were classified by Aristotle, who identified those that correspond to valid inferences. References D. van Dalen. Logic and Structure. Fourth Edition. Springer, H.-D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical Logic. Second Edition. Springer, H. B. Enderton. A Mathematical Introduction to Logic, Second Edition. Academic Press D. M. Gabbay and F. Guenthner, editors. Handbook of Philosophical Logic. 2nd edition. Springer. In eighteen volumes, the first published in K. Gödel. Collected Works. Oxford University Press. In five volumes, the first published in S. G. Simpson. Logic and Mathematics. In S. Rosen (ed.) The Examined Life: Readings from Western Philosophers from Plato to Kant. Random House Reference, A. Tarski. Logic, Semantics, Metamathematics, papers from 1923 to Hackett Publishing Company,

### The Ontological Argument for the existence of God. Pedro M. Guimarães Ferreira S.J. PUC-Rio Boston College, July 13th. 2011

The Ontological Argument for the existence of God Pedro M. Guimarães Ferreira S.J. PUC-Rio Boston College, July 13th. 2011 The ontological argument (henceforth, O.A.) for the existence of God has a long

### Constructive Logic, Truth and Warranted Assertibility

Constructive Logic, Truth and Warranted Assertibility Greg Restall Department of Philosophy Macquarie University Version of May 20, 2000....................................................................

### Haberdashers Aske s Boys School

1 Haberdashers Aske s Boys School Occasional Papers Series in the Humanities Occasional Paper Number Sixteen Are All Humans Persons? Ashna Ahmad Haberdashers Aske s Girls School March 2018 2 Haberdashers

### prohibition, moral commitment and other normative matters. Although often described as a branch

Logic, deontic. The study of principles of reasoning pertaining to obligation, permission, prohibition, moral commitment and other normative matters. Although often described as a branch of logic, deontic

### Semantic Foundations for Deductive Methods

Semantic Foundations for Deductive Methods delineating the scope of deductive reason Roger Bishop Jones Abstract. The scope of deductive reason is considered. First a connection is discussed between the

### Beyond Symbolic Logic

Beyond Symbolic Logic 1. The Problem of Incompleteness: Many believe that mathematics can explain *everything*. Gottlob Frege proposed that ALL truths can be captured in terms of mathematical entities;

### Can Gödel s Incompleteness Theorem be a Ground for Dialetheism? *

논리연구 20-2(2017) pp. 241-271 Can Gödel s Incompleteness Theorem be a Ground for Dialetheism? * 1) Seungrak Choi Abstract Dialetheism is the view that there exists a true contradiction. This paper ventures

### Etchemendy, Tarski, and Logical Consequence 1 Jared Bates, University of Missouri Southwest Philosophy Review 15 (1999):

Etchemendy, Tarski, and Logical Consequence 1 Jared Bates, University of Missouri Southwest Philosophy Review 15 (1999): 47 54. Abstract: John Etchemendy (1990) has argued that Tarski's definition of logical

### Intuitive evidence and formal evidence in proof-formation

Intuitive evidence and formal evidence in proof-formation Okada Mitsuhiro Section I. Introduction. I would like to discuss proof formation 1 as a general methodology of sciences and philosophy, with a

### UC Berkeley, Philosophy 142, Spring 2016

Logical Consequence UC Berkeley, Philosophy 142, Spring 2016 John MacFarlane 1 Intuitive characterizations of consequence Modal: It is necessary (or apriori) that, if the premises are true, the conclusion

### Informalizing Formal Logic

Informalizing Formal Logic Antonis Kakas Department of Computer Science, University of Cyprus, Cyprus antonis@ucy.ac.cy Abstract. This paper discusses how the basic notions of formal logic can be expressed

### Broad on Theological Arguments. I. The Ontological Argument

Broad on God Broad on Theological Arguments I. The Ontological Argument Sample Ontological Argument: Suppose that God is the most perfect or most excellent being. Consider two things: (1)An entity that

### Validity of Inferences *

1 Validity of Inferences * When the systematic study of inferences began with Aristotle, there was in Greek culture already a flourishing argumentative practice with the purpose of supporting or grounding

### Remarks on a Foundationalist Theory of Truth. Anil Gupta University of Pittsburgh

For Philosophy and Phenomenological Research Remarks on a Foundationalist Theory of Truth Anil Gupta University of Pittsburgh I Tim Maudlin s Truth and Paradox offers a theory of truth that arises from

### All things are possible Case study in the meaninglessness of all views By Colin leslie dean

All things are possible Case study in the meaninglessness of all views By Colin leslie dean All things are possible Case study in the meaninglessness of all views By Colin leslie dean 2 List of free Erotic

### What is the Nature of Logic? Judy Pelham Philosophy, York University, Canada July 16, 2013 Pan-Hellenic Logic Symposium Athens, Greece

What is the Nature of Logic? Judy Pelham Philosophy, York University, Canada July 16, 2013 Pan-Hellenic Logic Symposium Athens, Greece Outline of this Talk 1. What is the nature of logic? Some history

### Richard L. W. Clarke, Notes REASONING

1 REASONING Reasoning is, broadly speaking, the cognitive process of establishing reasons to justify beliefs, conclusions, actions or feelings. It also refers, more specifically, to the act or process

### Review of "The Tarskian Turn: Deflationism and Axiomatic Truth"

Essays in Philosophy Volume 13 Issue 2 Aesthetics and the Senses Article 19 August 2012 Review of "The Tarskian Turn: Deflationism and Axiomatic Truth" Matthew McKeon Michigan State University Follow this

### A Judgmental Formulation of Modal Logic

A Judgmental Formulation of Modal Logic Sungwoo Park Pohang University of Science and Technology South Korea Estonian Theory Days Jan 30, 2009 Outline Study of logic Model theory vs Proof theory Classical

### Ethical Consistency and the Logic of Ought

Ethical Consistency and the Logic of Ought Mathieu Beirlaen Ghent University In Ethical Consistency, Bernard Williams vindicated the possibility of moral conflicts; he proposed to consistently allow for

### Artificial Intelligence: Valid Arguments and Proof Systems. Prof. Deepak Khemani. Department of Computer Science and Engineering

Artificial Intelligence: Valid Arguments and Proof Systems Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Module 02 Lecture - 03 So in the last

### A Model of Decidable Introspective Reasoning with Quantifying-In

A Model of Decidable Introspective Reasoning with Quantifying-In Gerhard Lakemeyer* Institut fur Informatik III Universitat Bonn Romerstr. 164 W-5300 Bonn 1, Germany e-mail: gerhard@uran.informatik.uni-bonn,de

### How Do We Know Anything about Mathematics? - A Defence of Platonism

How Do We Know Anything about Mathematics? - A Defence of Platonism Majda Trobok University of Rijeka original scientific paper UDK: 141.131 1:51 510.21 ABSTRACT In this paper I will try to say something

### On the hard problem of consciousness: Why is physics not enough?

On the hard problem of consciousness: Why is physics not enough? Hrvoje Nikolić Theoretical Physics Division, Rudjer Bošković Institute, P.O.B. 180, HR-10002 Zagreb, Croatia e-mail: hnikolic@irb.hr Abstract

### Aquinas' Third Way Modalized

Philosophy of Religion Aquinas' Third Way Modalized Robert E. Maydole Davidson College bomaydole@davidson.edu ABSTRACT: The Third Way is the most interesting and insightful of Aquinas' five arguments for

### On the epistemological status of mathematical objects in Plato s philosophical system

On the epistemological status of mathematical objects in Plato s philosophical system Floris T. van Vugt University College Utrecht University, The Netherlands October 22, 2003 Abstract The main question

### Supplementary Section 6S.7

Supplementary Section 6S.7 The Propositions of Propositional Logic The central concern in Introduction to Formal Logic with Philosophical Applications is logical consequence: What follows from what? Relatedly,

### Oxford Scholarship Online Abstracts and Keywords

Oxford Scholarship Online Abstracts and Keywords ISBN 9780198802693 Title The Value of Rationality Author(s) Ralph Wedgwood Book abstract Book keywords Rationality is a central concept for epistemology,

### Understanding Truth Scott Soames Précis Philosophy and Phenomenological Research Volume LXV, No. 2, 2002

1 Symposium on Understanding Truth By Scott Soames Précis Philosophy and Phenomenological Research Volume LXV, No. 2, 2002 2 Precis of Understanding Truth Scott Soames Understanding Truth aims to illuminate

### TRUTH IN MATHEMATICS. H.G. Dales and G. Oliveri (eds.) (Clarendon: Oxford. 1998, pp. xv, 376, ISBN X) Reviewed by Mark Colyvan

TRUTH IN MATHEMATICS H.G. Dales and G. Oliveri (eds.) (Clarendon: Oxford. 1998, pp. xv, 376, ISBN 0-19-851476-X) Reviewed by Mark Colyvan The question of truth in mathematics has puzzled mathematicians

### Class #14: October 13 Gödel s Platonism

Philosophy 405: Knowledge, Truth and Mathematics Fall 2010 Hamilton College Russell Marcus Class #14: October 13 Gödel s Platonism I. The Continuum Hypothesis and Its Independence The continuum problem

### Overview of Today s Lecture

Branden Fitelson Philosophy 12A Notes 1 Overview of Today s Lecture Music: Robin Trower, Daydream (King Biscuit Flower Hour concert, 1977) Administrative Stuff (lots of it) Course Website/Syllabus [i.e.,

### PHILOSOPHY OF LOGIC AND LANGUAGE OVERVIEW LOGICAL CONSTANTS WEEK 5: MODEL-THEORETIC CONSEQUENCE JONNY MCINTOSH

PHILOSOPHY OF LOGIC AND LANGUAGE WEEK 5: MODEL-THEORETIC CONSEQUENCE JONNY MCINTOSH OVERVIEW Last week, I discussed various strands of thought about the concept of LOGICAL CONSEQUENCE, introducing Tarski's

### Other Logics: What Nonclassical Reasoning Is All About Dr. Michael A. Covington Associate Director Artificial Intelligence Center

Covington, Other Logics 1 Other Logics: What Nonclassical Reasoning Is All About Dr. Michael A. Covington Associate Director Artificial Intelligence Center Covington, Other Logics 2 Contents Classical

### AKC Lecture 1 Plato, Penrose, Popper

AKC Lecture 1 Plato, Penrose, Popper E. Brian Davies King s College London November 2011 E.B. Davies (KCL) AKC 1 November 2011 1 / 26 Introduction The problem with philosophical and religious questions

### DEPARTMENT OF PHILOSOPHY FALL 2014 COURSE DESCRIPTIONS

DEPARTMENT OF PHILOSOPHY FALL 2014 COURSE DESCRIPTIONS PHIL 2300-001 Beginning Philosophy 11:00-11:50 MWF ENG/PHIL 264 PHIL 2300-002 Beginning Philosophy 9:00-9:50 MWF ENG/PHIL 264 This is a general introduction

### KANT, MORAL DUTY AND THE DEMANDS OF PURE PRACTICAL REASON. The law is reason unaffected by desire.

KANT, MORAL DUTY AND THE DEMANDS OF PURE PRACTICAL REASON The law is reason unaffected by desire. Aristotle, Politics Book III (1287a32) THE BIG IDEAS TO MASTER Kantian formalism Kantian constructivism

### Intersubstitutivity Principles and the Generalization Function of Truth. Anil Gupta University of Pittsburgh. Shawn Standefer University of Melbourne

Intersubstitutivity Principles and the Generalization Function of Truth Anil Gupta University of Pittsburgh Shawn Standefer University of Melbourne Abstract We offer a defense of one aspect of Paul Horwich

### Argumentative Analogy versus Figurative Analogy

Argumentative Analogy versus Figurative Analogy By Timo Schmitz, Philosopher As argumentative analogy or simply analogism (ἀναλογισµός), one calls the comparison through inductive reasoning of at least

### Negative Introspection Is Mysterious

Negative Introspection Is Mysterious Abstract. The paper provides a short argument that negative introspection cannot be algorithmic. This result with respect to a principle of belief fits to what we know

### How Gödelian Ontological Arguments Fail

How Gödelian Ontological Arguments Fail Matthew W. Parker Abstract. Ontological arguments like those of Gödel (1995) and Pruss (2009; 2012) rely on premises that initially seem plausible, but on closer

### Philosophy of Logic and Artificial Intelligence

Philosophy of Logic and Artificial Intelligence Basic Studies in Natural Science 3 rd Semester, Fall 2008 Christos Karavasileiadis Stephan O'Bryan Group 6 / House 13.2 Supervisor: Torben Braüner Content

### Appeared in: Al-Mukhatabat. A Trilingual Journal For Logic, Epistemology and Analytical Philosophy, Issue 6: April 2013.

Appeared in: Al-Mukhatabat. A Trilingual Journal For Logic, Epistemology and Analytical Philosophy, Issue 6: April 2013. Panu Raatikainen Intuitionistic Logic and Its Philosophy Formally, intuitionistic

### The Philosophy of Logic

The Philosophy of Logic PHL 430-001 Spring 2003 MW: 10:20-11:40 EBH, Rm. 114 Instructor Information Matthew McKeon Office: 503 South Kedzie/Rm. 507 Office hours: Friday--10:30-1:00, and by appt. Telephone:

### Situations in Which Disjunctive Syllogism Can Lead from True Premises to a False Conclusion

398 Notre Dame Journal of Formal Logic Volume 38, Number 3, Summer 1997 Situations in Which Disjunctive Syllogism Can Lead from True Premises to a False Conclusion S. V. BHAVE Abstract Disjunctive Syllogism,

### Pictures, Proofs, and Mathematical Practice : Reply to James Robert Brown

Brit. J. Phil. Sci. 50 (1999), 425 429 DISCUSSION Pictures, Proofs, and Mathematical Practice : Reply to James Robert Brown In a recent article, James Robert Brown ([1997]) has argued that pictures and

### On the Aristotelian Square of Opposition

On the Aristotelian Square of Opposition Dag Westerståhl Göteborg University Abstract A common misunderstanding is that there is something logically amiss with the classical square of opposition, and that

### Lecture 9. A summary of scientific methods Realism and Anti-realism

Lecture 9 A summary of scientific methods Realism and Anti-realism A summary of scientific methods and attitudes What is a scientific approach? This question can be answered in a lot of different ways.

### Aspects of Western Philosophy Dr. Sreekumar Nellickappilly Department of Humanities and Social Sciences Indian Institute of Technology, Madras

Aspects of Western Philosophy Dr. Sreekumar Nellickappilly Department of Humanities and Social Sciences Indian Institute of Technology, Madras Module - 21 Lecture - 21 Kant Forms of sensibility Categories

### On Tarski On Models. Timothy Bays

On Tarski On Models Timothy Bays Abstract This paper concerns Tarski s use of the term model in his 1936 paper On the Concept of Logical Consequence. Against several of Tarski s recent defenders, I argue

### III Knowledge is true belief based on argument. Plato, Theaetetus, 201 c-d Is Justified True Belief Knowledge? Edmund Gettier

III Knowledge is true belief based on argument. Plato, Theaetetus, 201 c-d Is Justified True Belief Knowledge? Edmund Gettier In Theaetetus Plato introduced the definition of knowledge which is often translated

### Logic and Pragmatics: linear logic for inferential practice

Logic and Pragmatics: linear logic for inferential practice Daniele Porello danieleporello@gmail.com Institute for Logic, Language & Computation (ILLC) University of Amsterdam, Plantage Muidergracht 24

### Remarks on the philosophy of mathematics (1969) Paul Bernays

Bernays Project: Text No. 26 Remarks on the philosophy of mathematics (1969) Paul Bernays (Bemerkungen zur Philosophie der Mathematik) Translation by: Dirk Schlimm Comments: With corrections by Charles

### SAVING RELATIVISM FROM ITS SAVIOUR

CRÍTICA, Revista Hispanoamericana de Filosofía Vol. XXXI, No. 91 (abril 1999): 91 103 SAVING RELATIVISM FROM ITS SAVIOUR MAX KÖLBEL Doctoral Programme in Cognitive Science Universität Hamburg In his paper

### Logic: Deductive and Inductive by Carveth Read M.A. CHAPTER VI CONDITIONS OF IMMEDIATE INFERENCE

CHAPTER VI CONDITIONS OF IMMEDIATE INFERENCE Section 1. The word Inference is used in two different senses, which are often confused but should be carefully distinguished. In the first sense, it means

### Vol 2 Bk 7 Outline p 486 BOOK VII. Substance, Essence and Definition CONTENTS. Book VII

Vol 2 Bk 7 Outline p 486 BOOK VII Substance, Essence and Definition CONTENTS Book VII Lesson 1. The Primacy of Substance. Its Priority to Accidents Lesson 2. Substance as Form, as Matter, and as Body.

### On Priest on nonmonotonic and inductive logic

On Priest on nonmonotonic and inductive logic Greg Restall School of Historical and Philosophical Studies The University of Melbourne Parkville, 3010, Australia restall@unimelb.edu.au http://consequently.org/

### The British Empiricism

The British Empiricism Locke, Berkeley and Hume copyleft: nicolazuin.2018 nowxhere.wordpress.com The terrible heritage of Descartes: Skepticism, Empiricism, Rationalism The problem originates from the

### Review of Constructive Empiricism: Epistemology and the Philosophy of Science

Review of Constructive Empiricism: Epistemology and the Philosophy of Science Constructive Empiricism (CE) quickly became famous for its immunity from the most devastating criticisms that brought down

### Exercise Sets. KS Philosophical Logic: Modality, Conditionals Vagueness. Dirk Kindermann University of Graz July 2014

Exercise Sets KS Philosophical Logic: Modality, Conditionals Vagueness Dirk Kindermann University of Graz July 2014 1 Exercise Set 1 Propositional and Predicate Logic 1. Use Definition 1.1 (Handout I Propositional

### Difference between Science and Religion? A Superficial, yet Tragi-Comic Misunderstanding...

Difference between Science and Religion? A Superficial, yet Tragi-Comic Misunderstanding... Elemér E Rosinger Department of Mathematics and Applied Mathematics University of Pretoria Pretoria 0002 South

### 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

### QUESTIONING GÖDEL S ONTOLOGICAL PROOF: IS TRUTH POSITIVE?

QUESTIONING GÖDEL S ONTOLOGICAL PROOF: IS TRUTH POSITIVE? GREGOR DAMSCHEN Martin Luther University of Halle-Wittenberg Abstract. In his Ontological proof, Kurt Gödel introduces the notion of a second-order

### Leibniz, Principles, and Truth 1

Leibniz, Principles, and Truth 1 Leibniz was a man of principles. 2 Throughout his writings, one finds repeated assertions that his view is developed according to certain fundamental principles. Attempting

### CONTENTS A SYSTEM OF LOGIC

EDITOR'S INTRODUCTION NOTE ON THE TEXT. SELECTED BIBLIOGRAPHY XV xlix I /' ~, r ' o>

### Masters in Logic and Metaphysics

Masters in Logic and Metaphysics Programme Requirements The Department of Philosophy, in collaboration with the Department of Philosophy at the University of Stirling, offer the following postgraduate

### Semantic Entailment and Natural Deduction

Semantic Entailment and Natural Deduction Alice Gao Lecture 6, September 26, 2017 Entailment 1/55 Learning goals Semantic entailment Define semantic entailment. Explain subtleties of semantic entailment.

### VAGUENESS. Francis Jeffry Pelletier and István Berkeley Department of Philosophy University of Alberta Edmonton, Alberta, Canada

VAGUENESS Francis Jeffry Pelletier and István Berkeley Department of Philosophy University of Alberta Edmonton, Alberta, Canada Vagueness: an expression is vague if and only if it is possible that it give

### The Appeal to Reason. Introductory Logic pt. 1

The Appeal to Reason Introductory Logic pt. 1 Argument vs. Argumentation The difference is important as demonstrated by these famous philosophers. The Origins of Logic: (highlights) Aristotle (385-322

### Reductio ad Absurdum, Modulation, and Logical Forms. Miguel López-Astorga 1

International Journal of Philosophy and Theology June 25, Vol. 3, No., pp. 59-65 ISSN: 2333-575 (Print), 2333-5769 (Online) Copyright The Author(s). All Rights Reserved. Published by American Research

### Gödel's incompleteness theorems

Savaş Ali Tokmen Gödel's incompleteness theorems Page 1 / 5 In the twentieth century, mostly because of the different classes of infinity problem introduced by George Cantor (1845-1918), a crisis about

### LOGIC ANTHONY KAPOLKA FYF 101-9/3/2010

LOGIC ANTHONY KAPOLKA FYF 101-9/3/2010 LIBERALLY EDUCATED PEOPLE......RESPECT RIGOR NOT SO MUCH FOR ITS OWN SAKE BUT AS A WAY OF SEEKING TRUTH. LOGIC PUZZLE COOPER IS MURDERED. 3 SUSPECTS: SMITH, JONES,

### Computational Metaphysics

Computational Metaphysics John Rushby Computer Science Laboratory SRI International Menlo Park CA USA John Rushby, SR I Computational Metaphysics 1 Metaphysics The word comes from Andronicus of Rhodes,

### 5 A Modal Version of the

5 A Modal Version of the Ontological Argument E. J. L O W E Moreland, J. P.; Sweis, Khaldoun A.; Meister, Chad V., Jul 01, 2013, Debating Christian Theism The original version of the ontological argument

### Rethinking Knowledge: The Heuristic View

http://www.springer.com/gp/book/9783319532363 Carlo Cellucci Rethinking Knowledge: The Heuristic View 1 Preface From its very beginning, philosophy has been viewed as aimed at knowledge and methods to

### This is a repository copy of Does = 5? : In Defense of a Near Absurdity.

This is a repository copy of Does 2 + 3 = 5? : In Defense of a Near Absurdity. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/127022/ Version: Accepted Version Article: Leng,

### International Phenomenological Society

International Phenomenological Society The Semantic Conception of Truth: and the Foundations of Semantics Author(s): Alfred Tarski Source: Philosophy and Phenomenological Research, Vol. 4, No. 3 (Mar.,

### Against the No-Miracle Response to Indispensability Arguments

Against the No-Miracle Response to Indispensability Arguments I. Overview One of the most influential of the contemporary arguments for the existence of abstract entities is the so-called Quine-Putnam

### The Unbearable Lightness of Theory of Knowledge:

The Unbearable Lightness of Theory of Knowledge: Desert Mountain High School s Summer Reading in five easy steps! STEP ONE: Read these five pages important background about basic TOK concepts: Knowing

### In Search of the Ontological Argument. Richard Oxenberg

1 In Search of the Ontological Argument Richard Oxenberg Abstract We can attend to the logic of Anselm's ontological argument, and amuse ourselves for a few hours unraveling its convoluted word-play, or

### TWO VERSIONS OF HUME S LAW

DISCUSSION NOTE BY CAMPBELL BROWN JOURNAL OF ETHICS & SOCIAL PHILOSOPHY DISCUSSION NOTE MAY 2015 URL: WWW.JESP.ORG COPYRIGHT CAMPBELL BROWN 2015 Two Versions of Hume s Law MORAL CONCLUSIONS CANNOT VALIDLY

### PHI2391: Logical Empiricism I 8.0

1 2 3 4 5 PHI2391: Logical Empiricism I 8.0 Hume and Kant! Remember Hume s question:! Are we rationally justified in inferring causes from experimental observations?! Kant s answer: we can give a transcendental

### Al-Sijistani s and Maimonides s Double Negation Theology Explained by Constructive Logic

International Mathematical Forum, Vol. 10, 2015, no. 12, 587-593 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2015.5652 Al-Sijistani s and Maimonides s Double Negation Theology Explained

### Module 5. Knowledge Representation and Logic (Propositional Logic) Version 2 CSE IIT, Kharagpur

Module 5 Knowledge Representation and Logic (Propositional Logic) Lesson 12 Propositional Logic inference rules 5.5 Rules of Inference Here are some examples of sound rules of inference. Each can be shown

### JELIA Justification Logic. Sergei Artemov. The City University of New York

JELIA 2008 Justification Logic Sergei Artemov The City University of New York Dresden, September 29, 2008 This lecture outlook 1. What is Justification Logic? 2. Why do we need Justification Logic? 3.

### SYLLOGISTIC LOGIC CATEGORICAL PROPOSITIONS

Prof. C. Byrne Dept. of Philosophy SYLLOGISTIC LOGIC Syllogistic logic is the original form in which formal logic was developed; hence it is sometimes also referred to as Aristotelian logic after Aristotle,

### Philosophy 240: Symbolic Logic

Philosophy 240: Symbolic Logic Russell Marcus Hamilton College Fall 2011 Class 27: October 28 Truth and Liars Marcus, Symbolic Logic, Fall 2011 Slide 1 Philosophers and Truth P Sex! P Lots of technical

### On The Logical Status of Dialectic (*) -Historical Development of the Argument in Japan- Shigeo Nagai Naoki Takato

On The Logical Status of Dialectic (*) -Historical Development of the Argument in Japan- Shigeo Nagai Naoki Takato 1 The term "logic" seems to be used in two different ways. One is in its narrow sense;

### Kevin Scharp, Replacing Truth, Oxford: Oxford University Press, 2013, At 300-some pages, with narrow margins and small print, the work

Kevin Scharp, Replacing Truth, Oxford: Oxford University Press, 2013, 352pp., \$85.00, ISBN 9780199653850. At 300-some pages, with narrow margins and small print, the work under review, a spirited defense

### Selections from Aristotle s Prior Analytics 41a21 41b5

Lesson Seventeen The Conditional Syllogism Selections from Aristotle s Prior Analytics 41a21 41b5 It is clear then that the ostensive syllogisms are effected by means of the aforesaid figures; these considerations

### [3.] Bertrand Russell. 1

[3.] Bertrand Russell. 1 [3.1.] Biographical Background. 1872: born in the city of Trellech, in the county of Monmouthshire, now part of Wales 2 One of his grandfathers was Lord John Russell, who twice

### Qualitative and quantitative inference to the best theory. reply to iikka Niiniluoto Kuipers, Theodorus

University of Groningen Qualitative and quantitative inference to the best theory. reply to iikka Niiniluoto Kuipers, Theodorus Published in: EPRINTS-BOOK-TITLE IMPORTANT NOTE: You are advised to consult

### William Ockham on Universals

MP_C07.qxd 11/17/06 5:28 PM Page 71 7 William Ockham on Universals Ockham s First Theory: A Universal is a Fictum One can plausibly say that a universal is not a real thing inherent in a subject [habens

### BonJour Against Materialism. Just an intellectual bandwagon?

BonJour Against Materialism Just an intellectual bandwagon? What is physicalism/materialism? materialist (or physicalist) views: views that hold that mental states are entirely material or physical in

### THE LIAR PARADOX IS A REAL PROBLEM

THE LIAR PARADOX IS A REAL PROBLEM NIK WEAVER 1 I recently wrote a book [11] which, not to be falsely modest, I think says some important things about the foundations of logic. So I have been dismayed

### Necessity. Oxford: Oxford University Press. Pp. i-ix, 379. ISBN \$35.00.

Appeared in Linguistics and Philosophy 26 (2003), pp. 367-379. Scott Soames. 2002. Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity. Oxford: Oxford University Press. Pp. i-ix, 379.

### A Brief History of Thinking about Thinking Thomas Lombardo

A Brief History of Thinking about Thinking Thomas Lombardo "Education is nothing more nor less than learning to think." Peter Facione In this article I review the historical evolution of principles and

### A Defense of Contingent Logical Truths

Michael Nelson and Edward N. Zalta 2 A Defense of Contingent Logical Truths Michael Nelson University of California/Riverside and Edward N. Zalta Stanford University Abstract A formula is a contingent