| In Defense of the Mantra | Kiel Moreland Philosophy of Language Dr. Janice Dowell |
Introduction
There are a number of interesting philosophical issues pertaining to the epistemic modal “must”, and issue that I want to explore in this essay is the strength of “must”. Consider the following statements:
1. “It is raining.”
2. “It must be raining.”
I will use the following conventions to represent prejacents and “must” claims:
i. Bare Prejacent claim: “Φ”
ii. Modalized claim: “must-Φ”; “might-Φ”
Given these conventions, (1) is represented as “Φ” and (2) is represented as “must-Φ”.
Lauri Karttunen (1972) in “Possible and Must” pointed out that we encounter a problem whenever we analyze (1) and (2) via modal logic; since “must” is a necessity operator (2) comes out to be a stronger claim than (1), but this result is utterly counterintuitive. Thus there are philosophers and semanticists who argue for a more intuitive thesis that Kai von Fintel and Anthony Gillies call the Mantra. According to those who espouse the Mantra (1) is a stronger claim than (2); Angelika Kratzer (1991) weakens “must” by weakening “must-Φ” claims whereas Frank Veltman (1985) keeps the strength of “must-Φ” claims the same and strengthens the bare prejacent claim “Φ”. Kai von Fintel and Anthony Gillies, however, argue in their forthcoming article “Must…Stay…Strong!”[1] that Mantra theories are wrong, and modalized claims that contain “must” such as (2) are not weak in relation to their bare prejacent such as (1).
It is my thesis, however, to argue that Fintel and Gillies’ arguments against the Mantra are unsuccessful for three reasons. First, I will argue the examples that Fintel and Gillies use as objections to the Mantra do not conclusively prove that the Mantra is wrong. Secondly I will argue that the Mantra keeps “must” in its rightful position of epistemic strength, between bare prejacents and the epistemic modal “might”. Thirdly, Fintel and Gillies’ theory actually does provide us a theory as to why “must” is weak but their conclusion that “must” is strong is incorrect.
Karttunen’s Problem and the Mantra’s Answer
As stated in my Introduction, in “Possible and Must” Lauri Karttunen (1972) presents a dilemma concerning the strength of modalized claims such as “must-Φ” when compared to the strength of a bare prejacent “Φ” when analyzed using modal logic. Consider two sets of sentences that Karttunen labels (30) and (31)[2]:
| (30) | a. Necessarily p b. p |
| (31) | a. John must have left. b. John has left. |
Under standard modal logics, (30a) is a stronger claim that (30b) because □p entails that p is true in all possible worlds whereas p (without no modal operator) is only true in the actual world. In modal logics “must” is a necessity operator which then entails (30a) is equivalent to (31a) and (30b) equivalent to (31b) thus yielding the result that (31a) is a stronger claim than (31b). However, this strikes many as being counterintuitive, and the reason, Karttunen states, is that someone would utter (31a) when they do not yet know if John has in fact left because they do not have evidence to substantiate (31b). Therefore, intuitively, given the difference strengths in the evidence required to utter each of the claims, (31a) is weaker than (31b). So one motivation behind modern Mantra theories is to provide an account as to why our intuitions are (31b) is a stronger claim than (31a). For brevity and breadth of purpose I will focus on Mantra theories that weaken “must” in terms of truth-conditions and these are views associated with Angelika Kratzer (1991) in “Modality” and Frank Veltman (1985) in Logics for Conditionals. Fintel and Gillies’ discussion of these views is found in §3 of “Must…Stay…Strong!”
For Kratzer (1991), “must” is not solely a universal quantifier that ranges over a modal base but it ranges over possibilities as well. Fintel and Gillies explicate this facet of Kratzer’s theory in the following way:
A must at w is sensitive in addition, to an ordering over possibilities—an ordering
They provide the following definition for Kratzer’s weak “must”:
Definition 1 (Weak must à la Kratzer (1991)).[3]
i. min. (B,
ii. [[must Φ]]c,w = 1 iff (B,
Even though world w is a member of the modal base B and the indirect evidence of “must-Φ” is encoded into the modal base, it does not follow that w is a member of the ordered worlds where ordinary events would have occurred as they normally would have, because events may have gone differently as they were expected to go in w. Therefore, since “must-Φ” does not entail “Φ”, i.e., (“must-Φ”
For Frank Veltman (1985) answering the Karttunen Problem is a matter of strengthening the bare prejacent and keeping the strength of a “must-Φ” claim the same, but the result is the same as Kratzer’s in that “must-Φ” claims are weak because the bare prejacent comes out stronger than the modalized claim, therefore (“must-Φ”
Definition 2. If c′ extends the information in c, c
i. B+c
ii. B-c
If c′ contains as much information as c, then both contexts will settle the truth-value of a given atomic sentence, but it is possible that in one context, c allows for the atomic sentence “p and q” to be true but c′ renders “p and q” false because c′ contains information not found in c. Given this initial portion of the theory, Fintel and Gillies state:
Two things are relevant for our purposes. First: truth conditions so ground are partial—the fact that c might not settle whether an atomic Φ is true or false can ramify to complex sentences which embed Φ. Second: must in c quantifies all the ways of adding to the partial picture of the world that c represents. (forthcoming, 10)
This brings them to Definition 3:
Definition 3 (Strong prejacents à la Veltman (1985)).[5]
i. [[Φatomic]]c =
ii. [[must Φ]]c =
A “must-Φ” claim, “…looks to all ways of extending the current information, checking that none of them are information states that falsify the prejacent” (Fintel and Gillies, forthcoming, 11). So in a given context c, given the information in c, a “must-Φ” may be true given the partial information within that c but that information may not be able settle whether or not a prejacent “Φ” is true or false.
Thus, must Φ
The satisfactions conditions that a bare prejacent claim “Φ” has to meet in order to be true are much stronger than those of “must-Φ”. Thus for Veltman, the Karttunen Problem is solved because bare prejacents are stronger than modalized “must-Φ” claims.
Note that just like Kratzer’s theory, Veltman encodes a notion of evidentiality in the semantics: an information state can be seen as representing your direct evidence, and since your direct evidence can fail to satisfy Φ even though no way of adding more evidence can falsify Φ, it is possible that must Φ is supported by that evidence even though Φ isn’t (yet). (Fintel and Gillies, forthcoming, 11)
Fintel and Gillies’ Objections to the Mantra and Theory of “Must”
Turning to their criticisms of the Mantra, Fintel and Gillies begin by arguing in §4 of their essay that the indirectness associated with “must” does not entail weakness. “The Mantra is that, given the basic observations, must statements are weaker than bare prejacents. But that is an over-reaction to the evidentiality phenomenon and is empirically problematic” (Fintel and Gillies, forthcoming, 12). Those who espouse the Mantra often associate the indirectness of evidence with the weakness of “must-Φ” claims; the indirectness of one’s evidence entails the statements of the “must-Φ” are weaker than bare prejacents claims because as the Mantra assumes the prejacent “Φ” is based on direct evidence and thus is stronger than “must-Φ” which is based upon indirect evidence. If we consider (1) and (2) from the Introduction:
1. “It is raining.”
2. “It must be raining.”
If we consider a context involving two individuals Bill and Ted; Bill and Ted are looking out the window and sees that it is pouring rain and Ted says (2). According to the Mantra, Ted is strange because (2) entails that Ted has indirect evidence about whether or not it is raining but clearly he does have direct evidence that it is, i.e., he sees the pouring rain. Fintel and Gillies agree with this diagnosis but they state rarely are arguments given by the Mantra espousers to substantiate this claim and so it seems that those who espouse the Mantra assume and do not explain their fundamental premise that indirect evidence entails the weakness of “must-Φ” claims. Therefore, Fintel and Gillies claim the following:
But indirect knowledge is still knowledge, and so what follows from what is indirectly known must be true, and so there is no good sense in which must is weak. Our point is simple: weakness and indirectness are not two sides of a single coin at all. They are just different. Any arguments for a weak semantics need to be more than just reminders that must carries an indirect evidential signal. We have not seen such arguments, and in what follows we will argue on the contrary that there is no weakness in must. (forthcoming, 13)
To substantiate these arguments Fintel and Gillies give an argument labeled “Argument 4.2.1”[6]. Chris has lost her ball but she knows that the ball is in one of three boxes that are sitting in front of her labeled A, B, and C. By process of elimination Chris concludes that her ball is not in A or B, so she says in conclusion, “It must be in C.” Even though Chris has indirect evidence concerning the whereabouts of her ball and her claim ‘signals’[7] that she only possesses indirect evidence it makes no sense to argue that in this Chris’s claim that “It must be in C,” is weak. If Chris had been shown what box her ball was in it would not make sense for her to say, “It must be in C” given the directness of her evidence but this does not show that “It must be in C” is weak as argued by the Mantra.
In “Argument 4.2.2”[8], Fintel and Gillies consider a case considering Billy. Billy sees people coming inside wearing rain gear that is wet and so she utters (2), i.e., “It must be raining”. Again Fintel and Gillies conclude that even though she only has indirect evidence about the rain, her claim is not weak: “Thus, the basic observation has everything to do with the directness of the speaker’s information, not with the strength of the claim they make on the basis of it” (forthcoming, 14). From arguments such as 4.2.1 and 4.2.2, Fintel and Gillies conclude that “must-Φ” is never weak.
Since “must” is never weak, consider the following the case presented in “Argument 4.3.1”[9]:
| | Argument 4.3.1 | Logical Form |
| (14) | “If Carl is at the party, then Lenny must be at the party.” | (15) (Φ → must-Ψ) |
| | “Carl is at the party.” | Φ |
| | “So: Lenny is at the party.” | /:. Ψ |
If the Mantra is true then the premises are too weak to entail the conclusion in (4.3.1), but Fintel and Gillies count this argument as a strike against the Mantra because not only is the argument valid it is true as well.
According Argument 4.3.2[10], the Mantra cannot explain the interplay between the so-called weak “must” and uncontroversial weak modals such as “perhaps”. According to the Mantra “must-Φ” does not entail “Φ”, but if this is true then “must-Φ” should be compatible with “perhaps ~Φ”. Consider the following statements:
3. It must be raining but perhaps it isn’t raining.
4. Perhaps it isn’t raining but it must be.
These statements are contradictions of the Moorean breed and, “Our worry has do with the weaker perhaps ¬Φ. Whatever else a speaker does by uttering perhaps ¬Φ, she definitely does not reduce or suggest reducing the modal base to include only ¬Φ-worlds. And that is enough to cause trouble for the Mantra” (Fintel and Gillies, forthcoming, 16).
This argument leads to their Argument 4.3.3[11].
| (17) | a. Alex: It might be raining. b. Billy: [Opens curtains] No it isn’t. You were wrong. c. Alex: I was not! Look, I didn’t say that it was raining. I only said it might be raining. Stop picking on me![12] |
Whenever an individual uses “might”, “may” or “perhaps” in claim they are not committed to the truth of that claim, i.e., they are given distance from the claim’s truth, and thus when they are accused of asserting a falsehood, as is the case with (17a), they can defend their claim as Alex does in (17c). The modal “must”, on the other hand, does not grant someone that kind of flexibility (or distance) and to substantiate this claim another dialogue numbered (19) is given that again involves Alex and Billy:
| (19) | a. Alex: It must be raining. b. Billy: [Opens curtains] No it isn’t. You were wrong. c. Alex: #I was not! Look, I didn’t say that it was raining. I only said it must be raining. Stop picking on me! |
Given that Alex used “must” in (19a) she cannot assert (19c) since “must” is strong, uttering (19a) commits Alex to the truth of the prejacent, i.e., to the truth of the statement, “It is raining,” because as Fintel and Gillies state:
This is not puzzling from the strong must point of view: saying I only said it must be raining is as bizarre as saying I only ate all of the cookies. But if, as the Mantra maintains, must is not located at the very top of the scale of epistemic strength, one would expect only and must to combine like old friends. (forthcoming, 18)
Fintel and Gillies begin §6 that explicates their basic analysis of “must” by stating:
The Mantra is wrong. We say that the basic quantificational analysis is nearly right, and so too is the comment-dimension analysis. But both are also not quite right. Epistemic modals express their usual quantificational meanings relative to a contextually determine modal base. So must is strong at the level of content. But such modals signal that some privileged part of the modal base, the kernel, does not directly settle the question of the prejacent either way. This signal lives somewhere outside the main at-issue content dimension—we take it (subject to hedges we issue issued earlier) to be a presupposition—and is a signal about indirectness, not about weakness. (forthcoming, 23)
Beginning with the machinery of possible world semantics and a contextually supplied modal base which is information compatible with what is known at the world in a given context, they add a technical device called a kernel that is a set of propositions that describe direct information in a context. Therefore, with the addition of a kernel the modal base B is provided by Definition 4[13]:
Definition 4 (Kernels and Bases). K is a kernel for BK, BK is determined by the kernel K, only if:
i. K is a set of propositions (if P
ii. BK =
An individual cannot have direct information that P unless P is the case, and so whenever a modal expression such as “must-Φ” is uttered at w, then with respect to a given kernel K, they know that w
Definition 5 (Strong must + Evidentiality[15]). Fix a context-relevant kernel K:
i. [[must Φ]]c,w is defined only K does not directly settle [[Φ]]c
ii. [[must Φ]]c,w = 1 if BK
There can be cases where K can fail to directly settle the truth or falsity of a given proposition P even though K entails P thus there is a kind of ‘gap’ between “must-Φ” and their corresponding prejacents “Φ” and, “…epistemic modals carry an evidential signal that exploits that gap” (Fintel and Gillies, forthcoming, 25). So if we consider a case with Billy, in a given context she looks outside the sees that it is raining.
| (6) | a. “It is raining.” b. “It must be raining.” |
It would be wrong for Billy to say (6b) because there is a kernel K (i.e., seeing the rain) that directly settles the truth of the prejacent (6a). But consider a case where Billy sees people with wet umbrellas and knows that rain is the only cause for their wet umbrellas, Billy can rightly assert (6b) Billy could assert (6a) as well since she is not forced to say (6b), but this is something that the Mantra does not allow, i.e., in this case, according to the Mantra Billy cannot assert (6a) but must assert (6b).
Shifting to their formal analysis in §7.1 entitled “First Implementation,” they apply their basic analysis of “must” to the Billy case to give a more formalized theory to explain Billy’s utterance.
Implementation 1 (Explicit Representation). K directly settles whether P iff either X
In the case of Billy, her kernel contains two propositions:
| (25) | a. P = [[no wet rain gear]] b. Q = [[it’s raining]] |
Suppose that in a context Billy is indoors and sees people coming in with wet rain gear and knows that the only explanation is rain. This context determines the kernel K for her and it is {P
Thus Fintel and Gillies state in the last section, §8, of their article:
Speakers who say must Φ are just as strongly committed to the prejacent as those who assert Φ by itself. Of course, there are prejacents for which intuitively direct evidence is more convincing than indirect inferential evidence. So a speaker who nevertheless to use the strong must Φ incurs high degree of risk. So we judge that in many cases, must Φ is more likely to be false than Φ by itself would have been if there had been direct evidence for the prejacent. But a sentence being more likely to be false than another is far from an argument that it is weaker! (forthcoming, 35)
Therefore, Fintel and Gillies’ conclude that must is always strong.
Objections to Fintel and Gillies’ Cases
While Fintel and Gillies offer a persuasive theory, I believe that there are some problems with it because their cases they present against the Mantra are unsuccessful. I believe that if my objections are legitimate against a few of their cases then their theory of “must” is not on solid ground. First I will examine Argument 4.3.1. In this argument Fintel and Gillies state that the argument conclusion follows via modus ponens because the strength of the premises is carried throughout the argument.[17] For ease of reference:
| | Argument 4.3.1 | Logical Form |
| (14) | “If Carl is at the party, then Lenny must be at the party.” | (15) (Φ → must-Ψ) |
| | “Carl is at the party.” | Φ |
| | “So: Lenny is at the party.” | /:. Ψ |
The question to consider is, “Is Argument 4.3.1 a strike against the Mantra?” I argue that it is not and the reason is that the Mantra preserves our intuitions (at least my intuition) that the conclusion does not follow from the premises because while premises 1 and 2 are true the conclusion is false. Since Argument 4.3.1 has true premises and a false conclusion then it is not deductively valid this argument is a strike against Fintel and Gillies’ theory.
Let us say that the individual considering (4.3.1) is named Mark. For the sake of argument I will concede Fintel and Gillies’ thesis that “must-Ψ” presupposes that the individual uttering it only has indirect evidence concerning the truth of “Ψ” and does not possess a kernel K that settles the truth of “Ψ”. The antecedent “Φ” is based upon Mark’s direct evidence concerning the whereabouts of Carl, perhaps Mark saw Carl there at the party in question, and this analysis is conceded by espousers of the Mantra and Fintel and Gillies. Another point of agreement between Fintel and Gillies and Mantra espousers is that the consequent “must-Ψ” is based indirect evidence. Angelika Kratzer’s (forthcoming) argues in “Modals and Conditionals Again” that “must-Ψ” in the consequent is based upon indirect information/evidence:
(32) If the lights in his study are on, Roger must be home.
By using epistemic must in sentences like (32), a speaker indicates that the truth of the conditional was deduced from indirect evidence. The speaker may know, for example, that Roger always turns all lights off when he leaves his house. Overt must has the characteristic properties of so-called ‘indirect evidentials’… (forthcoming, 14)
The second premise is valid given Mark’s direct evidence concerning the whereabouts of Carl, and so given modus ponens, according to Fintel and Gillies, the conclusion “Ψ” follows. However, I would like to pose the following question: “As the question of the prejacent ‘Ψ’ been settled?” I believe that even under Fintel and Gillies’ theory that question has not been settled. I question the conclusion “Ψ” not on the grounds that I believe that modus ponens is an invalid rule of inference but that Mark has reasoned incorrectly. Even though the presence of Carl may provide evidence that suggests that Lenny is at the party, the evidence is not conclusive to substantiate his conclusion, even on Fintel and Gillies’ own theory. Recalling that kernels are sets of propositions that settles a prejacent and if we examine the kernel in this case and do not go beyond the information of the case then Mark’s kernel (Km) then could consist of the following:
| (Km) | 1. “Carl is the party.” 2. “Since Carl is here it is likely that Lenny is here too.” |
I argue that (Km) is not enough to settle “Ψ” because Mark simply does not have enough evidence, whether direct or indirect, to settle “Ψ” as provided by the case because even though Carl may be evidence that Lenny is at the party, there are too many other possibilities that must be eliminated such as Carl could have come alone, Lenny may not be at the party even though Carl is, etc. Therefore, the conclusion “Ψ” simply does not follow from the premises that Lenny is at the party because it is unsettled thus confirming the intuition that Mark’s reasoning is flawed. The Mantra predicts that the premises do not yield the conclusion and since this prediction is correct Argument 4.3.1 is not a strike against the Mantra. Fintel and Gillies seem to suggest in footnote (21) that the omission of “must” in the conclusion of 4.3.1 is inconsequential concerning the validity of the argument on their theory. Footnote (21) states, “Note that the point is not that the weak must accounts can’t deliver must Φ as the conclusion to the argument. That they presumably can. Our point here is that the bare Φ is also a valid conclusion and that the Mantra-analysis cannot deliver that conclusion” (Fintel and Gillies, forthcoming, 15). I argue to the contrary; the exclusion of “must” from the conclusion makes a significant difference concerning the validity of the argument because it entails that Mark does not have a kernel to settle the bare prejacent “Ψ” and this would be congruent with Mark’s evidence. So the inclusion of “must” in the conclusion would not only save the argument from being invalid and the argument would be consistent with Fintel and Gillies own theory. If the conclusion were, “So, Lenny must be here at the party,” it would follow from the premises on their theory because where the question of the prejacent is not settled, and is congruent with Definition 5.
In Argument 4.3.1, I interpreted premise 1 as an indicative conditional (p → q) that requires a connection between the antecedent and consequent whereas material conditionals (p
If premise 1 is interpreted as a material conditional, such as (Φ
M. “If I had breakfast this morning then tomorrow is Tuesday.” (b
(M) is true (so long as t is not false) even though intuitively the event of me having breakfast this morning and tomorrow being Tuesday are not unconnected.[19] If consider (M) and run a logical proof using modus ponens we get the following:
1. (b
2. b /:. t MP 1,2
This argument is logically valid if uttered on a Monday in order for t to be true but it strikes us as being deficient because the truth of b and is not connected with the truth of t. Returning to 4.3.1, if premise 1 is interpreted as (Φ
Furthermore, Mark’s conclusion “Ψ” is a knowledge claim, but if Lenny is in fact at the party then it appears to be nothing than a lucky guess on behalf of Mark that his conclusion “Ψ” but I doubt that we would be willing to attribute knowledge to Mark, i.e., that he knows that “Ψ” which the conclusion would be interpreted as, because intuitively lucky guesses, thanks to Gettier[20], do not constitute knowledge.
To drive home the point that Argument 4.3.1 fails, consider another case that I will label as (W) that I believe that further shows Argument 4.3.1 to be fallacious. It is said that after writing the Tractatus Logico-Philosophicus, Ludwig Wittgenstein was a gardener for a monastery in Vienna for a time and even considered joining the Church. So consider this purely fictional case. One day Brother Günter has just finished talking with Wittgenstein who said that he considering becoming a monk. Brother Günter, therefore, reasons as follows:
| W | Logical Form |
| W1. “If Wittgenstein is considering becoming a monk then he must want to become a monk.” | (Φ → must-Ψ) |
| W2. “Wittgenstein is considering becoming a monk.” | Φ |
| W3. “Therefore, Wittgenstein wants to become a monk.” | /:. Ψ MP 1,2 |
According to Fintel and Gillies the conclusion does follow due to the strength of “must” under their theory. However, the diagnosis will be the same in that conclusion does not follow. (W1) could be interpreted as an indicative conditional because if someone is considering performing a certain action then it is intuitively plausible to interpret them as wanting to perform that action given that there is (in most cases) a connection between considering an action and wanting to perform that action.[21] However, if we do not have enough evidence to know that an individual want to perform the action they are considering then I think that is entirely plausible to use “must” in a sentence such as, “They must want to do x.” Even if we grant this (W3) still does not follow. Using Fintel and Gillies’ theory, a possible kernel for Brother Günter (Kg) could consist of the following propositions:
| (Kg) | 1. “Wittgenstein has been our gardener for a while now so he must like it being here.” 2. “He is considering becoming a monk.” |
Now the question is, “Does (Kg) settle the prejacent ‘Wittgenstein wants to become a monk’?” Given the context that Brother Günter is in, (Kg) does not settle the prejacent claim because, just as in Argument 4.3.1, Brother Günter evidence is not conclusive enough to settle it. Brother Günter does not know that Wittgenstein actually wants to become monk.
Therefore, I believe from observing Argument 4.3.1 and (W) Fintel and Gillies’ accusation the Mantra cannot deliver the conclusion is not a real criticism; instead their criticism only confirms our intuitions about such cases, i.e., the conclusion does not follow the premises because in both cases, and so Argument 4.3.1 is not a strike against the Mantra.
Using Argument 4.3.3, Fintel and Gillies claim that whenever someone uses “must” in a sentence then they are committed to the truth of the bare prejacent. For ease of reference:
| (17) | a. Alex: It might be raining. b. Billy: [Opens curtains] No it isn’t. You were wrong. c. Alex: I was not! Look, I didn’t say that it was raining. I only said it might be raining. Stop picking on me! |
| (19) | a. Alex: It must be raining. b. Billy: [Opens curtains] No it isn’t. You were wrong. c. Alex: #I was not! Look, I didn’t say that it was raining. I only said it must be raining. Stop picking on me! |
Recalling that according to Fintel and Gillies, Alex cannot assert (19c) whereas Alex can assert (17c) given the differences in strength between “might” and “must”. In (19), since under Fintel and Gillies’ theory, (“must-Φ”
There are cases that do not involve belligerence and someone can defend their “must-Φ” claim and where they can say “only” and “must” in the same sentence. During a particularly hot summer Bill and Ted[22] are eating lunch in their break room at work where they load package delivery trucks. They overhear some drivers talking about how driving that afternoon was going to difficult because a thunderstorm was moving into the area that was forecasted to drop large amounts of rain. A few minutes later they overhear another set of drivers saying that some of the downtown streets were becoming difficult to drive on because some of them were flooded but, unbeknownst to Bill and Ted and not said by the drivers, this is due to a large water main break and not rain.
Ted says, “Hmm, it must be raining.”
“That’s not cool man,” Bill replies touching his hair. “I left my umbrella in my car and the rain will kill my new dew.”
“Go get it if you’re so worried,” Ted says.
So Bill leaves the break room to retrieve his umbrella and when he returns with umbrella in hand he has an extremely annoyed expression his on face and his uniform is wet and somewhat disheveled. Seeing Bill’s annoyed expression Ted starts laughing.
“What happened to you?” Ted asks.
“Dude, you were so wrong,” Bill says in an annoyed tone. “It’s not raining, it’s hailing!”
“Dude,” Ted replies still laughing, “I only said it must be raining, not that it is raining.”
I believe that this is a case where Ted can defend his “must” claim. Ted was not lying since he was not trying to be deceitful, nor was he playing a practical joke on Bill when he uttered “It must be raining.” He uttered “It must be raining” based the indirect evidence he had at the time, i.e., the testimony of the drivers. Could Ted had said, “It is raining”? I say “No,” because he has no direct evidence to settle that statement, i.e., he does not possess a kernel that settles it. In this particular case the “must” used by Ted has more in common with (though is not equivalent to) “might” in that the “must” in his claim does allow him a certain amount of distance from the prejacent, “It is raining”, and this distance allows him to defend his claim even though what he said was false. We could judge Ted however one wishes to (perhaps you think of him as a jerk for laughing at Bill’s plight), but the point remains, Ted can defend his “must” claim even though in order to do so he has to extremely literal. Furthermore, Ted’s use of “only” in his defense does not sound problematic.
But the critical question is, “Does this case show that ‘must’ is weak?” Fintel and Gillies could possibly reply that my cases does not show “must” to be weak by arguing the reason why Bill is so irritated with Ted is that Bill is not allowing Ted any “distance” from his “must-Φ” claim as we find with “might-Φ” as shown in (17). I believe that the Bill and Ted case does show that “must” is not as strong as Fintel and Gillies claim because if Ted’s “must” statement was not weak then we should think that Ted’s defense of his statement, “It must be raining,” is invalid but that is not the case. (19) is supposed to show that any defense of a false “must-Φ” claim is not plausible given that “must” is never weak, but in my case Ted is allowed a certain distance from his claim, distance that Fintel and Gillies say Ted does not have because under their theory Ted is committed to the truth of the prejacent since (“must-Φ”
I believe that from what has been argued in this section the cases that Fintel and Gillies bring against the Mantra are unsuccessful. Now we need to examine the strength of “must” under the Mantra and to explain why the Mantra’s placement of “must” between bare prejacents and “might-Φ” claims is so intuitively plausible.
The Strength of “Must” Under the Mantra
In Argument 4.3.3 which involves dialogue (19), Fintel and Gillies claim that, “…if, as the Mantra maintains, must is not located at the very top of the scale of epistemic strength, one would expect only and must to combine like old friends” (forthcoming, 18). For Fintel and Gillies the very top of the epistemic scale are bare prejacents and “must-Φ” claims. However, I believe that this thesis is questionable and so it seems fitting to give an account of the strength of “must” as viewed through the lens of the Mantra. Recalling from earlier, one of the main motivations behind the Mantra was to address the Karttunen Problem; the Mantra’s weakening of “must” as done by Kratzer or strengthening the prejacent as done by Veltman places the strength of “must” between the strengths of bare prejacents and “might-Φ” claims. So if we are considering the graduated strength of epistemic modals, “must” is the strongest epistemic modal insofar as English is concerned but, contrary to Fintel and Gillies, it is not equivalent in strength to bare prejacents. For brevity I will consider Kratzer’s theory of “must” as presented in “The Notional Category of Modality” (1981) and “Modality” (1991). As organized by Paul Portner in Modality (2009), Kratzer (1991) ranks the force the epistemic modals of English in the following fashion:
| Modal Status | Modal/Modalized Statement | Definition |
| Necessity | “Must” | A proposition p is a necessity in w with respect to a modal base f and an ordering source g iff all u i. v ii. for all z |
| Weak Necessity | “It is possible that…” | A proposition p is a weak necessity in w with respect to a modal base f and an ordering source g iff p is a better possibility than ~p in w with respect to f and g. |
| Possibility | “Might” | A proposition p is a possibility in w with respect to a modal base f and an ordering source g iff ~p is not a necessity in w with respect to f and g. |
| Slight Possibility | “There is a slight possibility that… | A proposition is a slight possibility in w with respect to a modal base f and an ordering source g iff i. p is compatible with f(w); and ii. ~p is a necessity in w with respect to f and g. |
| Good Possibility | “There is a good possibility that…” | A proposition p is a good possibility in w with respect to modal base f and an ordering source g iff there is a world u |
| Better Possibility | “It is more like that… than that…” | A proposition p is a better possibility than a proposition q in a world w, in view of a modal base f and ordering source g iff i. For all u ii. There is a world u |
As is evident from Kratzer’s theory, “must” carries that greatest amount of force in English thus making it the strongest epistemic modal even though it is weakened by Kratzer (1991) in order to address the Karttunen Problem. Consider the following example as provided by Portner where a doctor is diagnosing someone’s symptoms[23]:
| (105) | (a) You must have the flu. (b) {w: for all u i. v ii. for all z |
Portner sides the Mantra in that “must-Φ” claims are weaker than their corresponding prejacent claims “Φ”. Since the modal base is epistemic, there are certain facts that assumed to be beyond doubt such as the individual who is being diagnosed with the flu has a fever, cough, and body aches. There are other facts that are not beyond doubt such as medical conventions, testimony of people being sick with the flu, etc. For the modal base f and order source g, (105b) says that in the worlds where all of the facts hold true, the higher ranked worlds are worlds in which this individual actually does have the flu, but since the set of propositions in g (i.e., the ordering source) are subject to doubt or can change that makes “You must have the flu” weaker than “You have the flu.”
Some believe that since “must-Φ” claims are easier to doubt than bare prejacents as seen in Portner’s flu diagnosis example they are weak.[24] I do not agree that doubt concerning the truth of a “must-Φ” claim is not enough of a reason by itself to think that they are weaker than bare prejacents. Reason being is that even prejacents are not immune from doubt; simply tell a full-blooded skeptic (who denies human knowledge) or high-standards skeptic (who argues that humans know very little) a bare prejacent claim and see if they doubt it. Some philosophers have been doubted necessary truths or have even doubted the existence of such truths but that does not seem to be a valid enough reason to motivate the development of a weakened semantics for necessary truths. Be that as it may, I believe that doubt does point towards a genuine reason and explanation for weakening the semantics for “must”. If we examine the reason why some advance the thesis that “must” claims are easier to doubt I believe it is due to the inconclusiveness of evidence (not necessarily the indirectness of evidence) that this is utilized when asserting a “must-Φ” claim. While this is along similar lines of Fintel and Gillies, especially given Definition 5, the difference between the theory that I am advocating and theirs is that I take the inconclusiveness of evidence that is signaled by a “must-Φ” claims makes them weaker than prejacents. The weakness of “must” lies in the inherent weakness of inconclusive evidence that is utilized to assert it.
Inconclusiveness of evidence is not necessarily connected to either indirect or direct evidence because I believe that there are certainly cases where indirect evidence is conclusive enough to settle a prejacent claim. Concerning conclusive evidence that happens to be indirect consider a case with Bob the astrophysicist. Sometime ago scientists hypothesized that a possible explanation for why large spiral galaxies rotate was at their center there are “supermassive black holes”.[25] So let me set up a hypothetical scenario; a group of astrophysicists is discussing this very theory and in particular why the Milky Way rotates since it is a spiral galaxy. An astrophysicist named Bob, upon hearing this hypothesis, goes out and begins to observe the motions of stars at the center of the Milky Way as well as making inferences based upon what is known about the effects that black holes have upon objects and space around them. Unfortunately, his observations only give him indirect evidence for the existence of the black hole because there are no telescopes powerful to penetrate the dense bulge of stars and dust at the center of the Milky Way and furthermore black holes cannot be directly observed. After much work, calculations, and toil Bob comes to the conclusion that the most reasonable explanation that explains all the data for why the Milky Way rotates is that there is a supermassive black hole at its center. Thus given all of the evidence that his accumulated, in discussing his theory with his peers Bob says:
| B. | “There is a supermassive black hole at the center of the Milky Way galaxy that causes it galaxies to rotate.” |
Given Bob’s evidence for the existence of a supermassive black hole at the center of the Milky Way galaxy, he has enough conclusive evidence to assert (B) since all other relevant possibilities have been reasonably eliminated. Using Fintel and Gillies’ terminology Bob possesses a kernel that settles (B) since the existence of the supermassive black hole is the best explanation even though his evidence is only indirect he can assert the prejacent. If were to construct a possible set of propositions that are in Bob’s kernel (Kb) they could be the following:
| (Kb) | 1. The reason why stars are more densely clustered together is that they are being all being drawn to an object that has an incredible amount of mass and the only object in the universe known to have that much mass are black holes. 2. The bugle at the center of the Milky Way is caused by clustering of stars and dust due to immense gravitational forces which are caused only by objects with incredible amounts of mass, which in this case would be a black hole. 3. The Sagittarius “A” star is spinning around a center point of the Milky Way we know that black holes cause celestial objects to spin around given their immense tidal forces. |
Given (Kb), it would be strange for Bob to say:
| Must-B. | “There must be supermassive black hole at the center of the Milky Way galaxy that causes it to rotate.” |
In my terms, Bob’s evidence is conclusive enough for him to justifiably assert (B), whereas if his evidence was not conclusive then he would not be justified in asserting (B). Even if his evidence was inconclusive but strong enough he could assert (Must-B) because his evidence would allow him to assert a stronger claim than, say, “might-B”, i.e., “There might be a supermassive black hole at the center of the Milky Way galaxy that causes it galaxies to rotate.” For Bob to assert “might-B”, using Kratzer’s definition of “might,” he would have to be the case that “There is a supermassive black hole at the center of the Milky Way galaxy that causes it galaxies to rotate,” is a possibility in w with respect to a modal base f and an ordering source g if and only if, “There is not a supermassive black hole at the center of the Milky Way galaxy that causes it galaxies to rotate,” is not a necessity in w with respect to f and g. But “might-B” is eliminated because Bob’s evidence is conclusive enough.
Ultimately I side with Karttunen’s diagnosis of the evidentiary situation concerning “must”. Recalling his example involving John:
| (31) | a. John must have left. b. John has left. |
Intuitively (31a) is used in a sentence whenever someone’s evidence is inconclusiveness concerning whether or not John has in fact left. (31b) on the other hand is uttered whenever someone has conclusive evidence that John has left.[26] Examining this example, intuitively “must” claims are weaker than prejacent claims and it is based upon the evidence that is used to substantiate them. They are not weaker because they are easier to doubt or because they are based upon indirect evidence; instead “must-Φ” claims are weaker because they require weaker evidence to assert than their corresponding prejacent claims. The idea is that inconclusive is weaker than conclusive evidence and I believe if someone were to argue against such a position they would be hard-pressed to develop such an argument. Consider a case where there are two theories, theory T1 and T2, and both theories are supposed to explain how Mr. Johnson murdered his long time rival Mr. Bill. Detective Bresco has formulated T1 and T2 has been formulated by Private Investigator Fife. Let us the say that the theories are based upon the following pieces of evidence:
| (T1) | 1. Mr. Bill was murdered by being shot in the back. 2. Mr. Johnson’s gun was found near the murder scene and was covered with his fingerprints. 3. The striations on the bullet that killed Mr. Bill watch a test bullet fired from Mr. Johnson’s gun. 4. There are documented cases where Mr. Johnson had threatened Mr. Bill with bodily harm. 5. Multiple eyewitnesses place Mr. Johnson at the scene of the crime. |
| (T2) | 1. Mr. Bill was murdered by being shot in the back. 2. Mr. Johnson had been jealous of Mr. Bill’s success for a long while. 3. Mr. Johnson’s secretary said that he did not like Mr. Bill. 4. Multiple eyewitnesses place Mr. John at the scene of the crime. |
Now consider two statements.
| (J) | “Mr. Johnson killed Mr. Bill.” |
| (Must-J) | “Mr. John must have killed Mr. Bill.” |
Given their evidence, Detective Bresco can utter (J) whereas PI Fife can utter at most (Must-J) and this is due to the strength/conclusiveness of their evidence. The evidence accumulated for (T1) is considerably stronger than that for (T2) because it is more conclusive. (T2) is the weaker of the two and since that is the case PI Fife can only assert (Must-J). If PI Fife asserts (J), I think we would be puzzled given that the evidence that he has is inconclusive, i.e., his evidence does not prove that Mr. Johnson killed Mr. Bill. Furthermore, if Detective Bresco asserts (Must-J) we would be puzzled because his evidence is conclusive enough to prove that Mr. Johnson killed Mr. Bill. Therefore, our intuition that (J) is a much stronger claim than (Must-J) is confirmed thus rendering (Must-J) as a weaker claim.
Again, this is very similar to Fintel and Gillies’ theory of kernels and how if someone does not have a kernel that settles a prejacent then someone will (more than likely) assert a “must-Φ” claim. I think that Fintel and Gillies’ theory accurately captures this feature of “must” in English where if someone has conclusive evidence concerning a given prejacent it would be strange for them to assert the modalized claim “must-Φ”, and if someone’s evidence does not settle a prejacent but is strong then they will assert a “must-Φ” claim. But unlike their theory, I argue that it is for that very reason “must-Φ” claims are based upon inconclusive evidence is what makes such claims weaker and why the motivations behind the Mantra, i.e., developing semantics for a weak “must”, are correct.
Concluding Remarks
Fintel and Gillies’ arguments against the Mantra are unsuccessful despite the fact that I believe their theory does provide reasons for weakening “must”. First, I argued that some of the examples that Fintel and Gillies use as objections to the Mantra do not conclusively prove that the Mantra is wrong as shown by the failure of Argument 4.3.1 in that the conclusion “Ψ” does not follow the argument’s premises and the failure of 4.3.3 because there are contexts where it is plausible for someone to defend a false “must-Φ” claim contrary to what Fintel and Gillies argue. Secondly I argued that the Mantra keeps “must” in its position of epistemic strength, between bare prejacents and the epistemic modal “might” as in the case with Kratzer’s theory of “must” due to the weakness of the evidence used in asserting “must-Φ” claim. Thirdly, dovetailing from my second objection, even though Fintel and Gillies’ theory does provide us an account why “must” is weak in that they concede that “must” is used whenever someone does not have enough evidence (or in their terminology a kernel) that settles a prejacent claim, their conclusion that “must” is strong is incorrect. Conclusive evidence is always stronger than inconclusive evidence and if prejacents are asserted based upon conclusive evidence then they are stronger than “must-Φ” and, furthermore, since “must-Φ” claims are asserted based upon inconclusive evidence they are weaker thus rendering “must” weaker than what Fintel and Gillies propose.
Bibliography
Bennett, Jonathan. A Philosophical Guide to Conditionals. New York: Oxford University Press, 2003.
Gettier, Edmund L. 1963. Is Knowledge Justified True Belief? Analysis (Oxford University Press on behalf of The Analysis Committee) 23, no. 6: 121-123. http://www.jstor.org/stable/3326922 [Access November 8, 2009]
Gillies, Anthony, and Kai von Fintel. An Opinionated Guide to Epistemic Modality. In Oxford Studies in Epistemology, Volume 2. Oxford University Press, 2007. 32-62. http://books.google.com/books?id=QPXGJWvoxEUC&pg=PP1&dq=oxford+studies+in+epistemology,+volume+2&cd=1#v=onepage&q=oxford%20studies%20in%20epistemology%2C%20volume%202&f=false [Accessed January 6, 2010]
Gillies, Anthony, and Kai von Fintel. Forthcoming. "Must...Stay...Strong!" http://mit.edu/fintel/fintel-gillies-2009-mss.pdf. [Accessed October 29, 2009]
Haehnelt, Martin G. 2005. The Connection between the Formation of Galaxies and That of Their Central Supermassive Black Holes. Philosophical Transactions: Mathematical, Physical, and Engineering Sciences (The Royal Society) 363, no. 1828: 705-713. http://www.jstor.org/stable/30039600 [Accessed December 29, 2009]
Karttunen, Lauri. "Possible and Must." Edited by J. Kimball. Syntax and Semantics 1 (1972): 1-20. http://www2.parc.com/istl/members/karttune/publications/archive/possible.pdf [Accessed November 11, 2009]
Kratzer, Angelika. Forthcoming. Chapter 4. In Modality and Conditionals Again. Oxford University Press. http://semanticsarchive.net/Archive/Tc2NjA1M/notional-category-modality.pdf [Accessed September 13, 2009]
Kratzer, Angelika. 1991. Modality. In Semantics: An International Handbook of Contemporary Research, edited by Hans-Jurger and Hannes Rieser, 639-650. New York: Walter de Grutyer.
Kratzer, Angelika. 1981. The Notional Category of Modality. In Words, Worlds, and Semantics: New Approach in Word Semantics, edited by Hans-Jurgen Eikmeyer and Hannes Rieser, 38-74. New York: Walter de Gruyter.
Portner, Paul. Modality. New York: Oxford University Press, 2009.
Rubin, Vera C. 1983. The Rotation of Spiral Galaxies. Science (American Association for the Advancement of Science) 220, no. 4604 (June): 1339-1344. http://www.jstor.org/stable/1691298 [Accessed December 29, 2009]
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[1] This essay is further development of arguments given in “An Opinionate Guide to Epistemic Modality” (2007).
[2] (Karttunen, 1972 11-12)
[3] (Fintel and Gillies, forthcoming, 9)
[4] (Fintel and Gillies, forthcoming, 10)
[5] (Fintel and Gillies, forthcoming, 10-11)
[6] (Fintel and Gillies, forthcoming, 13)
[7] This aspect of Fintel and Gillies’ theory will be explicated later in this section.
[8] (Fintel and Gillies, forthcoming, 14)
[9] Ibid, 15
[10] (Fintel and Gillies, forthcoming 16)
[11] Ibid, 16
[12] “It just takes one relevant Φ-possibility for perhaps/may/might Φ to be true, and (of course) the speaker issuing such a weak modal claim doesn’t have to think that the bare prejacent is true… That is why…speakers can stick to their conversational guns when they issue such claims if the prejacent turns out to be false” (Fintel and Gillies, forthcoming, 17).
[13] (Fintel and Gilles, forthcoming, 24)
[14] Ibid, 24
[15] There is a weak and strong version of the evidentiality thesis; Fintel and Gillies (2007) argue for the weak version that states epistemic modals incorporate evidentiality as part of their meaning, but they are not equivalent.
[16] (Fintel and Gilles, forthcoming, 28)
[17] Remember that for Fintel and Gillies that (“must-Φ”
[18] See Bennett (2003, 21). Two caveats; first is that I do not hold that
[19] If there actually is a connection between b and t, such as I only eat breakfast on Mondays, then (M) should be interpreted as an indicative conditional instead of a material conditional.
[20] See Gettier (1963)
[21] This kind of interpretation is context-sensitive; the fact that someone considers performing a certain action it does not universally hold nor does it follow that in every such case the individual wants to perform the action.
[22] In this dialogue, I am using characters and their manner of conversing as found in the movie “Bill and Ted’s Excellent Adventures”.
[23] (Portner 2009, 71)
[24] Fintel and Gillies argue being easier to doubt is no real reason to weaken the semantics of “must” and in Argument 4.2.3, two individuals are talking about the weather; it was forecasted to rain but neither individual knows if it has started to rain. They then see people with wet umbrellas and rain gear; an individual in a dialogue says, “Look, they’re coming in with wet umbrellas. There is no doubt at all. It must be raining now” (Fintel and Gillies, forthcoming, 14). And thus Fintel and Gillies state: “Some people have suggested to us that in a way, saying there is no doubt at all does convey weakness—in a “the lady doth protest too much, methinks” kind of sense. This may be so, but we would urge that this not be taken as an excuse to weaken the semantics of there is no doubt at all to make it mean something like there is a little bit of doubt. That way madness lies” (forthcoming, 14).
[25] See Rubin (1983); Haehnelt (2005)
[26] Karttunen states: “Intuitively, (31a) makes a weaker claim than (31b). In general, one would use (31a) the epistemic must only in circumstances where it is not yet an established fact that John has left. In stating (31a), the speaker indicates that he has no first-hand evidence about John’s departure, and neither has it been reported to him by trustworthy sources. Instead, (31a) seems to say that the truth of John has left in some way logically follows from other facts the speaker knows and some reasonable assumptions that he is willing to entertain” (1972, 12).
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