# Facts and Free Logic R. M. Sainsbury

Size: px
Start display at page:

Transcription

1 Facts and Free Logic R. M. Sainsbury Facts are structures which are the case, and they are what true sentences affirm. It is a fact that Fido barks. It is easy to list some of its components, Fido and the property of barking. It is hard to say what the structure is (the glue is a notoriously tricky element), but happily this is not relevant for the present purpose. Intuitively, any sentence which refers to just these components, attributing barking to Fido, will affirm the same fact. By some standards, if Fido is the smartest dog on Elm Street, a sentence like the smartest dog on Elm Street barks meets this condition, and so also affirms the fact that Fido barks. This immediately provokes some uneasiness. Does not Elm Street have a claim to be a component of any fact which the more complex sentence affirms? More generally, should we qualify the intuition, so that it claims only that a sentence which refers just to Fido and the property of barking, and to nothing else, will affirm the fact that Fido barks? This question touches one central strand of Stephen Neale s subtle monograph. In a form which comes a little closer to the generality at which Neale s argument operates, a challenge to the very idea of facts can be made as follows: if a definite description the F refers at all, then it refers to the same thing as the thing which is both F and p, for any true sentence p. There is thus no upper limit to the additional material, up to a complete description of the world, that can be incorporated into a definite description. The conflicting intuitions are: (i) that all that matters to what fact is affirmed is what the definite description refers to; and (ii) that the extraneous material cannot be guaranteed to have no effect on which fact is affirmed. In light of the challenge, it is not surprising that Neale should applaud those fact theorists who, like Russell, denied that definite descriptions are referring expressions, thus cutting off the challenge before it can be so much as issued. 1

2 As his title indicates, Neale s primary focus is on facts but, as he makes plain, his considerations have a range of other bearings, for example on the nature of reference. A simple thought is that all referring expressions have essentially the same inferential properties, perhaps those captured, for singular referring expressions, by his principle PSST. A slingshot argument might be used to show, on the basis of this assumption, that definite descriptions are not referring expressions. This is one aspect of his work I wish to explore (see 3). The other aspect is how free logic bears on the issue. Here Neale s distinction between proofs dependent on a general principle of logical equivalence (PSLE) and proofs not so dependent has additional use. The free logician will deny that the supposed logical equivalences which have historically been offered are really equivalences. On the other hand, I agree with Neale that a free logician (of the kind I favour) can reconstruct the Gödelian proofs so that they are valid in his system. A free logician, as much as a classical one, will applaud the restrictions on theories of facts which Neale advocates, and I will shortly spell that out (see 2). There is also a more informal point to be made. The motivation behind free logic, or more precisely behind negative free logic, is at odds with usual views about facts. I begin by explaining why this is so. 1 According to negative free logic (NFL), some intelligible referring expressions have no referent. Any simple sentence (that is, one consisting of an n-ary predicate together with n referring expressions) 1 containing a referring expression with no referent is false. This follows from the composition axiom: a simple sentence R(t 1, t n ) is true iff each t i has a referent, a i, and <a 1, a n > satisfies R; otherwise it is false. Negation toggles truth and falsehood, just as in classical logic, so there are truths containing non-referring referring expressions. Quantification is restricted: existential generalization holds if the inputs are simple sentences, but for arbitrary sentences we need an additional premise affirming, for any referring expression t, the truth of t exists. The same additional premise is required 1 Simple sentences with complex referring expressions are not atomic, though all atomic sentences are simple. 2

3 if t is to be introduced into a conclusion of universal instantiation. A definite description ιxfx refers to something iff that thing uniquely satisfies F. The law of identity is that every object is self-identical, x x=x. Not every instance of x=x is true. The King of France is the King of France is false so its negation is true, but that is no counterexample to the claim that every object is self-identical (the King of France is not an object). Negative facts have always been problematic for theorists of facts. Should one say that Socrates is not alive affirms the negative fact that Socrates is not alive, which would presumably contain negation as a component? Or should one say that the sentence affirms just a positive fact, say the fact that Socrates is dead, or at least affirms that there is such a positive fact? However this is best resolved, it is classically not doubted that we can count on Socrates as a component. In negative free logic, by contrast, there are negative sentences which are true because they contain a non-referring referring expression, for example Pegasus is not a horse (how could he be? he doesn t even exist) 2. The assumption that such a statement affirms a fact is hard to reconcile with the absence of any object which could serve as a component corresponding to Pegasus. However happy we are to allow negation and the property of being a horse as components, we simply lack the resources to construct a suitable fact. This feature of NFL links with another: it is a logic for which standard kinds of model theory are inappropriate, at least as revealing the character of an appropriate semantics for the language. Certainly, some model theoretic approaches to free logic interpret nonreferring referring expressions by associating them with a special entity, one lying outside the domain used for interpreting non-empty referring expressions and quantifiers. It would even be possible to associate semantically different non-referring referring expressions with distinct such entities. But it would be a mistake to suppose that this would be an appropriate description of how such expressions are actually used. No such special objects guide or are supposed to guide speakers in their use of such expressions. By the same token, NFL sees no value in the notion of a Russellian proposition, a 2 The sentence is false in the myth, but we are concerned only with factual truth. 3

4 sequence of objects and properties, as a semantic representation. There are two reasons. The first is that NFL welcomes complex referring expressions, and it is plain that full justice to their semantics cannot be done simply in terms of their referent (supposing there is one); attention must also be paid to the complex means whereby the expression has this referent. The second reason is that in the case of non-referring referring expressions, there is no object to play the appropriate role in a supposed Russellian proposition. Enthusiasm for facts and enthusiasm for Russellian propositions are connected. One of Russell s early discussions (1912) introduces them in tandem. His account of belief factors out its various objects, those which later commentators regard as the constituents of Russellian propositions. The account of truth makes the truth of a belief consist in the existence of a complex, a fact, whose constituents are the objects of the belief, suitably united. NFL is at odds with both ways of thinking. In place of model theory or Russellian propositions, truth theory is the natural semantics for NFL, and truths do all the work one might have looked to facts to do. 2 One would expect this antipathy to facts and to Russellian propositions to be reflected in inferential principles. In particular, one would expect that NFL would put no fewer restrictions on fact theories than those placed by a powerful slingshot. The proof on Neale s p. 173 requires that ϕ and (α=ιx(x=α & ϕ) (x=b & ϕ)) be logically equivalent, but according to NFL they are not. Suppose ϕ is true and α lacks a referent. Then the identity is false and equivalence fails. The proof could be revised so as to deal with arbitrary simple sentences Fa and Gb in place of ϕ and ψ. This blocks the counterexample to equivalence just given, since the truth of Fa requires that a have a referent; and there are no other counterexamples. The upshot is a slight weakening of the force of this slingshot, though it would remain strong enough to provide a detailed reason to encourage a fact theorist s natural reluctance to think that a connective like the fact that Fa is the fact that permits substitution of logical equivalents salva veritate. 4

5 Neale implies, I think rightly, that one could reconstruct Gödel s slingshot within NFL. It cannot be used as it stands, since within NFL, ι-intr is not valid: T[Σ(x/α)] T[α=ιx(x=α & Σx)] Here is a counterexample. Put is not a horse for Σ and Pegasus for α. T is null. The premise then formalizes Pegasus is not a horse which is true according to NFL, whereas the conclusion formalizes Pegasus is identical to the thing which is identical to Pegasus and which is not a horse, and this, according to NFL, is false. It is a simple sentence composed of the binary identity predicate and two referring expressions, neither of which refers. I have assumed that in replacing Σ by is not a horse the target English sentence is one in which the negation sign has wide scope relative to Pegasus. If it has narrow scope, then the sentence attempts to predicate not being horse of Pegasus and there is no counterexample since, thus understood, the premise is false (according to NFL). If the sign for negation is introduced as a replacement for T, then it retains its wide scope in the conclusion, and so the conclusion is true (according to NFL). One might simply stipulate that negation has wide scope in the target sentence. 3 It is up to Neale to say whether is not a horse, with wide scope negation, makes for a legitimate replacement for Σ. One can infer that he has no objection, since he allows b as such a replacement (with, of course, negation having what the NFL theorist will see as wide scope) in applying ι-conv in the crucial derivation (pp ). So ι-intr, and hence ι-conv, are not NFL-valid. Does this mean that the slingshot is irrelevant for NFL? Surely not. As far as I know, a difficulty arises only when ι-conv is applied to a sentence with a non-referring referring expression. By adding an existence 3 The formal language of NFL has the resources to attribute semantically significant scope properties to negation relative to names. Occasions on which natural language requires this are, however, rare. In particular, it is not easy to hear Pegasus doesn t exist with narrow scope negation (and so as false). 5

6 assumption to the premises, the rule can be rendered immune to this obstacle to its NFLvalidity: T[Σ(x/α)], x x=α T[α=ιx(x=α & Σx)]. (The rule of ι-elim requires no change to meet NFL scruples.) This modification of ι- INTRO does not incapacitate the rule for use in the central proof (p ), for we already have a simple sentence containing the relevant name as a premise, and this guarantees that, if the premises are true, the name has a referent, and the conditions for the application of the NFL-version of ι-conv are met. It is one thing to protect ι-conv from an obstacle to its validity and another to affirm that the result is valid. Neale displays no doubts, but with no restrictions on what can replace T, some doubts are in order, independently of free logic. 4 On the face of it, John might have said that Fido barks, without having said that Fido is identical to the thing which is Fido and barks. If John said is a sentence connective which can replace T in ι- CONV, then the principle is not generally valid, and the same would apply to its NFL version. Even so, adopting NFL has only a rather minor impact on the force of slingshots. But the tables may be turned: may not slingshots prove too much, and thereby undermine views which a free logician would wish to adopt? In particular, do not slingshots, in conjunction with irresistible further assumptions, show that we cannot treat definite descriptions as referring expressions? This relates to the question whether it makes sense to deny that coreferring expressions are everywhere substitutable salva veritate. Since plural referring expressions will not be 3 4 As the example in the text shows, T must be restricted to exclude operators which are hyperintensional, and further restrictions may be in order. This is no doubt implicit in Neale s text. 6

7 at issue, we can narrow the question: does it make sense to suppose that PSST sometimes fails? If it never does, then treating (singular) definite descriptions as singular terms, as in NFL, would seem to help fuel the argument (as e.g. mentioned on p. 187) whose conclusion is that there are no non-truth functional sentence connectives, a conclusion I regard as a reductio of something that leads to it. Neale apparently thinks PSST must hold without exception, for he considers that a treatment of definite descriptions according to which they are singular terms is hence subject to PSST (p. 187). By contrast, I will suggest that slingshot arguments add to the considerations which favour the view that PSST should be restricted. Despite the efforts of theorists of direct reference, the majority (I would guess) still think that proper names (those uncontroversial examples of singular terms) cannot be substituted salva veritate within contexts of propositional attitudes. The ancient astronomers believed that Hesperus is Hesperus may be true, even though The ancient astronomers believed that Hesperus is Phosphorus is false. Frege said that it is one thing to know that Hesperus is Hesperus and another to know that Hesperus is Phosphorus is true (setting aside textual nuances) whereas Frege said that it is one thing to know that Hesperus is Hesperus and another to know that Hesperus is Hesperus is false. More controversially, some think that even in more ordinary contexts such substitution may not be truth preserving: allegedly, relative to some event in the story, Clark Kent entered the phone box and Superman came out is true though Clark Kent entered the phone box and Clark Kent came out is false (cf Saul 1997). Our question is whether we should restrict PSST in modal contexts as a response to a slingshot argument whose conclusion is that there are no genuinely modal (and so non-truth functional) sentence connectives. Such a slingshot, using Neale s devices, and in particular the presentation on p , might run on the following lines. Starting from Fa we conclude that Gb, for some arbitrary contingent truth concerning a distinct object, Gb. Regarding this conclusion as paradoxical, we look for something to reject in principles of inference the argument exploits. 7

8 1 [1] Fa Premise 2 [2] Gb Premise 3 [3] a b Premise 1 [4] Fa 1, -ELIM 1 [5] x x=a 4, -INTRO 1 [6] (a=ιx(x=a & Fx)) 1,5 ι-conv 1 [7] a=ιx(x=a & Fx 4,5 ι-conv 3 [8] a=ιx(x=a & x b) 3,5 ι-conv 1,3 [9] ιx(x=a & Fx) = ιx(x=a & x b) 7,8 =-TRAN 1,3 [10] (a=ιx(x=a & x b)) 6,9 PSST 2 [11] x x=b 2, -INTRO 1,3 [12] (a b) 10, ι-conv 1,2,3 [13] (b=ιx(x=b & a x) 11,12, ι-conv 2 [14] b = ιx(x=b & Gx) 2,11 ι-conv 2,3 [15] b = ιx(x=b & a x) 3,11 ι-conv 2,3 [16] ιx(x=b & Gx) = ιx(x=b & a x) 14,15 =-TRAN 1,2,3 [17] (b = ιx(x=b & Gx)) 13,16 PSST 1,2,3 [18] (Gb) 17, ι-conv On any reasonable view of modality, the premises cannot genuinely entail the conclusion, since Gb could be a contingent sentence. -ELIM (which need not have been used, and is not used in Neale s more general version) and -INTRO cannot be challenged, so the inference rules to be examined are ι-conv and PSST. An additional possible culprit, one which Neale does not mention, is the assumption that necessity is properly expressed by a sentence connective. A familiar alternative view is that necessity is properly expressed by an expression which forms a closed sentence from an open one, that is, a quantifier. On this view, necessarily p is misleading: necessarily is better written as for all worlds, w, and p would be better rewritten to show the variable w. 8

9 While recognizing that this is the right form of response for some expressions (e.g. it gives a good explanation for why we should not think of Nero fiddled while as a sentence connective, else we might infer Nero fiddled while Bush invaded from the premises Nero fiddled while Rome burned, Bush invaded and Nero Bush ), I will assume that it is not right for modality, so that attention focuses on the principles of inference. A free logician who treats definite descriptions as referring expressions may, like anyone else, have doubts about ι-conv in its full generality (we have mentioned doubts for the case in which T is replaced by an expression like John said that ), but there is little room for doubt about the specific applications in the proof above. The unembedded applications seem sure to be truth preserving. The bidirectional inference between Fa and a=(ιx x=a & Fx) is guaranteed by the logic of identity together with the guiding principle that a definite description ιxgx has as referent, if anything, the unique satisfier of Gx. The truth of Fa ensures that a has a referent, and this cannot diverge from the referent of ιx x=a; adding the conjunct Fx, given that Fa, cannot disturb the referent. The reasoning runs as well in the reverse direction. Everything I have just said could be prefixed by necessarily without loss of truth, so it seems likely that a free logician could not resist a limited version of ι-conv for which T is replaced by and only by. The upshot is that this theorist needs to have something to say about the validity in these contexts of PSST. If the extension of F varies from world to world, so will the extension of ιxfx. The definite description will be non-rigid. One ought not to expect a non-rigid designator to be substitutable salva veritate for a coreferring singular term in a modal context. Yet in effect this is what the proof does at line [17]. By hypothesis, Gb is contingent. So there are worlds at which not-gb, worlds at which G has an extension other than its actual extension. For example, it may have the null extension. With respect to such a world, ιx(x=b & Gx) has no referent. By contrast, the description which this one replaces at line [17] is rigid, assuming that a and b are rigid and that identity and distinctness are rigid relations (at least they should relate any pairs they actually relate at every world at which 9

10 these pairs exist). This is enough to explain why such a replacement in a modal context may fail to preserve truth. I conclude that it is prima facie acceptable to restrict PSST to singular terms which designate rigidly. There is a compelling explanation of why the restriction should be enforced, and (I am assuming) a compelling case in which some such restriction is required even for proper names. If one thought, with Russell, that PSST was a constitutive principle for singular terms, one would instead have to say that arbitrary definite descriptions cannot be treated as singular terms. One would also have to say, as Russell did, that ordinary proper names are not singular terms, in virtue of their failures of substitution in, for example, contexts of attributing beliefs and sayings. Very few would nowadays accept this extreme position. Restricting PSST is a more conservative response. Once it is restricted for proper names in attitude contexts, there is no general reason not to restrict it also for complex singular terms in modal contexts. Within free logic, this allows for the natural view that many definite descriptions are, as they seem, referring expressions. Philosophy Department, University of Texas at Austin. Philosophy Department, King s College London REFERENCES Russell, B. (1912). Problems of Philosophy. Oxford, Oxford University Press (1959). Saul, J. (1997). Substitution and Simple Sentences. Analysis 57:

### Facts and Free Logic. R. M. Sainsbury

R. M. Sainsbury 119 Facts are structures which are the case, and they are what true sentences affirm. It is a fact that Fido barks. It is easy to list some of its components, Fido and the property of barking.

### A Problem for a Direct-Reference Theory of Belief Reports. Stephen Schiffer New York University

A Problem for a Direct-Reference Theory of Belief Reports Stephen Schiffer New York University The direct-reference theory of belief reports to which I allude is the one held by such theorists as Nathan

### 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

### 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

### Cognitive Significance, Attitude Ascriptions, and Ways of Believing Propositions. David Braun. University of Rochester

Cognitive Significance, Attitude Ascriptions, and Ways of Believing Propositions by David Braun University of Rochester Presented at the Pacific APA in San Francisco on March 31, 2001 1. Naive Russellianism

### 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

### 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

### 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

### What is the Frege/Russell Analysis of Quantification? Scott Soames

What is the Frege/Russell Analysis of Quantification? Scott Soames The Frege-Russell analysis of quantification was a fundamental advance in semantics and philosophical logic. Abstracting away from details

### 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

### 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

### Millian responses to Frege s puzzle

Millian responses to Frege s puzzle phil 93914 Jeff Speaks February 28, 2008 1 Two kinds of Millian................................. 1 2 Conciliatory Millianism............................... 2 2.1 Hidden

### 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

### Russell: On Denoting

Russell: On Denoting DENOTING PHRASES Russell includes all kinds of quantified subject phrases ( a man, every man, some man etc.) but his main interest is in definite descriptions: the present King of

### Epistemic two-dimensionalism

Epistemic two-dimensionalism phil 93507 Jeff Speaks December 1, 2009 1 Four puzzles.......................................... 1 2 Epistemic two-dimensionalism................................ 3 2.1 Two-dimensional

### Coordination Problems

Philosophy and Phenomenological Research Philosophy and Phenomenological Research Vol. LXXXI No. 2, September 2010 Ó 2010 Philosophy and Phenomenological Research, LLC Coordination Problems scott soames

### Definite Descriptions and the Argument from Inference

Philosophia (2014) 42:1099 1109 DOI 10.1007/s11406-014-9519-9 Definite Descriptions and the Argument from Inference Wojciech Rostworowski Received: 20 November 2013 / Revised: 29 January 2014 / Accepted:

### 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

### A Liar Paradox. Richard G. Heck, Jr. Brown University

A Liar Paradox Richard G. Heck, Jr. Brown University It is widely supposed nowadays that, whatever the right theory of truth may be, it needs to satisfy a principle sometimes known as transparency : Any

### 16. Universal derivation

16. Universal derivation 16.1 An example: the Meno In one of Plato s dialogues, the Meno, Socrates uses questions and prompts to direct a young slave boy to see that if we want to make a square that has

### Theories of propositions

Theories of propositions phil 93515 Jeff Speaks January 16, 2007 1 Commitment to propositions.......................... 1 2 A Fregean theory of reference.......................... 2 3 Three theories of

### The distinction between truth-functional and non-truth-functional logical and linguistic

FORMAL CRITERIA OF NON-TRUTH-FUNCTIONALITY Dale Jacquette The Pennsylvania State University 1. Truth-Functional Meaning The distinction between truth-functional and non-truth-functional logical and linguistic

### A Defense of the Kripkean Account of Logical Truth in First-Order Modal Logic

A Defense of the Kripkean Account of Logical Truth in First-Order Modal Logic 1. Introduction The concern here is criticism of the Kripkean representation of modal, logical truth as truth at the actual-world

### 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

### 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

### Fatalism and Truth at a Time Chad Marxen

Stance Volume 6 2013 29 Fatalism and Truth at a Time Chad Marxen Abstract: In this paper, I will examine an argument for fatalism. I will offer a formalized version of the argument and analyze one of the

### 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

### Can logical consequence be deflated?

Can logical consequence be deflated? Michael De University of Utrecht Department of Philosophy Utrecht, Netherlands mikejde@gmail.com in Insolubles and Consequences : essays in honour of Stephen Read,

### Williams on Supervaluationism and Logical Revisionism

Williams on Supervaluationism and Logical Revisionism Nicholas K. Jones Non-citable draft: 26 02 2010. Final version appeared in: The Journal of Philosophy (2011) 108: 11: 633-641 Central to discussion

### Resemblance Nominalism and counterparts

ANAL63-3 4/15/2003 2:40 PM Page 221 Resemblance Nominalism and counterparts Alexander Bird 1. Introduction In his (2002) Gonzalo Rodriguez-Pereyra provides a powerful articulation of the claim that Resemblance

### From Necessary Truth to Necessary Existence

Prequel for Section 4.2 of Defending the Correspondence Theory Published by PJP VII, 1 From Necessary Truth to Necessary Existence Abstract I introduce new details in an argument for necessarily existing

### Does Deduction really rest on a more secure epistemological footing than Induction?

Does Deduction really rest on a more secure epistemological footing than Induction? We argue that, if deduction is taken to at least include classical logic (CL, henceforth), justifying CL - and thus deduction

### On possibly nonexistent propositions

On possibly nonexistent propositions Jeff Speaks January 25, 2011 abstract. Alvin Plantinga gave a reductio of the conjunction of the following three theses: Existentialism (the view that, e.g., the proposition

### Understanding Belief Reports. David Braun. In this paper, I defend a well-known theory of belief reports from an important objection.

Appeared in Philosophical Review 105 (1998), pp. 555-595. Understanding Belief Reports David Braun In this paper, I defend a well-known theory of belief reports from an important objection. The theory

### 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

### On Possibly Nonexistent Propositions

Philosophy and Phenomenological Research Philosophy and Phenomenological Research Vol. LXXXV No. 3, November 2012 Ó 2012 Philosophy and Phenomenological Research, LLC On Possibly Nonexistent Propositions

### 2.3. Failed proofs and counterexamples

2.3. Failed proofs and counterexamples 2.3.0. Overview Derivations can also be used to tell when a claim of entailment does not follow from the principles for conjunction. 2.3.1. When enough is enough

### Reply to Kit Fine. Theodore Sider July 19, 2013

Reply to Kit Fine Theodore Sider July 19, 2013 Kit Fine s paper raises important and difficult issues about my approach to the metaphysics of fundamentality. In chapters 7 and 8 I examined certain subtle

### 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

### 1. Introduction. Against GMR: The Incredulous Stare (Lewis 1986: 133 5).

Lecture 3 Modal Realism II James Openshaw 1. Introduction Against GMR: The Incredulous Stare (Lewis 1986: 133 5). Whatever else is true of them, today s views aim not to provoke the incredulous stare.

### Analyticity and reference determiners

Analyticity and reference determiners Jeff Speaks November 9, 2011 1. The language myth... 1 2. The definition of analyticity... 3 3. Defining containment... 4 4. Some remaining questions... 6 4.1. Reference

### 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

### Generic truth and mixed conjunctions: some alternatives

Analysis Advance Access published June 15, 2009 Generic truth and mixed conjunctions: some alternatives AARON J. COTNOIR Christine Tappolet (2000) posed a problem for alethic pluralism: either deny the

### Foreknowledge, evil, and compatibility arguments

Foreknowledge, evil, and compatibility arguments Jeff Speaks January 25, 2011 1 Warfield s argument for compatibilism................................ 1 2 Why the argument fails to show that free will and

### 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

### Bob Hale: Necessary Beings

Bob Hale: Necessary Beings Nils Kürbis In Necessary Beings, Bob Hale brings together his views on the source and explanation of necessity. It is a very thorough book and Hale covers a lot of ground. It

### Class 33 - November 13 Philosophy Friday #6: Quine and Ontological Commitment Fisher 59-69; Quine, On What There Is

Philosophy 240: Symbolic Logic Fall 2009 Mondays, Wednesdays, Fridays: 9am - 9:50am Hamilton College Russell Marcus rmarcus1@hamilton.edu I. The riddle of non-being Two basic philosophical questions are:

### Puzzles of attitude ascriptions

Puzzles of attitude ascriptions Jeff Speaks phil 43916 November 3, 2014 1 The puzzle of necessary consequence........................ 1 2 Structured intensions................................. 2 3 Frege

### Metaphysical Necessity: Understanding, Truth and Epistemology

Metaphysical Necessity: Understanding, Truth and Epistemology CHRISTOPHER PEACOCKE This paper presents an account of the understanding of statements involving metaphysical modality, together with dovetailing

### 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

### Lecture 3. I argued in the previous lecture for a relationist solution to Frege's puzzle, one which

1 Lecture 3 I argued in the previous lecture for a relationist solution to Frege's puzzle, one which posits a semantic difference between the pairs of names 'Cicero', 'Cicero' and 'Cicero', 'Tully' even

### Durham Research Online

Durham Research Online Deposited in DRO: 20 October 2016 Version of attached le: Published Version Peer-review status of attached le: Not peer-reviewed Citation for published item: Uckelman, Sara L. (2016)

### 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

### 15. Russell on definite descriptions

15. Russell on definite descriptions Martín Abreu Zavaleta July 30, 2015 Russell was another top logician and philosopher of his time. Like Frege, Russell got interested in denotational expressions as

### ILLOCUTIONARY ORIGINS OF FAMILIAR LOGICAL OPERATORS

ILLOCUTIONARY ORIGINS OF FAMILIAR LOGICAL OPERATORS 1. ACTS OF USING LANGUAGE Illocutionary logic is the logic of speech acts, or language acts. Systems of illocutionary logic have both an ontological,

### What would count as Ibn Sīnā (11th century Persia) having first order logic?

1 2 What would count as Ibn Sīnā (11th century Persia) having first order logic? Wilfrid Hodges Herons Brook, Sticklepath, Okehampton March 2012 http://wilfridhodges.co.uk Ibn Sina, 980 1037 3 4 Ibn Sīnā

### 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...............................

### Modal Realism, Counterpart Theory, and Unactualized Possibilities

This is the author version of the following article: Baltimore, Joseph A. (2014). Modal Realism, Counterpart Theory, and Unactualized Possibilities. Metaphysica, 15 (1), 209 217. The final publication

### 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

### Boghossian & Harman on the analytic theory of the a priori

Boghossian & Harman on the analytic theory of the a priori PHIL 83104 November 2, 2011 Both Boghossian and Harman address themselves to the question of whether our a priori knowledge can be explained in

### SOME RADICAL CONSEQUENCES OF GEACH'S LOGICAL THEORIES

SOME RADICAL CONSEQUENCES OF GEACH'S LOGICAL THEORIES By james CAIN ETER Geach's views of relative identity, together with his Paccount of proper names and quantifiers, 1 while presenting what I believe

### 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

### 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

### A flaw in Kripke s modal argument? Kripke states his modal argument against the description theory of names at a number

A flaw in Kripke s modal argument? Kripke states his modal argument against the description theory of names at a number of places (1980: 53, 57, 61, and 74). A full statement in the original text of Naming

### Study Guides. Chapter 1 - Basic Training

Study Guides Chapter 1 - Basic Training Argument: A group of propositions is an argument when one or more of the propositions in the group is/are used to give evidence (or if you like, reasons, or grounds)

### Reflexivity NATHAN SALMON*

Notre Dame Journal of Formal Logic Volume 27, Number 3, July 1986 401 Reflexivity NATHAN SALMON* In [38], Mark Richard formulated a new and interesting problem for theories of direct reference with regard

### A Solution to the Gettier Problem Keota Fields. the three traditional conditions for knowledge, have been discussed extensively in the

A Solution to the Gettier Problem Keota Fields Problem cases by Edmund Gettier 1 and others 2, intended to undermine the sufficiency of the three traditional conditions for knowledge, have been discussed

### On Truth At Jeffrey C. King Rutgers University

On Truth At Jeffrey C. King Rutgers University I. Introduction A. At least some propositions exist contingently (Fine 1977, 1985) B. Given this, motivations for a notion of truth on which propositions

### 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.

### Quantifiers: Their Semantic Type (Part 3) Heim and Kratzer Chapter 6

Quantifiers: Their Semantic Type (Part 3) Heim and Kratzer Chapter 6 1 6.7 Presuppositional quantifier phrases 2 6.7.1 Both and neither (1a) Neither cat has stripes. (1b) Both cats have stripes. (1a) and

### A BRIEF INTRODUCTION TO LOGIC FOR METAPHYSICIANS

A BRIEF INTRODUCTION TO LOGIC FOR METAPHYSICIANS 0. Logic, Probability, and Formal Structure Logic is often divided into two distinct areas, inductive logic and deductive logic. Inductive logic is concerned

### Why the Traditional Conceptions of Propositions can t be Correct

Why the Traditional Conceptions of Propositions can t be Correct By Scott Soames USC School of Philosophy Chapter 3 New Thinking about Propositions By Jeff King, Scott Soames, Jeff Speaks Oxford University

### 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

### THE MEANING OF OUGHT. Ralph Wedgwood. What does the word ought mean? Strictly speaking, this is an empirical question, about the

THE MEANING OF OUGHT Ralph Wedgwood What does the word ought mean? Strictly speaking, this is an empirical question, about the meaning of a word in English. Such empirical semantic questions should ideally

### From Grounding to Truth-Making: Some Thoughts

From Grounding to Truth-Making: Some Thoughts Fabrice Correia University of Geneva ABSTRACT. The number of writings on truth-making which have been published since Kevin Mulligan, Peter Simons and Barry

### 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

### Constructive Logic, Truth and Warranted Assertibility

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

### Chalmers on Epistemic Content. Alex Byrne, MIT

Veracruz SOFIA conference, 12/01 Chalmers on Epistemic Content Alex Byrne, MIT 1. Let us say that a thought is about an object o just in case the truth value of the thought at any possible world W depends

### Grounding and Analyticity. David Chalmers

Grounding and Analyticity David Chalmers Interlevel Metaphysics Interlevel metaphysics: how the macro relates to the micro how nonfundamental levels relate to fundamental levels Grounding Triumphalism

### Handout for: Ibn Sīnā: analysis with modal syllogisms

Handout for: Ibn Sīnā: analysis with modal syllogisms Wilfrid Hodges wilfrid.hodges@btinternet.com November 2011 1 Peiorem rule Ibn Sīnā introduces the peiorem rule at Qiyās 108.8 11 as follows: Know that

### Identity and Plurals

Identity and Plurals Paul Hovda February 6, 2006 Abstract We challenge a principle connecting identity with plural expressions, one that has been assumed or ignored in most recent philosophical discussions

### part one MACROSTRUCTURE Cambridge University Press X - A Theory of Argument Mark Vorobej Excerpt More information

part one MACROSTRUCTURE 1 Arguments 1.1 Authors and Audiences An argument is a social activity, the goal of which is interpersonal rational persuasion. More precisely, we ll say that an argument occurs

### Lecture 4. Before beginning the present lecture, I should give the solution to the homework problem

1 Lecture 4 Before beginning the present lecture, I should give the solution to the homework problem posed in the last lecture: how, within the framework of coordinated content, might we define the notion

### Announcements. CS243: Discrete Structures. First Order Logic, Rules of Inference. Review of Last Lecture. Translating English into First-Order Logic

Announcements CS243: Discrete Structures First Order Logic, Rules of Inference Işıl Dillig Homework 1 is due now Homework 2 is handed out today Homework 2 is due next Tuesday Işıl Dillig, CS243: Discrete

### Vagueness and supervaluations

Vagueness and supervaluations UC Berkeley, Philosophy 142, Spring 2016 John MacFarlane 1 Supervaluations We saw two problems with the three-valued approach: 1. sharp boundaries 2. counterintuitive consequences

### 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

### Varieties of Apriority

S E V E N T H E X C U R S U S Varieties of Apriority T he notions of a priori knowledge and justification play a central role in this work. There are many ways in which one can understand the a priori,

### Ling 98a: The Meaning of Negation (Week 1)

Yimei Xiang yxiang@fas.harvard.edu 17 September 2013 1 What is negation? Negation in two-valued propositional logic Based on your understanding, select out the metaphors that best describe the meaning

### A Note on a Remark of Evans *

Penultimate draft of a paper published in the Polish Journal of Philosophy 10 (2016), 7-15. DOI: 10.5840/pjphil20161028 A Note on a Remark of Evans * Wolfgang Barz Johann Wolfgang Goethe-Universität Frankfurt

### Objections to the two-dimensionalism of The Conscious Mind

Objections to the two-dimensionalism of The Conscious Mind phil 93515 Jeff Speaks February 7, 2007 1 Problems with the rigidification of names..................... 2 1.1 Names as actually -rigidified descriptions..................

### 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/

### Revisiting the Socrates Example

Section 1.6 Section Summary Valid Arguments Inference Rules for Propositional Logic Using Rules of Inference to Build Arguments Rules of Inference for Quantified Statements Building Arguments for Quantified

### Generalizing Soames Argument Against Rigidified Descriptivism

Generalizing Soames Argument Against Rigidified Descriptivism Semantic Descriptivism about proper names holds that each ordinary proper name has the same semantic content as some definite description.

### 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.

### On a priori knowledge of necessity 1

< Draft, April 14, 2018. > On a priori knowledge of necessity 1 MARGOT STROHMINGER AND JUHANI YLI-VAKKURI 1. A priori principles in the epistemology of modality It is widely thought that the epistemology

### Kripke on the distinctness of the mind from the body

Kripke on the distinctness of the mind from the body Jeff Speaks April 13, 2005 At pp. 144 ff., Kripke turns his attention to the mind-body problem. The discussion here brings to bear many of the results

### On Infinite Size. Bruno Whittle

To appear in Oxford Studies in Metaphysics On Infinite Size Bruno Whittle Late in the 19th century, Cantor introduced the notion of the power, or the cardinality, of an infinite set. 1 According to Cantor

### Nature of Necessity Chapter IV

Nature of Necessity Chapter IV Robert C. Koons Department of Philosophy University of Texas at Austin koons@mail.utexas.edu February 11, 2005 1 Chapter IV. Worlds, Books and Essential Properties Worlds