νµθωερτψυιοπασδφγηϕκλζξχϖβνµθωερτ ψυιοπασδφγηϕκλζξχϖβνµθωερτψυιοπα σδφγηϕκλζξχϖβνµθωερτψυιοπασδφγηϕκ χϖβνµθωερτψυιοπασδφγηϕκλζξχϖβνµθ

Size: px
Start display at page:

Download "νµθωερτψυιοπασδφγηϕκλζξχϖβνµθωερτ ψυιοπασδφγηϕκλζξχϖβνµθωερτψυιοπα σδφγηϕκλζξχϖβνµθωερτψυιοπασδφγηϕκ χϖβνµθωερτψυιοπασδφγηϕκλζξχϖβνµθ"

Transcription

1 θωερτψυιοπασδφγηϕκλζξχϖβνµθωερτψ υιοπασδφγηϕκλζξχϖβνµθωερτψυιοπασδ φγηϕκλζξχϖβνµθωερτψυιοπασδφγηϕκλζ ξχϖβνµθωερτψυιοπασδφγηϕκλζξχϖβνµ Mathematics as Fiction θωερτψυιοπασδφγηϕκλζξχϖβνµθωερτψ A Common Sense Approach υιοπασδφγηϕκτψυιοπασδφγηϕκλζξχϖβν Adam Taylor µθωερτψυιοπασδφγηϕκλζξχϖβνµθωερτ ψυιοπασδφγηϕκλζξχϖβνµθωερτψυιοπα σδφγηϕκλζξχϖβνµθωερτψυιοπασδφγηϕκ λζξχϖβνµθωερτψυιοπασδφγηϕκλζξχϖβ νµθωερτψυιοπασδφγηϕκλζξχϖβνµθωερτ ψυιοπασδφγηϕκλζξχϖβνµθωερτψυιοπα σδφγηϕκλζξχϖβνµθωερτψυιοπασδφγηϕκ λζξχϖβνµρτψυιοπασδφγηϕκλζξχϖβνµθ ωερτψυιοπασδφγηϕκλζξχϖβνµθωερτψυι οπασδφγηϕκλζξχϖβνµθωερτψυιοπασδφγ ηϕκλζξχϖβνµθωερτψυιοπασδφγηϕκλζξ χϖβνµθωερτψυιοπασδφγηϕκλζξχϖβνµθ ωερτψυιοπασδφγηϕκλζξχϖβνµθωερτψυι οπασδφγηϕκλζξχϖβνµθωερτψυιοπασδφγ

2 The study of fictional discourse, while rich in enough subtle puzzles to keep the analytic philosopher busy for a lifetime, might be looked at as a field of study that contains problems only for these philosophers. The problem lies in taking the truth value of a proposition based on whether or not it refers to a true state of affairs in the world; John went to the store comes up true if and only if the man to which John refers actually has the properties which are attributed to him by the proposition, that he has in fact gone to the store. The philosopher s problem then, when dealing with propositions about fictional entities, is that the words in these propositions fail to refer to any existing object in the world. It is then impossible to check if such an entity has a property attributed to it, and hence, to determine a truth- value of the proposition. It has come to be in philosophical circles that a proposition has been taken as false when its subject fails to refer in this way. 1 It follows that all propositions about fictional entities are false. However, regardless of the outcome of these inquiries, the common users of the language, those who lack a subscription to the American Philosophical Quarterly and don t seem to care, still find little frustration in using and understanding sentences which reference Sherlock Holmes. They will use the phrases Unicorns do not exist 2 and Spongebob Squarepants lives under the sea indiscriminately, and think nothing of claiming that both are true; and what is more, unless their philosopher- uncle has come over for dinner, these assertions will go completely unchallenged by the rest of the community. 1 A proposition P(x) can be taken in this way to contain a hidden existential 2 It is interesting to note the this specific proposition turns out false by the standards outlined earlier, precisely because Unicorns do not exist.

3 If it is true that these sentences, which refer to fictional entities, have a functional role in society that is interdependent of any philosophizing about them, can it be said that there is any practical purpose for this philosophizing about the nature of fictional discourse? It turns out that there is at least one; the ontological issues at the foundations of mathematics can be uniquely and practically addressed when framed as a discussion about fictional entities. And so it might be said that the philosophical question of the nature of fictional discourse has a very important concrete application, if it can help to ground this abstract science, which has more direct practical applications in our world than any other. Of course, the initial criticism could be readdressed; it is obvious that mathematics has an incredible, near- universal range of application, which is in no way contingent upon the justification of its axioms or of the ontology of its most primitive entities. Many of the most successful mathematicians, both applied and purely theoretical, excel in their science with little to no care about its philosophical groundings. Gottlob Frege once addressed such possible critics in this way: Now, is it not humiliating for science to be in the dark about its nearest and apparently simple objects? So much less could one say what number is. If a concept fundamental to such a great science presents difficulties, then it is surely a mandatory task to investigate it more exactly and to overcome these difficulties; especially as it may be hard to succeed in bringing complete clarity to the negative numbers, fractional, complex numbers, as long as insight into the foundations of the entire edifice of arithmetic is still deficient. 3 3 Gottlob Frege, The Foundations of Arithmetic, Introduction, Paragraph 2.

4 I think, with Frege, that in order to have a fully consistent science, one must at least give at coherent story of the fundamental objects used in constructing the scientific edifice. Mathematics presents a particularly striking difficulty in this respect, because, contrary to physics or chemistry, its fundamental entities appear to be completely non- physical and non- empirical. However, Frege here was supporting a project to literally uncover and define these mathematical objects. This implies that he believes mathematical entities like number hold some sort of real existence; that they exist as non- physical, non- mental, abstract entities, which obviously cannot be observed but only comprehended through the use of the faculty of reason. This conception of the nature of number and other abstract objects assumes a rather non- intuitive ontological category under which these objects are said to subsist; it is then assumed that mathematical propositions are true if they accurately describe the characteristics of these objects. However, for those of us that do not claim to be metaphysicians, and cannot find it within ourselves to endorse Platonism when attempting to ground a rather practical science, it becomes useful to frame propositions which reference mathematical objects, at least casually, as fictional discourse, so that we can attempt to preserve their meaning without endorsing an indefensible ontology. What then does it mean to say that the objects which are referenced in mathematical statements are fictional? The simplest answer is that they do not exist in any real sense; that they are fabrications, which we use to tell a certain story. Of course the individual projects of mathematics have no need for philosophical justification, as they have proved themselves over the course of human history to be

5 incredibly useful in quantifying, understanding, and manipulating the world; the reason why Platonism has been endorsed by so many mathematical thinkers is simply because it seems most natural, practical, and un- inhibiting when employing mathematical language to speak as if there are straightforward mathematical entities which are being addressed, i.e. the number 47 or a perfect right triangle. However, ease of language can never justify a grand metaphysical claim about a class of ontological entities, the existence of which is non- falsifiable. Many a capable philosopher has disagreed with this claim. Consider a form of what has come to be known as the Quine- Putnam Indispensability Thesis. 4 i) Propositions that reference mathematical objects, i.e. mathematical sentences, play an indispensable role in empirical science and in our understanding of nature as a whole. ii) The conclusions drawn from these applications are accurate, useful, and appear to be correct and truthful descriptions of the world. C) We ought to hold that the mathematical statements are true and that they reference existing objects. The argument clearly assumes that in order for mathematics to be useful and 4 Perhaps the best argument I have seen for the claim that we ought to adopt an ontology that contains abstract objects like number is found near the end of Quine s Two Dogmas of Empiricism. While the argument is quite convincing, its strength lies purely in an appeal to a coherency of the whole scientific system. I will here argue that that coherency can be maintained without the unjustifiable metaphysical assumptions.

6 applicable to the world, the statements within it must be strictly true; the appeal is then to the non- Platonist to avoid a contradiction when assuming that scientific conclusions are true and reference existing states in the world, by adding to their ontology a set of abstract mathematical objects. Assuming that theorems in mathematics are not empirically verifiable, it seems absurd to say that a change in the truth value of a mathematical theorem could effect the practical applicability that the theorem has had in the world; as if, by presenting a new rigorous proof that the Pythagorean theorem is in fact incorrect, a buttress might collapse, sending a cathedral wall crashing to the ground. The truth- value of a proposition cannot alter the effect that its meaning might have on the minds of those that contemplate and apply it. Consider, if I may drift in to metaphor, an adherent to a false religion, who, using a set of principles therein, brings prosperity and wealth to his family and countrymen. The benefits of his devotion in no way prove the truthfulness of his beliefs; and in the same way, the theorems of geometry and calculus have been indispensable to the advancement of the human race, but not because they are strictly true in the sense that they reference objects existing in a metaphysical realm. It is the theorems themselves that are indispensable, not the objects. For even if the objects existed in the Platonic sense, they could never interact with the world in any useful way. It follows that where before it seemed natural to defend the existence of a class of abstract entities, a position which was neither verifiable nor falsifiable, it now seems much less forced to liken the structure of mathematics to a set of highly useful stories which logically follow from one another after a series of non- existent entities are, for utility s sake, assumed to exist.

7 It might seem highly unnatural, metaphorical, or perhaps sophistical to posit that the hypotenuse of an isosceles right triangle and Harry Potter play the same semantic role as fiction within our language. Perhaps this stems from the high prevalence of Platonism with regards to mathematics, which we all may have unconsciously adopted. I have already argued that, if the question is looked upon with a clear head, this claim seems much more true- to- life than maintaining that the hypotenuse, and perhaps Harry too (for the Meinongian), exist unchanging in an abstract realm, a- spatiotemporally. In this respect, I hope that I have not put the cart before the horse; what then is the significance of the claim that mathematics is indeed a type of fictional discourse? It has also already been claimed that this type of philosophical switch away from Platonism could not possibly alter the usefulness or the progress of mathematics. Is the only net- gain earned through this exchange to dispose of unwanted ontology, to minimize metaphysics? Some may take issue with this, claiming that this is no fair trade when rendering all of the beloved theorems of millennia of successful mathematics false. However, when doing philosophy, one ought not be guided by a desired outcome to make metaphysical or ontological commitments; sometimes it is wiser when critically examining the world to accept conclusions that we d rather not have, instead of making unwarranted and indefensible claims in order to fulfill our own desires. And so, the most consistent conclusion to draw seems to be that mathematical propositions fail to refer, and are therefore false, while remaining highly useful. However, a serious problem emerges when one claims that all mathematical propositions are false because they fail to reference any existing object. Assuming

8 that we think that mathematical statements are true or false based on whether or not they describe real objects, and that mathematical objects are non- existent, then we agree that the statement = 4 has a strictly false truth value. However, we recognize instantly that there is something inherently correct about the statement; and while = 31, being equally false in that it refers to no existing objects, also seems to be incorrect by another standard. This seems to be the strongest possible argument against fictionalism in mathematics, although I don t see it as crippling. It is obviously the case that doing mathematics is more rigorous than simply inventing an arbitrary fiction, and that there are right and wrong ways of doing mathematics. To argue differently would be indeed to argue for the destruction of mathematics. However, this added rigor still does not imply that the propositions are true in the sense that they reference real abstract objects. It is only because of the strict assumption of axioms and definitions at the foundations of the mathematical enterprise that there are correct and incorrect answers to mathematical problems. If numbers, sets, geometric figures, and the mathematical operations which we perform on them did not have a meaning defined before the operations, then there would be no correct or incorrect way to do mathematics, but it would follow that mathematics would become a useless game of manipulating vague symbols. There is a less strict standard for consistency of objects in fictions that are designed purely for artistic, aesthetic, or entertainment purposes. Consider the sentence Sherlock Homes suddenly sprouted several Hydra s heads, which spouted fire and incinerated Moriarty, who was donned in traditional samurai armor. While those familiar with Arthur Conan Doyle might recognize this proposition as strange,

9 because it is inconsistent with the fiction containing the characters referenced, there would be nothing necessarily incorrect about it if Doyle himself wrote it into the end of one of his novels. While this might seriously surprise or puzzle his readers, it would not logically contradict anything strictly defined before, and it could be viewed as having artistic or literary value in a strange way. However, the proposition that = 31 has no such value inside the system of mathematics, except perhaps that it calls recognition to a failure in understanding a basic mathematical operation. This difference between mathematical and literary fiction is an obvious and necessary one, as the former is supposed to be a rigorous science, the latter a form of entertainment. This is not to say that there is no room for creativity and innovation in mathematics; it is only that these mathematical advancements, in order to be considered as a part of the mathematical narrative, must be shared and understood by others who take part in the forging of this structure. For mathematics, if viewed as one coherent structure, is one that is formed through highly social actions, not within one community, but within largely varying societies and cultures throughout time. In order to maintain coherency over such broad variations in time and space, mathematical terms must be strictly defined, with operations on them limited and intricately explained. Of course, the most creative and cutting- edge mathematicians can invent new notations and reference new objects in their mathematical utterances, but the community will only accept these if they are as rigorously defined as the rest of the structure, fit within it neatly, and serve some purpose within the science. It would, however, be absurd to assert that when this clever mathematician performs such an action, that he is in

10 fact giving birth to a real and existent abstract entity, or that he is uncovering with his mind a timeless existence which has been waiting for his discovery. He is merely being creative with language in order to solve a specific problem within an existing semantic system by positing the existence of an unreal object, just as one might save a hero in an adventure novel by inventing a sexy sidekick. And so, it seems that mathematics is wildly different from normal fictional discourse only in respect to its internal rigor. Perhaps then it can be concluded without contradiction that mathematics constitutes an exceptionally exact, unique type of fiction. If this account of mathematics as a unique and intricate brand of fictional discourse is not met with any fatal objections, and I can think of none, then it appears that a fictionalist account of this science explains its nature and success at least as well as the standard Platonist position that its propositions reference existing objects. If these two philosophical accounts are equal in their description of the phenomena of mathematics, I think it obvious that the empiricist, the levelheaded mathematician, and the common user of the language would all opt to endorse the former; for the fictionalist description of mathematics seems less like a philosophical argument and more like a common sense description of what goes on when people mathematize. For at most it removes fully, and at least it minimizes, any metaphysical speculation in connection with the practice of mathematics. It has been argued that the rendering of mathematical theorems as strictly false in respect to reference can in no way negatively affect the endeavors of pure mathematics, or its practical application. It has also been shown that the apparently correctness and incorrectness of statements made in the context of mathematical discourse can be

11 accounted for while also allowing that all of the statements are false in the sense discussed. And so I conclude that the position that mathematics is a highly useful fiction ought to be adopted by all those who have no expressly evident reasons for endorsing Platonism. And if this is indeed the case, then the swelling of converts to this reasonable position may very well breathe new life into the philosophical study of the nature fictional discourse, as well as in the ways that our mathematical creations interact and describe the world.

Philosophy of Mathematics Nominalism

Philosophy of Mathematics Nominalism Philosophy of Mathematics Nominalism Owen Griffiths oeg21@cam.ac.uk Churchill and Newnham, Cambridge 8/11/18 Last week Ante rem structuralism accepts mathematical structures as Platonic universals. We

More information

Remarks on the philosophy of mathematics (1969) Paul Bernays

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

More information

A Logical Approach to Metametaphysics

A Logical Approach to Metametaphysics A Logical Approach to Metametaphysics Daniel Durante Departamento de Filosofia UFRN durante10@gmail.com 3º Filomena - 2017 What we take as true commits us. Quine took advantage of this fact to introduce

More information

Ayer on the criterion of verifiability

Ayer on the criterion of verifiability Ayer on the criterion of verifiability November 19, 2004 1 The critique of metaphysics............................. 1 2 Observation statements............................... 2 3 In principle verifiability...............................

More information

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 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

More information

Conventionalism and the linguistic doctrine of logical truth

Conventionalism and the linguistic doctrine of logical truth 1 Conventionalism and the linguistic doctrine of logical truth 1.1 Introduction Quine s work on analyticity, translation, and reference has sweeping philosophical implications. In his first important philosophical

More information

Verificationism. PHIL September 27, 2011

Verificationism. PHIL September 27, 2011 Verificationism PHIL 83104 September 27, 2011 1. The critique of metaphysics... 1 2. Observation statements... 2 3. In principle verifiability... 3 4. Strong verifiability... 3 4.1. Conclusive verifiability

More information

1. Introduction. 2. Clearing Up Some Confusions About the Philosophy of Mathematics

1. Introduction. 2. Clearing Up Some Confusions About the Philosophy of Mathematics Mark Balaguer Department of Philosophy California State University, Los Angeles A Guide for the Perplexed: What Mathematicians Need to Know to Understand Philosophers of Mathematics 1. Introduction When

More information

Fictionalism, Theft, and the Story of Mathematics. 1. Introduction. Philosophia Mathematica (III) 17 (2009),

Fictionalism, Theft, and the Story of Mathematics. 1. Introduction. Philosophia Mathematica (III) 17 (2009), Philosophia Mathematica (III) 17 (2009), 131 162. doi:10.1093/philmat/nkn019 Advance Access publication September 17, 2008 Fictionalism, Theft, and the Story of Mathematics Mark Balaguer This paper develops

More information

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

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

More information

Mathematics as we know it has been created and used by

Mathematics as we know it has been created and used by 0465037704-01.qxd 8/23/00 9:52 AM Page 1 Introduction: Why Cognitive Science Matters to Mathematics Mathematics as we know it has been created and used by human beings: mathematicians, physicists, computer

More information

Deflationary Nominalism s Commitment to Meinongianism

Deflationary Nominalism s Commitment to Meinongianism Res Cogitans Volume 7 Issue 1 Article 8 6-24-2016 Deflationary Nominalism s Commitment to Meinongianism Anthony Nguyen Reed College Follow this and additional works at: http://commons.pacificu.edu/rescogitans

More information

2.1 Review. 2.2 Inference and justifications

2.1 Review. 2.2 Inference and justifications Applied Logic Lecture 2: Evidence Semantics for Intuitionistic Propositional Logic Formal logic and evidence CS 4860 Fall 2012 Tuesday, August 28, 2012 2.1 Review The purpose of logic is to make reasoning

More information

PHI2391: Logical Empiricism I 8.0

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

More information

WHAT IS HUME S FORK? Certainty does not exist in science.

WHAT IS HUME S FORK?  Certainty does not exist in science. WHAT IS HUME S FORK? www.prshockley.org Certainty does not exist in science. I. Introduction: A. Hume divides all objects of human reason into two different kinds: Relation of Ideas & Matters of Fact.

More information

SUBSISTENCE DEMYSTIFIED. Arnold Cusmariu

SUBSISTENCE DEMYSTIFIED. Arnold Cusmariu SUBSISTENCE DEMYSTIFIED Arnold Cusmariu * n T n e Problems of Philosophy, Russell held that universals do not exist, they subsist. In the same work, he held also that universals are nonetheless "something.

More information

Development of Thought. The word "philosophy" comes from the Ancient Greek philosophia, which

Development of Thought. The word philosophy comes from the Ancient Greek philosophia, which Development of Thought The word "philosophy" comes from the Ancient Greek philosophia, which literally means "love of wisdom". The pre-socratics were 6 th and 5 th century BCE Greek thinkers who introduced

More information

In Search of the Ontological Argument. Richard Oxenberg

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

More information

Ayer s linguistic theory of the a priori

Ayer s linguistic theory of the a priori Ayer s linguistic theory of the a priori phil 43904 Jeff Speaks December 4, 2007 1 The problem of a priori knowledge....................... 1 2 Necessity and the a priori............................ 2

More information

Empty Names and Two-Valued Positive Free Logic

Empty Names and Two-Valued Positive Free Logic Empty Names and Two-Valued Positive Free Logic 1 Introduction Zahra Ahmadianhosseini In order to tackle the problem of handling empty names in logic, Andrew Bacon (2013) takes on an approach based on positive

More information

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 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

More information

A theory of adjudication is a theory primarily about what judges do when they decide cases in courts of law.

A theory of adjudication is a theory primarily about what judges do when they decide cases in courts of law. SLIDE 1 Theories of Adjudication: Legal Formalism A theory of adjudication is a theory primarily about what judges do when they decide cases in courts of law. American legal realism was a legal movement,

More information

Possibility and Necessity

Possibility and Necessity Possibility and Necessity 1. Modality: Modality is the study of possibility and necessity. These concepts are intuitive enough. Possibility: Some things could have been different. For instance, I could

More information

Has Nagel uncovered a form of idealism?

Has Nagel uncovered a form of idealism? Has Nagel uncovered a form of idealism? Author: Terence Rajivan Edward, University of Manchester. Abstract. In the sixth chapter of The View from Nowhere, Thomas Nagel attempts to identify a form of idealism.

More information

Truth At a World for Modal Propositions

Truth At a World for Modal Propositions Truth At a World for Modal Propositions 1 Introduction Existentialism is a thesis that concerns the ontological status of individual essences and singular propositions. Let us define an individual essence

More information

(1) a phrase may be denoting, and yet not denote anything e.g. the present King of France

(1) a phrase may be denoting, and yet not denote anything e.g. the present King of France Main Goals: Phil/Ling 375: Meaning and Mind [Handout #14] Bertrand Russell: On Denoting/Descriptions Professor JeeLoo Liu 1. To show that both Frege s and Meinong s theories are inadequate. 2. To defend

More information

This is a longer version of the review that appeared in Philosophical Quarterly Vol. 47 (1997)

This is a longer version of the review that appeared in Philosophical Quarterly Vol. 47 (1997) This is a longer version of the review that appeared in Philosophical Quarterly Vol. 47 (1997) Frege by Anthony Kenny (Penguin, 1995. Pp. xi + 223) Frege s Theory of Sense and Reference by Wolfgang Carl

More information

The Sea-Fight Tomorrow by Aristotle

The Sea-Fight Tomorrow by Aristotle The Sea-Fight Tomorrow by Aristotle Aristotle, Antiquities Project About the author.... Aristotle (384-322) studied for twenty years at Plato s Academy in Athens. Following Plato s death, Aristotle left

More information

Is there a good epistemological argument against platonism? DAVID LIGGINS

Is there a good epistemological argument against platonism? DAVID LIGGINS [This is the penultimate draft of an article that appeared in Analysis 66.2 (April 2006), 135-41, available here by permission of Analysis, the Analysis Trust, and Blackwell Publishing. The definitive

More information

Introduction to Philosophy

Introduction to Philosophy 1 Introduction to Philosophy What is Philosophy? It has many different meanings. In everyday life, to have a philosophy means much the same as having a specified set of attitudes, objectives or values

More information

Ayer and Quine on the a priori

Ayer and Quine on the a priori Ayer and Quine on the a priori November 23, 2004 1 The problem of a priori knowledge Ayer s book is a defense of a thoroughgoing empiricism, not only about what is required for a belief to be justified

More information

Chapter 6. Fate. (F) Fatalism is the belief that whatever happens is unavoidable. (55)

Chapter 6. Fate. (F) Fatalism is the belief that whatever happens is unavoidable. (55) Chapter 6. Fate (F) Fatalism is the belief that whatever happens is unavoidable. (55) The first, and most important thing, to note about Taylor s characterization of fatalism is that it is in modal terms,

More information

Cory Juhl, Eric Loomis, Analyticity (New York: Routledge, 2010).

Cory Juhl, Eric Loomis, Analyticity (New York: Routledge, 2010). Cory Juhl, Eric Loomis, Analyticity (New York: Routledge, 2010). Reviewed by Viorel Ţuţui 1 Since it was introduced by Immanuel Kant in the Critique of Pure Reason, the analytic synthetic distinction had

More information

a0rxh/ On Van Inwagen s Argument Against the Doctrine of Arbitrary Undetached Parts WESLEY H. BRONSON Princeton University

a0rxh/ On Van Inwagen s Argument Against the Doctrine of Arbitrary Undetached Parts WESLEY H. BRONSON Princeton University a0rxh/ On Van Inwagen s Argument Against the Doctrine of Arbitrary Undetached Parts WESLEY H. BRONSON Princeton University Imagine you are looking at a pen. It has a blue ink cartridge inside, along with

More information

Comments on Truth at A World for Modal Propositions

Comments on Truth at A World for Modal Propositions Comments on Truth at A World for Modal Propositions Christopher Menzel Texas A&M University March 16, 2008 Since Arthur Prior first made us aware of the issue, a lot of philosophical thought has gone into

More information

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. 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

More information

Philosophy 125 Day 21: Overview

Philosophy 125 Day 21: Overview Branden Fitelson Philosophy 125 Lecture 1 Philosophy 125 Day 21: Overview 1st Papers/SQ s to be returned this week (stay tuned... ) Vanessa s handout on Realism about propositions to be posted Second papers/s.q.

More information

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 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

More information

In Defense of Radical Empiricism. Joseph Benjamin Riegel. Chapel Hill 2006

In Defense of Radical Empiricism. Joseph Benjamin Riegel. Chapel Hill 2006 In Defense of Radical Empiricism Joseph Benjamin Riegel A thesis submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of

More information

PHILOSOPHY OF LOGIC AND LANGUAGE OVERVIEW FREGE JONNY MCINTOSH 1. FREGE'S CONCEPTION OF LOGIC

PHILOSOPHY OF LOGIC AND LANGUAGE OVERVIEW FREGE JONNY MCINTOSH 1. FREGE'S CONCEPTION OF LOGIC PHILOSOPHY OF LOGIC AND LANGUAGE JONNY MCINTOSH 1. FREGE'S CONCEPTION OF LOGIC OVERVIEW These lectures cover material for paper 108, Philosophy of Logic and Language. They will focus on issues in philosophy

More information

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

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,

More information

1/5. The Critique of Theology

1/5. The Critique of Theology 1/5 The Critique of Theology The argument of the Transcendental Dialectic has demonstrated that there is no science of rational psychology and that the province of any rational cosmology is strictly limited.

More information

Ibuanyidanda (Complementary Reflection), African Philosophy and General Issues in Philosophy

Ibuanyidanda (Complementary Reflection), African Philosophy and General Issues in Philosophy HOME Ibuanyidanda (Complementary Reflection), African Philosophy and General Issues in Philosophy Back to Home Page: http://www.frasouzu.com/ for more essays from a complementary perspective THE IDEA OF

More information

PHILOSOPHICAL PROBLEMS & THE ANALYSIS OF LANGUAGE

PHILOSOPHICAL PROBLEMS & THE ANALYSIS OF LANGUAGE PHILOSOPHICAL PROBLEMS & THE ANALYSIS OF LANGUAGE Now, it is a defect of [natural] languages that expressions are possible within them, which, in their grammatical form, seemingly determined to designate

More information

Philosophy of Mathematics Kant

Philosophy of Mathematics Kant Philosophy of Mathematics Kant Owen Griffiths oeg21@cam.ac.uk St John s College, Cambridge 20/10/15 Immanuel Kant Born in 1724 in Königsberg, Prussia. Enrolled at the University of Königsberg in 1740 and

More information

Issue 4, Special Conference Proceedings Published by the Durham University Undergraduate Philosophy Society

Issue 4, Special Conference Proceedings Published by the Durham University Undergraduate Philosophy Society Issue 4, Special Conference Proceedings 2017 Published by the Durham University Undergraduate Philosophy Society An Alternative Approach to Mathematical Ontology Amber Donovan (Durham University) Introduction

More information

Metaphysical Problems and Methods

Metaphysical Problems and Methods Metaphysical Problems and Methods Roger Bishop Jones Abstract. Positivists have often been antipathetic to metaphysics. Here, however. a positive role for metaphysics is sought. Problems about reality

More information

On Naturalism in Mathematics

On Naturalism in Mathematics On Naturalism in Mathematics Alfred Lundberg Bachelor s Thesis, Spring 2007 Supervison: Christian Bennet Department of Philosophy Göteborg University 1 Contents Contents...2 Introduction... 3 Naïve Questions...

More information

The Rightness Error: An Evaluation of Normative Ethics in the Absence of Moral Realism

The Rightness Error: An Evaluation of Normative Ethics in the Absence of Moral Realism An Evaluation of Normative Ethics in the Absence of Moral Realism Mathais Sarrazin J.L. Mackie s Error Theory postulates that all normative claims are false. It does this based upon his denial of moral

More information

What one needs to know to prepare for'spinoza's method is to be found in the treatise, On the Improvement

What one needs to know to prepare for'spinoza's method is to be found in the treatise, On the Improvement SPINOZA'S METHOD Donald Mangum The primary aim of this paper will be to provide the reader of Spinoza with a certain approach to the Ethics. The approach is designed to prevent what I believe to be certain

More information

UNIVERSITY OF ALBERTA MATHEMATICS AS MAKE-BELIEVE: A CONSTRUCTIVE EMPIRICIST ACCOUNT SARAH HOFFMAN

UNIVERSITY OF ALBERTA MATHEMATICS AS MAKE-BELIEVE: A CONSTRUCTIVE EMPIRICIST ACCOUNT SARAH HOFFMAN UNIVERSITY OF ALBERTA MATHEMATICS AS MAKE-BELIEVE: A CONSTRUCTIVE EMPIRICIST ACCOUNT SARAH HOFFMAN A thesis submitted to the Faculty of graduate Studies and Research in partial fulfillment of the requirements

More information

Broad on Theological Arguments. I. The Ontological Argument

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

More information

Phil/Ling 375: Meaning and Mind [Handout #10]

Phil/Ling 375: Meaning and Mind [Handout #10] Phil/Ling 375: Meaning and Mind [Handout #10] W. V. Quine: Two Dogmas of Empiricism Professor JeeLoo Liu Main Theses 1. Anti-analytic/synthetic divide: The belief in the divide between analytic and synthetic

More information

Wittgenstein on The Realm of Ineffable

Wittgenstein on The Realm of Ineffable Wittgenstein on The Realm of Ineffable by Manoranjan Mallick and Vikram S. Sirola Abstract The paper attempts to delve into the distinction Wittgenstein makes between factual discourse and moral thoughts.

More information

Has Logical Positivism Eliminated Metaphysics?

Has Logical Positivism Eliminated Metaphysics? International Journal of Humanities and Social Science Invention ISSN (Online): 2319 7722, ISSN (Print): 2319 7714 Volume 3 Issue 11 ǁ November. 2014 ǁ PP.38-42 Has Logical Positivism Eliminated Metaphysics?

More information

Class #14: October 13 Gödel s Platonism

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

More information

About the Origin: Is Mathematics Discovered or Invented?

About the Origin: Is Mathematics Discovered or Invented? Lehigh University Lehigh Preserve Volume 24-2016 Lehigh Review Spring 2016 About the Origin: Is Mathematics Discovered or Invented? Michael Lessel Lehigh University Follow this and additional works at:

More information

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

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

More information

It doesn t take long in reading the Critique before we are faced with interpretive challenges. Consider the very first sentence in the A edition:

It doesn t take long in reading the Critique before we are faced with interpretive challenges. Consider the very first sentence in the A edition: The Preface(s) to the Critique of Pure Reason It doesn t take long in reading the Critique before we are faced with interpretive challenges. Consider the very first sentence in the A edition: Human reason

More information

Moral Objectivism. RUSSELL CORNETT University of Calgary

Moral Objectivism. RUSSELL CORNETT University of Calgary Moral Objectivism RUSSELL CORNETT University of Calgary The possibility, let alone the actuality, of an objective morality has intrigued philosophers for well over two millennia. Though much discussed,

More information

Is Innate Foreknowledge Possible to a Temporal God?

Is Innate Foreknowledge Possible to a Temporal God? Is Innate Foreknowledge Possible to a Temporal God? by Kel Good A very interesting attempt to avoid the conclusion that God's foreknowledge is inconsistent with creaturely freedom is an essay entitled

More information

Quantificational logic and empty names

Quantificational logic and empty names Quantificational logic and empty names Andrew Bacon 26th of March 2013 1 A Puzzle For Classical Quantificational Theory Empty Names: Consider the sentence 1. There is something identical to Pegasus On

More information

Brief Remarks on Putnam and Realism in Mathematics * Charles Parsons. Hilary Putnam has through much of his philosophical life meditated on

Brief Remarks on Putnam and Realism in Mathematics * Charles Parsons. Hilary Putnam has through much of his philosophical life meditated on Version 3.0, 10/26/11. Brief Remarks on Putnam and Realism in Mathematics * Charles Parsons Hilary Putnam has through much of his philosophical life meditated on the notion of realism, what it is, what

More information

5: Preliminaries to the Argument

5: Preliminaries to the Argument 5: Preliminaries to the Argument In this chapter, we set forth the logical structure of the argument we will use in chapter six in our attempt to show that Nfc is self-refuting. Thus, our main topics in

More information

KANT S EXPLANATION OF THE NECESSITY OF GEOMETRICAL TRUTHS. John Watling

KANT S EXPLANATION OF THE NECESSITY OF GEOMETRICAL TRUTHS. John Watling KANT S EXPLANATION OF THE NECESSITY OF GEOMETRICAL TRUTHS John Watling Kant was an idealist. His idealism was in some ways, it is true, less extreme than that of Berkeley. He distinguished his own by calling

More information

Semantic Foundations for Deductive Methods

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

More information

Phil 435: Philosophy of Language. [Handout 7] W. V. Quine, Quantifiers and Propositional Attitudes (1956)

Phil 435: Philosophy of Language. [Handout 7] W. V. Quine, Quantifiers and Propositional Attitudes (1956) Quine & Kripke 1 Phil 435: Philosophy of Language [Handout 7] Quine & Kripke Reporting Beliefs Professor JeeLoo Liu W. V. Quine, Quantifiers and Propositional Attitudes (1956) * The problem: The logical

More information

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

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

More information

Quine on the analytic/synthetic distinction

Quine on the analytic/synthetic distinction Quine on the analytic/synthetic distinction Jeff Speaks March 14, 2005 1 Analyticity and synonymy.............................. 1 2 Synonymy and definition ( 2)............................ 2 3 Synonymy

More information

6. Truth and Possible Worlds

6. Truth and Possible Worlds 6. Truth and Possible Worlds We have defined logical entailment, consistency, and the connectives,,, all in terms of belief. In view of the close connection between belief and truth, described in the first

More information

Curriculum Guide for Pre-Algebra

Curriculum Guide for Pre-Algebra Unit 1: Variable, Expressions, & Integers 2 Weeks PA: 1, 2, 3, 9 Where did Math originate? Why is Math possible? What should we expect as we use Math? How should we use Math? What is the purpose of using

More information

THE REFUTATION OF PHENOMENALISM

THE REFUTATION OF PHENOMENALISM The Isaiah Berlin Virtual Library THE REFUTATION OF PHENOMENALISM A draft of section I of Empirical Propositions and Hypothetical Statements 1 The rights and wrongs of phenomenalism are perhaps more frequently

More information

ABSOLUTISM. The absolutist believes mathematics is:

ABSOLUTISM. The absolutist believes mathematics is: FALLIBILISM ABSOLUTISM The absolutist believes mathematics is: universal objective certain discovered by mathematicians through intuition established by proof after discovery. Most mathematicians share

More information

Absolutism. The absolutist believes mathematics is:

Absolutism. The absolutist believes mathematics is: Fallibilism Absolutism The absolutist believes mathematics is: universal objective certain discovered by mathematicians through intuition established by proof after discovery. Most mathematicians share

More information

Is the Existence of the Best Possible World Logically Impossible?

Is the Existence of the Best Possible World Logically Impossible? Is the Existence of the Best Possible World Logically Impossible? Anders Kraal ABSTRACT: Since the 1960s an increasing number of philosophers have endorsed the thesis that there can be no such thing as

More information

In Defense of Pure Reason: A Rationalist Account of A Priori Justification, by Laurence BonJour. Cambridge: Cambridge University Press,

In Defense of Pure Reason: A Rationalist Account of A Priori Justification, by Laurence BonJour. Cambridge: Cambridge University Press, Book Reviews 1 In Defense of Pure Reason: A Rationalist Account of A Priori Justification, by Laurence BonJour. Cambridge: Cambridge University Press, 1998. Pp. xiv + 232. H/b 37.50, $54.95, P/b 13.95,

More information

xiv Truth Without Objectivity

xiv Truth Without Objectivity Introduction There is a certain approach to theorizing about language that is called truthconditional semantics. The underlying idea of truth-conditional semantics is often summarized as the idea that

More information

Aristotle on the Principle of Contradiction :

Aristotle on the Principle of Contradiction : Aristotle on the Principle of Contradiction : Book Gamma of the Metaphysics Robert L. Latta Having argued that there is a science which studies being as being, Aristotle goes on to inquire, at the beginning

More information

1. Lukasiewicz s Logic

1. Lukasiewicz s Logic Bulletin of the Section of Logic Volume 29/3 (2000), pp. 115 124 Dale Jacquette AN INTERNAL DETERMINACY METATHEOREM FOR LUKASIEWICZ S AUSSAGENKALKÜLS Abstract An internal determinacy metatheorem is proved

More information

DEFEASIBLE A PRIORI JUSTIFICATION: A REPLY TO THUROW

DEFEASIBLE A PRIORI JUSTIFICATION: A REPLY TO THUROW The Philosophical Quarterly Vol. 58, No. 231 April 2008 ISSN 0031 8094 doi: 10.1111/j.1467-9213.2007.512.x DEFEASIBLE A PRIORI JUSTIFICATION: A REPLY TO THUROW BY ALBERT CASULLO Joshua Thurow offers a

More information

METHODENSTREIT WHY CARL MENGER WAS, AND IS, RIGHT

METHODENSTREIT WHY CARL MENGER WAS, AND IS, RIGHT METHODENSTREIT WHY CARL MENGER WAS, AND IS, RIGHT BY THORSTEN POLLEIT* PRESENTED AT THE SPRING CONFERENCE RESEARCH ON MONEY IN THE ECONOMY (ROME) FRANKFURT, 20 MAY 2011 *FRANKFURT SCHOOL OF FINANCE & MANAGEMENT

More information

SAVING RELATIVISM FROM ITS SAVIOUR

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

More information

Analyticity, Reductionism, and Semantic Holism. The verification theory is an empirical theory of meaning which asserts that the meaning of a

Analyticity, Reductionism, and Semantic Holism. The verification theory is an empirical theory of meaning which asserts that the meaning of a 24.251: Philosophy of Language Paper 1: W.V.O. Quine, Two Dogmas of Empiricism 14 October 2011 Analyticity, Reductionism, and Semantic Holism The verification theory is an empirical theory of meaning which

More information

Spinoza and the Axiomatic Method. Ever since Euclid first laid out his geometry in the Elements, his axiomatic approach to

Spinoza and the Axiomatic Method. Ever since Euclid first laid out his geometry in the Elements, his axiomatic approach to Haruyama 1 Justin Haruyama Bryan Smith HON 213 17 April 2008 Spinoza and the Axiomatic Method Ever since Euclid first laid out his geometry in the Elements, his axiomatic approach to geometry has been

More information

Mathematical Ontology and Epistemology: An Analysis of Quine s and Maddy s Unique Arguments. Luke B. D. Quigley

Mathematical Ontology and Epistemology: An Analysis of Quine s and Maddy s Unique Arguments. Luke B. D. Quigley Mathematical Ontology and Epistemology: An Analysis of Quine s and Maddy s Unique Arguments Luke B. D. Quigley 2016 i Contents I. Introduction..............................................................

More information

Chapter 18 David Hume: Theory of Knowledge

Chapter 18 David Hume: Theory of Knowledge Key Words Chapter 18 David Hume: Theory of Knowledge Empiricism, skepticism, personal identity, necessary connection, causal connection, induction, impressions, ideas. DAVID HUME (1711-76) is one of the

More information

Perceiving Abstract Objects

Perceiving Abstract Objects Perceiving Abstract Objects Inheriting Ohmori Shōzō's Philosophy of Perception Takashi Iida 1 1 Department of Philosophy, College of Humanities and Sciences, Nihon University 1. Introduction This paper

More information

But we may go further: not only Jones, but no actual man, enters into my statement. This becomes obvious when the statement is false, since then

But we may go further: not only Jones, but no actual man, enters into my statement. This becomes obvious when the statement is false, since then CHAPTER XVI DESCRIPTIONS We dealt in the preceding chapter with the words all and some; in this chapter we shall consider the word the in the singular, and in the next chapter we shall consider the word

More information

Today we turn to the work of one of the most important, and also most difficult, philosophers: Immanuel Kant.

Today we turn to the work of one of the most important, and also most difficult, philosophers: Immanuel Kant. Kant s antinomies Today we turn to the work of one of the most important, and also most difficult, philosophers: Immanuel Kant. Kant was born in 1724 in Prussia, and his philosophical work has exerted

More information

Under contract with Oxford University Press Karen Bennett Cornell University

Under contract with Oxford University Press Karen Bennett Cornell University 1. INTRODUCTION MAKING THINGS UP Under contract with Oxford University Press Karen Bennett Cornell University The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible

More information

Faults and Mathematical Disagreement

Faults and Mathematical Disagreement 45 Faults and Mathematical Disagreement María Ponte ILCLI. University of the Basque Country mariaponteazca@gmail.com Abstract: My aim in this paper is to analyse the notion of mathematical disagreements

More information

Bertrand Russell Proper Names, Adjectives and Verbs 1

Bertrand Russell Proper Names, Adjectives and Verbs 1 Bertrand Russell Proper Names, Adjectives and Verbs 1 Analysis 46 Philosophical grammar can shed light on philosophical questions. Grammatical differences can be used as a source of discovery and a guide

More information

- We might, now, wonder whether the resulting concept of justification is sufficiently strong. According to BonJour, apparent rational insight is

- We might, now, wonder whether the resulting concept of justification is sufficiently strong. According to BonJour, apparent rational insight is BonJour I PHIL410 BonJour s Moderate Rationalism - BonJour develops and defends a moderate form of Rationalism. - Rationalism, generally (as used here), is the view according to which the primary tool

More information

Searle vs. Chalmers Debate, 8/2005 with Death Monkey (Kevin Dolan)

Searle vs. Chalmers Debate, 8/2005 with Death Monkey (Kevin Dolan) Searle vs. Chalmers Debate, 8/2005 with Death Monkey (Kevin Dolan) : Searle says of Chalmers book, The Conscious Mind, "it is one thing to bite the occasional bullet here and there, but this book consumes

More information

How to Mistake a Trivial Fact About Probability For a. Substantive Fact About Justified Belief

How to Mistake a Trivial Fact About Probability For a. Substantive Fact About Justified Belief How to Mistake a Trivial Fact About Probability For a Substantive Fact About Justified Belief Jonathan Sutton It is sometimes thought that the lottery paradox and the paradox of the preface demand a uniform

More information

Nominalism in the Philosophy of Mathematics First published Mon Sep 16, 2013

Nominalism in the Philosophy of Mathematics First published Mon Sep 16, 2013 Open access to the SEP is made possible by a world-wide funding initiative. Please Read How You Can Help Keep the Encyclopedia Free Nominalism in the Philosophy of Mathematics First published Mon Sep 16,

More information

Metaphysics by Aristotle

Metaphysics by Aristotle Metaphysics by Aristotle Translated by W. D. Ross ebooks@adelaide 2007 This web edition published by ebooks@adelaide. Rendered into HTML by Steve Thomas. Last updated Wed Apr 11 12:12:00 2007. This work

More information

BENEDIKT PAUL GÖCKE. Ruhr-Universität Bochum

BENEDIKT PAUL GÖCKE. Ruhr-Universität Bochum 264 BOOK REVIEWS AND NOTICES BENEDIKT PAUL GÖCKE Ruhr-Universität Bochum István Aranyosi. God, Mind, and Logical Space: A Revisionary Approach to Divinity. Palgrave Frontiers in Philosophy of Religion.

More information

CONTENTS A SYSTEM OF LOGIC

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

More information