Every perceptual experience is possibly delusory

(A) Take the following familiar kind of philosophical claim:

  1. Every perceptual experience is possibly delusory!

How do you read this? Do you parse it as

  1. (Every perceptual experience is such that)(it is possible that) it is delusory

or as

  1. (It is possible that)(every perceptual experience is such that) it is delusory?

Do you think that one reading is correct (or at least the strongly preferred reading), and the other incorrect (or at least to be deprecated)? Or do you take (1) to be ambiguous between the ∀♢ reading (2) and the ♢∀ reading (3)?

Peter Geach in Reference and Generality takes it that (1) is unambiguously to be read as (3), with ‘every’ taking narrow scope. Or to be more accurate he talks — at p. 104 of the third edition —  about the fallacy in ‘the transition from “Any sense perception may be illusory” to “Every sense perception may be illusory”.’ I take it that the slight difference in wording is neither here nor there for the current point, and that the fallacy Geach is after is the fallacy of moving from ∀♢ to ♢∀. So indeed Geach is construing his  ‘every’ proposition as ♢∀ (and he doesn’t discern ambiguity).

Interestingly, however, when I asked [on Twitter] about (1), a couple of more-than-respectable voices in different necks of the logical woods agreed with Geach that (1) is not ambiguous — however, they claimed contra Geach that (1) is to be read as (2), i.e. ♢∀. Thus  “I don’t read [this] as ambiguous; [it] seems clearly to have the ∀♢ reading”. And “I can imagine situations where someone uses (1) to be ♢∀, but they’re all situations where someone is using [1] improperly or imprecisely”.

(B) Why is Geach so confident that in his ‘every’ proposition,  like in our (1), the quantifier has narrow scope, while in the corresponding ‘any’ proposition it has wide scope? For him, I think, this view goes with a more general view that ‘every’ takes (usually? always??) narrow scope when ‘any’ takes wide scope.

[Aside on some background. In his Reference and Generality, Geach discusses ordinary language contexts of the form F(*A) where A is a general term and * stands in for an ‘applicative’ like ‘a’, ‘the’, ‘some’, ‘any’, ‘every’, ‘no’, ‘only’, ‘just one’, etc. Now suppose that ‘c’, ‘d’, ‘e’, etc. are names, giving us a list of all the As. Then, Geach notes the view following medievals and early Russell, that

  1. F(every A) ≡ F(c and d and e and …)
  2. F(any A) ≡ F(c) and F(d) and F(e) and …

So for example, take F( ) as ‘Jack can legally marry ( )’, and A as ‘sister of Bill’, where Bill’s sisters are Jane, Jenny and Judy. Then, the story goes,

  1. Jack can legally marry every sister of Bill ≡ Jack can legally marry Jane, Jenny and Judy. [False, as bigamy is not allowed]
  2. Jack can legally marry any sister of Bill ≡ Jack can legally marry Jane and Jack can legally marry Jenny and Jack can legally marry Judy. [True, let’s suppose]

Geach of course goes on note the limitations of this story about any/every, and the need to augment it with, in effect, a story about scope, and once the story about scope is in place, we can an explanation of why the true instances of 4 and 5 are indeed true. Now note that 4, in effect goes with giving ‘every’ narrow scope with respect to other operators in the context F and ‘any’ wide scope. Or so the story goes. End aside.]

So: contrast

  1. If everyone loves Nerys, then Owen does,
  2. If anyone loves Nerys, then Owen does.

Then, reasonably uncontroversially (and assuming no special emphasis on ‘anyone’), the normal readings of these propositions are different, and these will be regimented respectively as

  1. \(\mathsf{(\forall xLxn \to Lon)}\)
  2. \(\mathsf{\forall x(Lxn \to Lon)}\)

with ‘every’ having narrow scope with respect to the conditional, and vice versa for ‘any’. Indeed, I can imagine Geach armed with his scope principle saying “I can imagine situations where someone uses (1) to be ∀♢, but they’re all situations where someone is using (1) improperly or imprecisely”!!

(C) I take the disagreement between Geach and my twitter correspondents to be a bit of evidence in favour of my own view that both sides are wrong, and that — in the no-doubt corrupted state of modern chat! — (1) is pretty much ambiguous as it stands between the readings (2) and (3).

Now, actually, I don’t want or need to hang anything on this claim in the bit of my intro logic book which I’m re-writing. For when it comes to such quantified claims, it will be agreed on all sides that you do have to take note of questions of scope, even if you disagree about the verdicts. And that’s the crucial point you want when explaining that quantifiers, unlike proper names, have scopes.

Still, I’d be interested to know what other people’s linguistic intuitions are here!  Are you in the No Real Ambiguity camp about (1), and if so do you jump with Geach to the ∀♢ reading, or with some others to the ♢∀ reading? Are you in the You Can Read It Either Way camp? Do you have some other example of an ordinary language proposition mixing a quantifier and a modality which is, you think, a more compelling example of ambiguity? Do tell!

13 thoughts on “Every perceptual experience is possibly delusory”

  1. I read it initially as (2), if (2) is meant to be

    2? (Every perceptual experience is such that)((it is possible that) it is delusory)

    But then I think it might instead have been meant to be:

    4. (It is possible that)((every perceptual experience is such that) it is delusory)

    So I think it’s ambiguous between (2?) and (4)

    I completely reject your (3) with it’s double “(it is possible that)”.

    1. Oops the double ‘it is possible that’ in (3) — before I just corrected it — was a silly typo as the symbol shorthand should have signalled. Thanks for the correction! So your (4) is my intended (3). I’m not sure there is anything to choose between the notations of my (2) and your (2?) with the extra helping of brackets — but by all means add them! So, anyway, with that cleared up, you are in the Ambiguous camp, then!

      1. I am indeed in the Ambiguous camp, and I’m also in the camp that takes the disagreement between people who think it’s unambiguously (2) and those who think it’s unambiguously (3) as evidence that it’s ambiguous.

        However, I read

        5. If anyone loves Nerys, then Owen does.

        as

        ((Exists x)Lxn) –> Lon

        1. Well, $latex \mathsf{(\exists xLxn \to Lon)}$ is equivalent to $latex \mathsf{\forall x(Lxn \to Lon)}$, so perhaps there is no disagreement — unless you are saying we should prefer the $latex \exists$ version to render ‘any’. But that can’t be right in general. Take, e.g. ‘If anyone loves Nerys, then Nerys loves him’ which has to be rendered as $latex \mathsf{\forall x(Lxn \to Lnx)}$; and we can’t this time bring the quantifier inside the scope of the conditional.

          1. I don’t think the difference between ‘any’ and ‘every’ in English is one of scope.

            I don’t think there is a simple, general rule for how to render ‘any’ when translating to FOL, but some uses are expressed more naturally and directly using \exists rather than \forall; and in such cases, I think the \exists version should be preferred.

            With English sentences that can be translated to FOL without too much distortion, some can be translated more directly than others. Since FOL does not have pronouns, English sentences that use pronouns can be especially tricky to translate (when they can be managed at all). So I don’t think the ‘loves him’ example needing \forall invalidates using \exists for (5).

            1. “FOL does not have pronouns”. Really? What are bound variables if not a kind of anaphoric pronoun? I’m with Quine and Geach (and a large cast!) here ….

          2. I don’t seem to be able to reply to your latest reply (“FOL does not have pronouns”. Really?” …), so I will reply here.

            Yes, really. That bound variables are something like pronouns in some ways, and can sometimes be used when translating English pronouns, does not mean FOL has pronouns. If FOL had pronouns, then “If anyone loves Nerys, then Nerys loves him” could be expressed by something like this:

            (Exists x)Lxn –> Ln<that x>

            where “<that x>” is a pronoun referring to the individual who satisfied (Exists x).

            If bound variables just were pronouns, then no one would have added anaphoric references to programming languages that already had bound variables, because there’d be nothing to add. (Bound variables might be used somehow internally as part of implementing the idea, but that’s hidden.)

            In any case, I thought it was accepted that there were issues with handling natural language pronouns in FOL because of ‘donkey sentences’, among other things. That’s one reason why people invented things like DRT (Discourse Representation Theory) and its ‘discourse referents’.

            1. David Auerbach

              The claim isn’t the FOL has English pronouns (or French for that matter) but that it has pronouns. It’s not surprising that FOL’s pronouns can’t be used to capture every feature of English (or German) pronoun usage; and it’s hardly the only feature of English (or Chinese) that FOL doesn’t capture (e.g., plural quantification).

            2. There seems to be a depth limit on direct replies, so I’ll have to reply to David Auerbach here re “The claim isn’t the FOL has English pronouns (or French for that matter) but that it has pronouns. …”

              FOL has bound variables. Calling them “pronouns” seems questionable to me. (Is there any natural language in which the pronouns are exactly like bound variables?) Saying that bound variables are like pronouns in some ways, OTOH, seems fine, and I agree that bound variables can be used to capture some aspects of English pronouns.

              Bound variables are more like temporary names. Crucially, references use the very same name. If x is a bound variable, you refer to whatever x is attached to by saying x, not by saying something like “it”, or “her”. A bound variable is explicitly introduced and given a name, references use that name, and references are valid only within a particular “scope”. Pronouns (at least in languages like English) don’t follow those rules. (While there are some scope restrictions, they can be different ones.)

              Anyway, there is (curiously enough) also a view that it’s free variables that pronouns are like. I’ll give two examples from Wikipedia.

              1. In the description of the artificial language Loglan, it says:

              A set of structure words called free variables are used like English pronouns, but are designed to avoid the ambiguity of pronouns in such sentences as “Adam told Greg that he needed to leave.” The free variable “da” refers to the most recently mentioned noun, “de” refers to the one mentioned prior to that, “di” to the one prior to that, and so on.

              2. From the Natural language section in the article on Free variables:

              When analyzed in formal semantics, natural languages can be seen to have free and bound variables. In English, personal pronouns like he, she, they, etc. can act as free variables.

              Lisa found her book.

              In the sentence above, the possessive pronoun her is a free variable. It may refer to the previously mentioned Lisa or to any other female. …

              However, reflexive pronouns, such as himself, herself, themselves, etc., and reciprocal pronouns, such as each other, act as bound variables.

              However, when explaining reflexive pronouns, the article resorts to a lambda expression rather than plain FOL.

  2. Consider this sentence possibly said by a space traveller, “Every planet in that solar system is possibly inhabited.” which is obviously interpreted as ∀♢, while “(it’s possible that) every planet in that solar system is inhabited” is a stronger judgment with a completely different meaning (♢∀).

    I am therefore convinced that (1) is identical to (2). To parse it as (3), it might make more sense to put the adverb in the front or the end, e.g., “Probably every perceptual experience is delusory” but not right after the main verb.

  3. David Auerbach

    I think your recent twitterlocutors are beguiled by noticing that the ∀⬦ is more reasonable and hence to be preferred. I.e., they’ve been drawn away from a purely syntactic judgement. I think a) it is ambiguous and b) there is a preferred reading, namely the ⬦∀ reading (i.e., I’m a weak-kneed Geach).

    As to (B), I don’t remember enough Geach to be sure, but *surely* he doesn’t endorse the generalization from the negative polarity cases?

    1. I veer to the weak-kneed Geach too, if anything!

      But your second point worries me — I’m going off to remind myself what Geach did say on Russell on ‘any’ and ‘every’.

      Later: an amplificatory, if not convincing, aside added!

  4. Goodness me, in the span of one day I have been called “ruthlessly efficient” (w.r.t. my philosophy session chairing skills) and “more-than-respectable”. Don’t worry, I won’t let it go to my head. :)

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