DEFINITE DESCRIPTIONS IN A 2-D SEMANTICS FOR EPISTEMIC MODALS
A thesis submitted to the faculty of / San Francisco State University 2 ,f. In partial fulfillment of The Requirements for The Degree
Master of Arts In Philosophy
by
Patrick Daniel Skeels
San Francisco, California
May 2016 Copyright by Patrick Daniel Skeels ©2016 CERTIFICATION OF APPROVAL
I certify that I have read Definite Descriptions in a 2-D
Semantics for Epistemic Modals by Patrick Daniel Skeels,
and that in my opinion this work meets the criteria for approving a thesis submitted in partial fulfillment of
the requirements for the degree: Master of Arts in Phi losophy at San Francisco State University
Dr. Carlos Montemayor Associate Professor of Philosophy
Dr. Bas C. van Fraassen Professor of Philosophy DEFINITE DESCRIPTIONS IN A 2-D SEMANTICS FOR EPISTEMIC MODALS
Patrick Daniel Skeels San Francisco State University 2016
In the following, I begin with some puzzles of epistemic modality, after which I present a 2-Dimensional semantics developed by Holliday that aims to solve them. I then detail how Holliday's semantics interacts with both the Russellian and the Fregean theories of definite descriptions. I conclude that it is compatible with both.
I certify that the Abstract is a correct representation of the content of this thesis.
Chair, Thesis Committee Date TABLE OF CONTENTS
List of Appendices ...... vi
Introduction...... 1
1 A Few Puzzles of Epistemic Modality ...... 4
2 A Two-Dimensional Solution ...... 6 2.1 Informal Introduction...... 6 2.2 Holliday 2015 ...... 8 2.3 Applications...... 11
3 Definite D escriptions...... 13 3.1 Russellian Theory of Definite Descriptions...... 14 3.2 Fregean Theory of Definite Descriptions...... 17
4 Concluding Remarks...... 24
5 Appendix...... 26
6 Works C it e d ...... 34
v List of Appendices
A.l ...... 26 A.2 ...... 26 A.3 ...... 27 A.4: Expanded Truth Conditions for ...... 28 A.5 ...... 28 A.6 ...... 29 A.7 ...... 30 A.8: Equivalence of <3 and 9 R ...... 31 A.9 ...... 32 A .1 0 ...... 32 A . l l ...... 33
vi 1
Introduction
Imagine that we are chatting as we walk past a schoolyard. We notice that some children are about to have a footrace. The mood is playful, yet competitive, and our attention is momentarily pried from our usual philosophical discussion to some thing more visceral. The race begins. It's a close one. But in the end, as you may have guessed, the winner won. After the race unfolds, I utter:
(1) The winner of the race could have lost.
You agree. After all, the race was close, and it wasn't a forgone conclusion that that child was to be the winner. The most natural reading of "could" in this context classifies it as a metaphysical modal. This means that there is a possible world, metaphysically accessible from our own, where that very child didn't win. This is easy enough to imagine. Kripke semantics gives (1) the following truth conditions:
(IT) The person x, who was the winner of the race in zv is such that there is
some world w' metaphysically accessible from zv such that x is not the winner
of the race.
(IT) is perfectly coherent, as we'd expect. Kripke taught us that an object can have nontrivial modal properties independent from its means of individuation ([3] pp 63-67). All in all, a sentence like (1) is perfectly fine, according to both our semantics and our ears. 2
Now suppose that the conversation went just a little differently. The scenario plays out exactly the same as before, but instead of uttering (1 ), I utter:
(2) #The winner of the race might have lost.
Rather than agreement, I'm met with a perplexed look. Something about this sen tence isn't quite right. Unlike "could", "might" is most naturally read as an epis- temic modal. An epistemic modal allows for possibility and necessity, but only relative to an information state. An information state is a set of possible worlds, each of which is seen as a candidate for the real world. As an agent comes to be lieve a proposition, she eliminates worlds from the information state where that proposition is not true ([6] pp 86-87). Recall that we came to believe that a particu lar individual won, which means that we've eliminated all worlds where that same individual didn't win from our information state. But this means that an utterance of (2) says that the very worlds that have been eliminated are somehow still candi dates for the real world. Understood this way, (2) doesn't just sound strange. It is contradictory. We expect this to be apparent in the truth conditions:
(2T) The person x, who was the winner of the race in w is such that there is
some world w' in information state I that is epistemically accessible from w
such that x is not the winner of the race.
Interestingly, (2T) is satisfiable, despite the contradiction! A state of ignorance regarding the race result would include both w and w' and would satisfy (2T), but 3
(2) is contradictory, and should not have satisfiable truth conditions. Something is wrong.
We find ourselves in a predicament. An utterance of (2) is infelicitous because it is contradictory to individuate an object with a property while simultaneously entertaining that it does not have that property. Nonetheless, (2) has perfectly sat isfiable truth-conditions. The problem generalizes. It appears that the epistemic modal properties of an object must be dependent on the way the object is indi viduated, if the sentence containing the modal is to be felicitous ([8] pp 475-477).
Returning to (2), the information state can only include worlds where the winner in w won, since we've individuated this child as "the winner". Standard possible world semantics does not account for this unique behavior. We need a semantics that does.
In the following, we'll take a look at a brand new two-dimensional semantics that predicts the behavior of epistemic modals. The semantics, which we'll call
Holliday 2015, is a work in progress, and presently lacks a theory of definite de scriptions. The technical aim of the paper is to provide Holliday 2015 with a theory of definite descriptions which allows it to make the proper predictions. There are many theories fit for candidacy, the two most prevalent of which are the familiar
Fregean and Russellian theories. We shall outfit the system with each and observe the formal results. As we shall see, both theories are compatible. The philosoph ical implications of these results are of no small consequence, as other semantics 4
designed to predict the behavior of epistemic modals, most notably Yalcin 2015, are not compatible with the Fregean theory of definite descriptions ([11] pp 7-8).
As such, the broader, more philosophical goal of the paper will be to see what the newer problem of epistemic modals has to say about the much older problem of definite descriptions. More narrowly, I'll argue that with the introduction of Hol liday 2015, the Fregean is, in fact, capable of predicting the behavior of epistemic modals.
1 A Few Puzzles of Epistemic Modality1
We began with a puzzling asymmetry between (1 ) and (2). The problem is not limited to epistemic modals bound by definite descriptions. We notice further asymmetries with indefinites. The following universally or existentially quanti fied sentences are reported as infelicitous:
(3) #Some person who is not infected, might be infected.
(4) ??2 Some person who might be infected, is not infected.
(5) #Some person who is not infected and might be infected, is quarantined.
(6) # Every person who is not infected, might be infected.
(7) #Every person who is not infected and might be infected, is quarantined.
'The data and examples are taken from the handout in Modalities of Discourse Seminar at UC Berkeley Spring 2015. "Problems of Quantification." Seth Yalcin. 1/28/2015. 2This sentence is reported as less marked than the others. 5
Like (1) and (2), a standard relational semantics predicts satisfiable truth conditions for (3)-(7). For example:
(3T) There is some person x who is not infected in w such that there is some
world w’ in information state I epistemically accessible from zv such that x is
infected.
(3T) is satisfiable, despite the fact that (3) is marked. The situation is the same for (4)-(7). Things are further complicated by the fact that (4) is reported as "less marked" than (3) while still being infelicitous. The only difference between the two is the order of the restrictor and the nuclear scope. The phenomenon generalizes, and propositions containing epistemic modals of the form -x^A
Let us take stock. First, we noticed the difference between (1) and (2), and that the epistemic modal properties of an object can be dependent on they way that the object is individuated. Secondly, the differing reports of (3) and (4) suggest that order is relevant to felicity. Lastly, standard relational semantics are of no help regarding these difficulties since it allows for sentences that cannot be felicitous to have satisfiable truth conditions. We need an alternative. 6
2 A Two-Dimensional Solution
In the following we'll consider a recent contribution to semantics developed by
Holliday. I'll introduce the system informally before diving into the details.
2.1 Informal Introduction
We notice a discrepancy in felicity between structurally similar sentences. Sen tences of the form are okay when the modal is metaphysical, but not when it is epistemic. To solve our problem, we need to account for the fact that each world in the information state must be compatible with the means of individuat ing the object in question. 2-D semantics is especially appropriate for the job.
For Holliday 2015, as well as any other 2-D semantics, each sentence has two dimensions of evaluation. Each of these dimensions or "slots" is filled by a world.
We'll call the slots wi and w2. We'll use zv, vo', zv", and so on for particular worlds, and v for arbitrary worlds. Each semantic evaluation will begin with the home world, zv inhabiting both slots Wi and zv2- The trick here is that modal operators shift which worlds fill the two slots. We recognize two such primitive modal op erators: (>e, and 0 *, which represent epistemic and metaphysical possibility, re spectively3. To capture the difference in modal behavior, they shift the worlds of evaluation differently. Consider (1), where the modal is metaphysical. We start with both slots inhabited by the home world w. The metaphysical modal (skip
3For simplicity, we restrict our attention to these two types of modality 7
ahead to semantic clause 4 for details) shifts the world inhabiting the second slot to a new metaphysically accessible world, w' where the winner in zv did not win.
This is merely the 2-D version of (IT), and yields satisfiable truth-conditions.
Now consider the epistemic modal. Merely changing the accessibility relation from metaphysical to epistemic isn't good enough. Instead, the semantic clause for epistemic modals (semantic clause 5) shifts the worlds in both slots to a world, u in the information state. This allows us to capture the contradiction that eluded us earlier. Consider (3). The epistemic modal clause shifts both worlds of evaluation to a world v where someone is infected. It then sees if that very same someone is not infected at that world. This is impossible, making (3) unsatisfiable. This is the prediction we'd like to see, as sentences that are not satisfiable won't be felicitous.
It should also be noted that Holliday 2015 makes use of dyadic quantifiers.
It is widely held that determiners semantically combine with a restrictor and nu clear scope, which dyadic quantifiers allow us to capture ([9] pp 3-5). All of the sentences that we will be dealing with consider objects with at least two proper ties, making dyadic quantification appropriate. Holliday 2015 possesses monadic quantifiers, but they will not play a role in the present conversation. We now turn our attention to the formal details. 8
2.2 Holliday 20154
Given a set Var = {xi, x2, . . .} of variables and a set of Pred" = {P", P2, . . .} of n-ary predicate symbols for each n e N, our language C is defined by the following grammar:
• 4> ::= P(yi, . . . ,y n)\~4>\ (
, yn, x € Var, P e Pred", and k e { 1 , 2} .
For simplicity, we do not include function or constant symbols. We define the following abbreviations:
• Om :=
• □ e(/) '.=
• VfeX {(j>, ip) := -<3fcx ((j) , -t0)
A model for our language is a tuple M =
1. W and D are nonempty sets of worlds and objects, respectively;
2. Rm is a binary relation on W, representing metaphysical accessibility;
3. F is a set of partial functions/: W i—> D, called individual concepts;
4. V is a valuation function such that for any P e Pred" and
w eW , V(P, w) C D".
4This section is taken directly from the handout "Notes on Seth's Puzzles v. 3.2". 9
A variable assignment is a function /j, that sends each variable x to an individual concept n(x) : W i— > D, which is not required to be a member of F. If /i(x) is defined at w, then fj,(x)(iv) is an object. Given a variable assignment //, variable x, and individual concept/, we define n[x >—> f] as follows: /i[x i—> *](*) =/ and for all y
^ x, iAx i— >f](y) = ^(y)-
We define the truth of a formula relative to a model At, information state I C
W, pair of worlds < u>i,zu2 >, and variable assignment n as follows:
1 . At, I, W\, u>2 |=^ P(yi,. . . , y„) iff /^(y^) is defined at Wj for 1 < z < n and <
M(yi)(wi),.. •, ntyn){wi)> € v (P, w2);
2. At, I, Wi, w2 |=> _1 < t > -M/ ¥=» 3. A t f, Wi, w2 4. At, I, Wi, w2 h/i iff 3i> 6 W: w2R™ and At, /, wu v (=M 5. At, I, u>i, w2 -O’e 6. At, I, zvi, zv2 \=n 3kxcp iff there is a g € F such that: (a) for all u (b) g is defined at wk; (c)M , I, zvk, w2 (t)- 7. At, I, Wi, w2 f=M 3 kx{(j) , ip) iff At, I, w2, w2 1=^ 3kxtp and there is a g e F such that: 10 (a) for all u e W, if g is defined at u, then M , I, u, u ; (b) g is defined at wk; (c)M , I, wk, w2 \ = ^ g] ip. 8. M , I, Wi, w2 (=M 3kX((j>, ip) iff M , I, w2, w2 %xip of there is no g e F such that: (a) for all u e W, if g is defined at u, then M , I, u, u 4>', (b) g is defined at zvk; (c)M, I, wk, w2 '0 - A formula (j) is satisfiable iff there is some model M, information state I, world w, and variable assignment fi such that M , I, w, w |=M 4>; otherwise it is unsatisfi- able. A formula 4> is acceptable iff De A formula Notice that all quantifiers are indexed with a 1 or a 2. This index determines which world the quantifier is "talking about." Consider the following: (8) It could have been that everyone rich was nice. This sentence has two readings. The first reading says that there is an accessible world where everyone who is rich in the actual world is nice there. The second reading says that there is an accessible world where everyone rich in that world is also nice in that world. These readings can be represented as: 11 (8i') OmVix(Rx,Nx) (82O OmV2X(Rx,Nx) (81') and (82') are formalizations of the first and second readings, respectively. The quantifier index determines at which of the two worlds in question the quantifier is evaluated5. This allows us to capture readings that are otherwise unavailable. 2.3 Applications6 Holliday 2015 allows us to determine truth conditions and predict felicity when quantifiers bind into metaphysical or epistemic modals. Sentences that are not satisfiable in Holliday 2015 should be infelicitous when uttered in context and will be marked with a #. Consider the sentences: (9) Some person who is not infected, could have been infected. (3) #Some person who is not infected, might be infected. These may be formalized as: (9') 3ix(->In(x), OmIn(x)) (3') 3lXH n (x ), 0 eH x)) 5You may also notice that both the existential and universal quantifiers are primitive. This has been done to solve some puzzles regarding duality that are beyond the scope of the present discussion. 6Some, but not all example sentences have been taken from the handout, Notes on Seth's Puz zles v. 3.2 from Modalities of Discourse Seminar at UC Berkeley Spring 2015. 12 Observe that (9') is satisfiable7 while (3') is not8. These are precisely the results that we'd like to see. (3') instantiates the "bad thing" (~«j>A^e ), and cannot be uttered felicitously (9') on the other hand, is just fine because the modal is metaphysical. We may now return our attention to sentence 4, which can be formalized as: (4') 3lX(0eIn(x), ^ln(x)) (4') is satisfiable9. Recall that (4) is merely a reordering of the restrictor and nuclear scope of (3). (4) was controversial, insofar as it was considered marked, but notably less so than sentences of the opposite ordering. The semantics above distinguishes these two with the notion of acceptability. A formula 503). The formal notion of acceptability provides a way to predict the data in the terms presented, but is more speculative than the rest of the system since ?? cases are unclear. For this reason we shall focus on which sentences are satisfiable within Holliday 2015 and leave questions of acceptability for the future. For the purposes 7Proof in Appendix A.l 8Proof in Appendix A.2 9Proof in Appendix A.3 13 of this paper, felicitous sentences and borderline sentences should be satisfiable, while infelicitous ones should not be satisfiable. The following sentences quantify into epistemic modals and are not satisfiable: (10) #Everyone who is not infected might be infected. (11) #Someone who is not infected and might be infected is quarantined. (12) ^Someone who might be infected and is not infected is quarantined. Notice that sentences like (10), where objects have epistemic modal properties that conflict with the way they are individuated are always unsatisfiable and predicted as marked. Sentences that do this with metaphysical modal properties are fine10. Sentences such as (11) and (12), with epistemic contradictions of any order within the restrictor or nuclear scope, are also unsatisfiable. Holliday 2015 is able to take quantified modal sentences and determine felicity. It allows objects to have metaphysical modal properties independent from how the object was specified, but does not allow objects to have epistemic modal properties of this sort. 3 Definite Descriptions While Holliday 2015 can predict the behavior of simple quantified sentences, it falters as soon as we introduce sentences with definite descriptions such as (1 ) and 10For 13-15, if you replaced "might" with "could" (changing the modal from epistemic to meta physical) they would be felicitous. 14 (2). The obvious thing to do is to outfit Holliday 2015 with a suitable theory of definite descriptions. We'll consider both the Russellian and the Fregean theories. 3.1 Russellian Theory of Definite Descriptions The Russellian theory offers a quantificational account of definite descriptions. While there is variation, all Russellian theories make the same fundamental claim, namely, that each sentence of the form: (13) The F is G. can be broken down into three smaller claims: • There is an F. • At most, one thing is F. • Something that is F, is G. Any sentence with the form of (13) is comprised of three smaller sentences. In order for the sentence to be true, all three of its constitutive sentences must also be true ([7] pp 481-483). If one fails to hold, the entire sentence is false. Russell's classic example: (14) The present King of France is bald. is false, because it fails to satisfy (at least) one of the three criteria. There is no present King of France. The standard formalization for sentences of this type is: 15 (13'R) 3x(FxAVy(Fy—>x=y)AGx) This formalization is entirely quantificational and does not require any specific object to satisfy the aforementioned criteria. In other words, the theory is not object dependent ([4] pp 25-28). We won't discuss the general philosophical strengths and weaknesses of the Russellian theory and shall maintain a narrow focus on how the Russellian theory of definite descriptions interacts with Holliday 2015. Since the Russellian view is quantificational and our semantics is equipped with existential as well as universal quantifiers, we already possess the requisite machinery to construct a Russellian definite description. Holliday 2015, however, makes use of dyadic quantifiers, so we cannot simply take the formalization (13'R) and plug it into our 2D semantics11. Happily, a dyadic quantifier can be con structed out of the existing grammar. Consider again, the system presented in section 2.2. We can add the following definition to the abbreviations provided: • 43kx{(j)x, Tpx) =Def 3fcx((xAVy(0y, x=y)), V>x)12 As with (13'R), this formalization has an existential claim, a uniqueness claim, and a maximality claim. As with other quantifiers in Holliday 2015, i3 is indexed with a k to determine at which world the quantifier is to be evaluated. When formal izing natural language sentences, the i3 quantifier will be used for the definite description, "the". For example, a sentence such as (1) will be formalized as: u Our specific puzzles are quantified dyadically, so our definite description will follow suit. 12Expanded truth conditions for this definition in Appendix A.4. 16 (l'R) l3 iX(Wx, Om ^Wx) Using the definition for i3 provided (l'R) can be expanded. Truth conditions can then be determined as normal using the semantic clauses. As desired, (l'R) is satis fiable. This method, while tedious, predicts correctly that the following sentences are unsatisfiable13: (14) #The man in sunglasses is standing next to the man in sunglasses. (14'R) l3 ix(Mx, t3iy,{My, Sxy)) (15) #The person who isn't infected, might be infected. (15'R) i3ix(->Inx, 0 Inx) Sentences like 16'R, however, are satisfiable14. Observe: (16) ?? The person who might be infected, isn't infected. (16'R) L=iix(()Inx, - As desired, sentences structurally equivalent to (15'R) and (16'R) with metaphysi cal instead of epistemic modals are perfectly satisfiable. Thus far t3 makes the predictions that we're looking for. Proofs, however, are noticeably more protracted than structurally similar sentences involving indefinite descriptions. A shortcut is in order. Recall semantic clause 7 from section 2.2 for dyadic existential quantifiers. This clause can be modified slightly to become: 13Proofs in A.5 and A.6 14Proof in A.7 17 9R. M , I, W\, ZV2 \=^i3kx{(!), xp) iff M , I, w 2, u>2 1=^ 3 kX ip and there is a unique g e F such that: (a) for all u e W, if g is defined at u, then M , I, u, u (b) g is defined at wk-, (c) M , I, wk, w2 V'- Observe that semantic rule 9R is exactly like 7 except for the individual concept g must be unique. Further, 9R is equivalent to the expanded definition for the i3 quantifier15. As such, derived rule 9R can be used to determine truth conditions for l3 quantified sentences. This method is significantly simpler. From a technical perspective, The Russellian theory has provided everything we need, and makes the proper satisfiability predictions when definite descrip tions bind into epistemic modals. Let's now consider the Fregean alternative. 3.2 Fregean Theory of Definite Descriptions Unlike the Russellian, a Fregean definite description cannot be captured quantifi- cationally; not just any object will do. Consider a sentence like (13). For the Rus sellian, (13) is true iff there is some unique object F that is also G. It doesn't matter which object. Not so for the Fregean, who claims that the truth of the proposition is dependent on one very specific F, and whether or not it is G. For the Fregean the definite descriptive phrase must (if working correctly) semantically refer. Thus, 15Proof in Appendix A.8 18 [The F], refers to one, and only one, object16. ([1], pp 45.) When a Fregean definite descriptive phrase does not refer, e.g. [The present King of France], the sentence receives no truth-value, rather than a truth-value of false ([4] pp 26). From a formal perspective, this means that Fregean definite descriptions are terms as opposed to quantifiers. Consider the Fregean formalization of (13): (13'F) G(lF) Here, we have the term " if' which behaves like any other term (e.g. a constant or a variable under a variable assignment) in that it picks out a particular individual in the domain, in this case, "the F". This term falls under the predicate G in the usual way, and we get "The F is G". The question arises as to how Fregean definite descriptions pick out unique objects. Consider again, an utterance of (1). The world contains multitudes of races and their winners, yet the Fregean theory demands uniqueness. To solve this problem, modern Fregeans make use of a situation pronoun. A situation pro noun accompanies each determiner phrase17, ([1] pp 38, [5], pp 2.) These situation pronouns are not visible at the level of surface grammar. Each situation pronoun tells us what situation the determiner phrase is "talking about". A situation is a nonempty set of objects under certain relations, in other words a part of a possible world, ([1], pp 30-32.) Since the situation under which the determiner is oper ating is determined by the situation pronoun, the object denoted by the definite 1616 A Russellian definite description isn't required to semantically refer ([4] pp 25). 17"The" is the only determiner phrase we need to worry about for the present discussion. 19 description need only be unique relative to that situation. Under this model, def inite descriptions are functions from worlds to objects, ([9], pp 8.) The situation pronoun is the input, and the unique object is the output. Let's look at an attempt at a formal theory. Consider again the original frame work presented in Section 2.2. As of now, the only terms Holliday 2015 supports are variables, which means that new grammar must be introduced. Accordingly, the following will be added to the existing grammar of Holliday 2015: f t ::= \)i I tkP I iOeP I LkOmP | We now have four kinds of terms in our language: variables and three definite descriptions. Each definite description is a function from worlds to objects. The type of property of the definite description (either vanilla, metaphysical modal, or epistemic modal) determines the unique presuppositions associated with its deno tation. Here are the definitions for the new grammar: The interpretation [f] M, I, W\, w?, n of a term fin a model M. and infor mation state I, at worlds W\ and zv2 with respect to assignment fi is an object given by: [i/<] m J, wi,w2,/^ = a*(i/*); [tfcP] = the individual concept g € F which takes a world, € W and returns the unique object which is P at Wk if such there be, otherwise undefined18. 18[tfeP] presupposes M, I, wk, w2 (=M Px. 20 [tfcOmf’] M:L Z0i,w2, n = the individual concept g 6 F which takes a world, wk G W and returns the unique object which is P at some world v e W : WkRmv, if such there be, otherwise undefined19. [< returns the unique object which is P at v if such there be, otherwise unde fined20. Each Fregean definite description is a function from worlds to objects, which means that uniqueness is at the object level rather than the individual concept level. It also ensures that sentences containing non-referring definite descriptions will be undefined as opposed to false. The denotation function of each Fregean definite description presupposes the existence of the unique object relative to a sit uation. Notice that semantic clauses 4 and 5 from section 2.2, apply to properties, not terms. The Fregean cannot use them to shift the worlds of modal properties within the describing phrase. My strategy will be to use the presuppositions of fered by the denotation of each term to do the world shifting. Different kinds of terms were required since their denotations come with differing presuppositions. In this way, the presuppositions allow the definite descriptions to do the world shifting without a quantifier. However, we still have the problem of multiple read ings. Consider: (17) The winner of the race could have been nice. presupposes 3wk e W: wkRmv and M , I, wk, v |=M Px. 20[(-OeP] presupposes 3v e I: M , I, v, v |=M Px. 21 This sentence has two readings. Since the Fregean theory is not quantificational we cannot rely on a quantifier index to determine which reading we are trying to capture. Instead, terms are indexed, and the index determines the situation pronoun associated with the presupposition. Observe: (17'iF) 0 m N ( n W ) (17'2F) O m N (L 2 W ) This allows us to distinguish between the two readings because it determines how the presuppositions will shift the worlds. With these new terms in tow, let's look at a few sentences: (18) The person who is infected, could have not been infected. (18'F) Om^In(tln) (18'F) is satisfiable21, just as we'd expect, since the modal is metaphysical. If we return our attention to (16), the new Fregean formalization will be: (16'F) - In(cOeIn) which is satisfiable22. Things become more complicated when modal properties are contained within the term. Consider again (16)'s evil twin, (15), which is for malized: 21 Proof in Appendix A.9. 22Proof in Appendix A.10. 22 (15'F) 0 eIn(i->In) Here, albeit in a Fregean guise, we have "the bad thing." (15'F) is unsatisfiable23. So far, the Fregean theory has been able to predict the behavior of epistemic modals for the sentences considered. This is significant given the Fregean's in compatibility with Yalcin's dynamic approach. The Fregean theory I've proposed is substantially more complicated than the Russellian alternative. This comes as no surprise, since the Fregean claims that definite descriptions do quite a bit more than the Russellian does (namely, refer.) Also unsurprisingly, increased complexity breeds new problems, two of which I'd like to discuss. The first problem may be called the problem of complex modal terms. Notice that the three Fregean terms contain, at most, one modal operator. Given that the denotation of each kind of term requires a different presupposition, a term with embedded modals, especially of differing kinds, will have to have new and uniquely structured presuppositions when it is denoted. The number of terms re quired would continue to grow as we embed modals. This process could continue indefinitely, resulting in an arbitrarily large number of different terms whose de notation functions each have unique presuppositions. I haven't figured out how to systematize this, but I suspect it's perfectly doable. Recall, however, that the purpose of Holliday 2015 is to predict the behavior of epistemic modals in natural language. None of the sentences we've considered 23Proof in Appendix A .ll. 23 have been of the form "might be could be The second problem has to do with free variables in the describing phrase24. Consider the definite description, "The brother of y"25. Since the Fregean insists that definite descriptions refer by themselves, we cannot use variable assignment /i to get rid of y. Until we know what y points to, the denoting phrase doesn't refer. To redress this, I'll appeal to the notion of a minimal situation. Given a proposi tion p, a minimal situation s, is a situation which contains the smallest number of particulars, properties, and relations that will make p true, ([1], pp 24-25.) As I've already mentioned, the determiner phrase "the" contains a situation pronoun. Consider: (18) The brother of her is infected. (Her brother is infected.) (18'F) In(iiBy) In order to make (18) true, we need a thin particular a, that has relation B with the denoted particular, which has property In. If the situation pronoun of the deter miner phrase is minimal, then the free variable y must refer to a; there's no other option26. If we require that situation pronouns be minimal situations, describing phrases with a free variable aren't a problem, since we'll always know exactly 24This is a problem for the Fregean in general and is not specific to Holliday 2015. 25This is interchangeable with the less awkward "Her brother". 26 We know automatically that B isn't reflexive. If it were, a would not be in the minimal situation. what particular the free variable refers to. This tactic was initially developed to solve problems concerning anaphora, ([1], pp 25,133-134.) but I'm happy to help myself to it here. Unfortunately, the problem rears its head again in certain describ ing phrases with two or more free variables27. In such situations there must be at least two thin particulars that are not the object denoted, but it is unclear which is which. It is my suspicion that sentences such as these would not be felicitous in the absence of ostention by the speaker, but to defend this would require another paper entirely I find neither of these responses to be wholly satisfactory, so these problems will have to remain open for the time being. Ultimately these issues may prove in tractable, but my hope is that the solutions I've proffered warrant some optimism. 4 Concluding Remarks This project began with the modest goal of providing a theory of definite descrip tions for a very nascent static alternative to Yalcin 2015. This goal has been met and surpassed. The real winner here is Holliday 2015. Between the two semantics, we now can model the behavior of epistemic modals dynamically or statically. Holl iday 2015 not only supports a Russellian theory of definite descriptions, but also brings the Fregean theory into the fray. The Fregean proposal is a bit rough around the edges, but shows promise, and demands further research. 27Consider, [The object one third of the way between this and that]. The minimal situation cannot tell us which thin particular is [this] and which is [that]. 25 As it stands, the Russellian still has the upper hand regarding our two-dimensional approach. The theory is simpler, requires no new grammar, and brings with it no new problems. Those uninterested in the Frege Russell debate are incentivized to pick the Russellian theory, as the Fregean theory offers no local advantages. Philos ophy, however, is a holistic affair, and there is no shortage of independent reasons to espouse the Fregean theory. To tip my hand a bit, I support the Russellian the ory both in Holliday 2015 and in general, but the Fregean, often to my frustration, remains a stalwart adversary. The century long back and forth between the two has been a painstaking game of inches. However the chips may fall regarding my Fregean proposal for Holliday 2015, the Russellian can no longer lay claim to epistemic modal territory by forfeit. 26 5 Appendix A.l (9) Someone who is not infected could have been infected. (9') 3lxHn(x), OmMx)) M , I, w, w f=M 3ix(-iln(x), <>mIn(x)) iff there is a g e F such that (a) for every u o 3w' € W: wRmw’ and M , I, w, w 1 = ^ In(x) «=> 3w' e W: wRmw' and ^[x\— »g](x) is defined at w and /j,[x\— »g](x)(w) € V(ln, w 0 3w' 6 W: zvRmzv' and and g is defined at w and g(w) e V(In, w'). which is clearly compatible with the other conditions so 9' is satisfiable. A.2 (3) #Some person who is not infected, might be infected. (30 3ixH n(x), OeIn(x)) M , I, vo, w |=M 3ix(- 3zv' E I: M , zv, zv h * ^ In(x) 4$ 3zv' 6 I: n[x\—>#](*) is defined at zv and p[x\— >g](x)(w) E V(In, zv') & 3zv' E I: and g is defined at zv' and g(zv') E V(In, zv'). But if g is defined at zv', then by (a) above, g(zv) V(In, zv'), so we cannot have g(zv') E V(In, zv'). Thus 3' is not satisfiable. A.3 (4) Someone who might be infected, isn't infected. (4') 31x(0eIn(x), -iln(x)) M , I, zv, zv [=„ 3ix({}eIn(x), -^In(x)) iff M , I, zv2, zv2 (=AJ[M?| 3ix(->Inx) and there is a g E F such that (a) for all u E W if g is defined at u, if g is defined at v, then M , I, u,u O eln(x), iff 3zv' E I: M , I, zv', zv'Hu*-*] Inx iff 3zv' E I: n[xi—»g](x) is defined at zv' and n[x<— >g](x)(w') e V(In, zv') iff 3zv' E I: g is defined at zv' and g(zv') E V(In, zv') (b) g is defined at zvi and (c) M , I, zv!, zv2 ~'In(x). iff fi[x\— ►#](*) is defined at zv and n(x)(zv) £ V(In, zv) 28 These are compatible, so 4' is satisfiable. A.4: Expanded Truth Conditions for l3 B kx{(j)x, tpx)= D ef 3fex(( M , I, w, w \=n[x^ y^ 3 kx{{(t)xr\Vy(^y, x=y)), ^x) iff M , I, w2, w2 (=m and there is a g € F such that: (b) g is defined at (c) M , I , n>i, w2 K (a) For all u e W if g is defined at u, M , I , u , u ^Vy(0y, x=y) iff either X , I , u , u 3fcy(x^y) or there is no/ € F such that: (a) (b) F is defined at u; (c) m , i , v , v A.5 (14) #The man in sunglasses is standing next to the man in sunglasses. (14'R) l3x(Mx, i3y(My, Sxy)) M , I, w, w t3kx(Mx, i3ky{My, Sxy)) iff M , I, w2, w2 K [ ^ ,y^ 3kXi3ky(My, Sxy)) and there is a unique g € F such that: 29 (a) for all u e W, if g is defined at u, then M , I, u, u (b) g is defined at wk; (c) M , I, wfe, w2 \=^gy^ i3 ky{My,Sxy) iff At, I, w2, w2 ' r ^ ^ S x y and there is a unique g E F such that: (a) for all u G W, if g is defined at u, then M , I, u,u (b) g is defined at wk; (c) M , I, wkr w2 )rnw dky(My) We can stop here by noticing that the only way for the g to be unique is if x=y. If we assume that the standing next to relation S is not reflexive, then 14'R is not satisfiable. A.6 (15) #The person who isn't infected, might be infected. (15'R) i3ix(-‘ln(x), $ eIn(x)) M , I, w, w f=M x(-^In(x), OeIn(x)) iff there is a unique g e F such that (a) for every u e W, if g is defined at u, then g(u) £ V(In, u), and (c) we have &3w' € I: M , w, w In(x) <=>3w' G I: /.i[xi—>-g](x) is defined at w and /i[x— >g](x)(w) e V(In, w') &3w' e I: and g is defined at w' and g{w’) e V(In, zv'). 30 But if g is defined at zv', then by (a) above, g(w) V(In, zv'), so we cannot have g(zv') 6 V(In, zv’). Thus 15'R is not satisfiable. A.7 (16) The person who might be infected, isn't infected. (16'R) 13^ (0 Jn(x), ->In(x)) M , I, zv, zv [=Mi31x (0 eIn(x), ~'In(x)) iff M , I, zv2, zv2 (=/1[r^?| 3ix(-^Inx) and there is a unique g E F such that: (a) for all u e W if g is defined at u, if g is defined at v, then M , I, u, u i_+x| OeMx), iff 3zv' e I: M , I, zv’, w '\ = ^ g] Inx iff 3zv' e I: fi[xi—^g](x) is defined at zv' and n[x\— >g](x)(w') e V(In, zv') iff 3zv' G I: g is defined at zv' and g(zv') e V(In, zv’) (b) g is defined at zvi and (c) M , I, zvi, zv2 ~ iff /i[xi— )-§-](x) is defined at zv and n{x)(zv) £ V(In, zv) These are compatible, so 16'R is satisfiable. 31 A.8: Equivalence of l3 and 9R Observe the definition of i3: B kx{(j)x, 4)x) =Def 3fcx((^xAVy(0y, x=y)), ipx) M , I, w, w \ = ^ g^ A 3fcX(W>xAVy(y, x=y)), ipx) iff M , I, w2/ w2 |=m 3kxip and there is a g e F such that: (b) g is defined at wk; (c) M , I, wu w2 1 (a) For all u e W if g is defined at u, M , I, u, u X=V) Now, observe the truth conditions for l3: M , I, W\, w2 , ip) iff M , I, w2, w2 \=n 3kxrp and there is a unique g e F such that: (a) for all u e W, if g is defined at u, then M , I, u, u 0; (b) g is defined at zvk; (c) M , I, wk/ w2 ^ ip . Notice that with the exception of the parts underlined, the two formulations are exactly the same. An individual concept g is unique iff for all worlds, if the con cept is defined at that world, then any other individual concepts that pick out that same thing, is also g. If we accept this definition of "unique", then the underlined sections are interchangeable, and the two are equivalent. 32 A.9 (18) The person who is infected, could have not been infected. (18'F) Om^In(dn) M , I, zv, iv \=^ 0 m~'In(dn) iff 3zv' e I: w ^ w ' and M , I, zv, zv' [=M -iln(dn) iff M , I, zv, zv' In(dn) iff {tin) is defined at zv and dn V(In, zv') This says that the individual concept dn that picks out the unique infected individ ual at zv picks out an uninfected individual in zv' that is metaphysically accessible to zv. 18'F is satisfiable. A.10 (16) The person who might be infected, isn't infected. (16'F) -fn(tOefn) M , I, zv, zv f=/i-'/tt(iOJrt) iff M , I, zv, zv ^-iZtt(tOeJn) iff (i(}eIn) is defined at zv and (t<>eIn)(zv) ^ V(In, zv) (i<0>eln presupposes): Bzv' e I: M , zv’, zv’ \=»[x^g] Inx iff n[x i— > g] (x) € V(In, zv') iff g is defined at zv' and g(zv') e V(In, zv') 33 This says that the individual concept c()eIn that picks out the person that isn't infected at xv picks out someone who is infected in xv'. 16'F is satisfiable. A .ll (15) #The person that isn't infected, might be infected. (15'F) OeIn(L-iIn) M , I, xv, w |=M 3xv' e I: M , I, xv', xv' f=M In) iff (t-^ln) is defined at xv' and (t->In)(xv') e V(In, xv') This says that the individual concept that picks out an infected person at xv' picks out an uninfected person at xv'. 15'F is not satisfiable. 34 6 Works Cited [1] Elbourne, Paul. Definite Descriptions. New York: Oxford University Press, 2013. [2] Holliday, Wesley. "Notes on Seth's Puzzles v.3.2" Handout from Phil 290-6: Modalities of Discourse Seminar at UC Berkeley Spring 2015. [3] Kripke, Saul. Naming and Necessity. Cambridge, Massachusetts: Harvard Uni versity Press, 1980. [4] Neale, Stephen. Descriptions. Cambridge, Massachusetts: The MIT Press, 1990. [5] Schwarz, Florian. "Situation Pronouns in Determiner Phrases." Natural Lan guage Semantics. (2012) 20:431475. [6] Stalnaker, Robert. Context and Content. New York: Oxford University press, 1999. [7] Russell, Bertrand. "On Denoting." Mind. (1905) 14.56: 479-493. [8] Yalcin, Seth. "Epistemic Modality De Re." Ergo. (2015) 2.19:475-527. [9] Yalcin, Seth. "Problems About Quantification." Handout from Phil 290-6: Modal ities of Discourse Seminar at UC Berkeley Spring 2015. 1-28-15 [10] Yalcin, Seth. "Epistemic Modals." MIT Working Papers in Linguistics. (2005) 51:231-272. [11] Yalcin, Seth. "Quantification, Conditionals, and Description Dynamically." Handout from Phil 290-6: Modalities of Discourse Seminar at UC Berkeley Spring 2015. 1-28-15