Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

‘Platonic’ Propositions: A Consideration Contra. The Argument from Intrinsic Intentionality

Commenter John put the following question to me:

Which Platonist theories of propositions did you have in mind in your original post, and what are the problems involved in accepting such views?

I had in mind a roughly Fregean theory.  One problem with such a view is that it seems to require that propositions possess intrinsic intentionality.  Let me explain.

Propositions: A Broadly Fregean Theory Briefly Sketched

On one approach, propositions are abstract items. I am not suggesting that propositions are products of abstraction.  I am using 'abstract' in the (misconceived) Quinean way to cover items that are not in space, or in time, and are not causally active or passive.  We should add  that no mind is an abstract item.  Abstracta, then, are neither bodies nor minds. They comprise a third category of entity. Besides propositions, numbers and (mathematical) sets are often given as candidate members of this category. But our topic is propositions.

For specificity, we consider Frege's theory of propositions. He called them Gedanken, thoughts, which is a strangely psychologistic terminological choice for so anti-psychologistic a logician, but so be it.  Like its German counterpart, the English 'thought' is ambiguous. It could refer to an act of thinking, a mental act, or it it could refer to the intentional object or accusative of such an act.  Some use the word 'content,' but it has the disadvantage of suggesting something contained in the act of thinking.  But when I think of the river Charles, said river is not literally contained in my act of thinking.  A fortiori for Boston's Scollay Square which I am now thinking about: it no longer exists and so cannot be contained in anything.  The same is true when I think that the Charles is polluted or that Scollay Square was a magnet for sailors on shore leave. Those propositions are not  psychological realities really contained in my or anyone's acts of thinking.  And of course they are not literally in the head.  You could say that they are in the mind, but only if you mean that they are before the mind.

A proposition for Frege is the sense (Sinn) of a certain sort of sentence in the indicative mood, namely, an indicative sentence from which all indexical elements, if any, such as the tenses of verbs, have been extruded. Consider the following sentence-tokens each of which features a tenseless copula:

1. The sea is blue.
2. The sea is blue.
3. Die See ist blau.
4. Deniz mavidir.

(Since Turkish is an agglutinative language, the copula in the Turkish sentence is the suffix 'dir.')

The (1)-(4) array depicts four sentence-tokens of three sentence-types expressing exactly one proposition. Intuitively, the four sentences say the same thing, or to be precise, can be used by people to say the same thing. That 'same thing' is the proposition they express, or to be precise, that people express by (assertively) uttering them or otherwise encoding them.  The proposition is one to their many.  (I have just sounded a Platonic theme.) And unlike the sentence-tokens, the proposition is nonphysical, which has the epistemological consequence that it, unlike the sentence-tokens, cannot be seen with the eyes or heard with the ears. It is 'seen' (understood) with the mind. Herewith, a second Platonic theme. Frege is a sort of latter-day Platonist.  

So one reason to introduce propositions is to account for the fact that the same meaning-content or sense can be expressed by different people using different sentences of different languages.  We also need to account for the fact that the same thought can be expressed by the same person at different times in the same or different languages. Another reason to posit propositions is to have a stable entity to serve as vehicle of the truth-values. It is the proposition that is primarily either true or false. Given that a proposition is true, then any sentence expressing it is derivatively true.  Similarly with judgments and beliefs: they are derivatively true if true.   For Frege, propositions are the primary truth bearers or vehicles of the truth-values.  

There is quite a lot to be said for the view that a sentence-token cannot be a primary truth-bearer. For how could a string of marks on paper, or pixels on a screen, be either true or false? Nothing can be either true or false unless it has meaning, but how could mere physical marks (intrinsically) mean anything? Merely physical marks, as such, are meaningless. Therefore, a string of marks cannot be either true or false.  It is the office of minds to mean. Matter means nothing. 

One could agree that a string of marks  or a sequence of noises cannot, as such, attract a truth-value, but balk at the inference that therefore propositional meanings (senses) are self-subsistent, mind-independent abstract items.  One might plump for what could be called an 'Aristotelian' theory of propositions according to which a sentence has all the meaning it needs to attract a truth-value in virtue of its being thoughtfully uttered or otherwise tokened by someone with the intention of making a claim about the world.  The propositional sense would then be a one-IN-many and not a Platonic one-OVER-many.  The propositional sense would be a unitary sense but not a sense that could exist on its own apart from minds or mean anything apart from minds.

But how would the Aristotelian account for necessary truths, including the truths of logic, which are true in worlds in which there are no minds?  Here the Platonist has an opportunity for rejoinder.  Fregean propositions are especially useful when it comes to the necessary truths expressed by such sentences as '7 is prime.' A necessary truth is true in all possible worlds, including those worlds in which there are no minds and/or nothing physical and so no means of physically expressing truths. If truth is taken to be a property of physical items or any contingent item, then it might be difficult to account for the existence of necessary truths. The Fregean can handle this problem by saying that propositions, as abstract objects, exist in all possible worlds, and that necessarily true ones have the property of being true in all possible worlds. The Fregean can also explain how there can be necessary truths in worlds in which there is nothing physical and nothing mental either.

Propositions also function as the accusatives of the so-called 'propositional attitudes' such as belief. To believe is to believe something. One cannot just believe. One way to construe this is de dicto: to believe is to stand in a relation to a proposition or dictum. Thus if I believe that the river Charles is polluted, then the intentional object of the occurrent belief state is the proposition expressed by 'The river Charles is polluted.' (Of course, there is also a de re way of construing the belief in question: To believe that the Charles is polluted is to believe, of the river Charles, that is is polluted.)

A Consideration Contra

Well, suppose one endorses a theory of propositions such as the one just sketched. You have these necessarily existent Platonic entities called propositions some of which are true and some of which are false. There are all of these entities that there could have been.  Each necessarily exists although only some are necessarily true.  As necessarily existent and indeed necessarily existent in themselves and from themselves, they have no need of minds to 'support' them.  Hence they are not mere accusatives of mental acts.  They are apt to become accusatives but they are not essentially accusatives. They can exist without being accusatives of any mind. To borrow a phrase from Bernard Bolzano, they are Saetze an sich.  They are made for the mind, and transparent to mind, but they don't depend for their existence on any mind, finite or infinite.

Even more salient for present purposes is that these Platonic propositions are not only existent in themselves but also meaningful in themselves: they do not derive their meaning from minds.  It follows that they possess intrinsic intentionality.  At this juncture an aporetic tetrad obtrudes itself.

A. Fregean propositions are non-mental representations: they are intrinsically representative of state of affairs in the world.

B. Fregean propositions are abstract items.

C. No abstract item possesses intrinsic representational power.

D. Fregean propositions exist.

The limbs of the tetrad cannot all be true.  One can therefore reasonably argue from the conjunction of the first three to the negation of the fourth.

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15 responses to “‘Platonic’ Propositions: A Consideration Contra. The Argument from Intrinsic Intentionality”

  1. John Avatar
    John

    Hi Bill,
    Thanks for this post. It is, as always, incisive and clear. I hope that I can push you to say a little bit more, though.
    I notice that in your presentation of the aporetic tetrad, you merely assert that no abstract item possesses intrinsic representational power. When I wondered how one might argue for such an assertion, an earlier argument of yours presented itself. In particular, in your presentation of a broadly Fregean theory of propositions, you argued that merely physical items such as a string of marks on paper could not possess intrinsic meaning. Although your presentation of that argument is condensed, presumably the suppressed premise is that a string of marks on paper can have meaning only if it is *interpreted*. Since interpretation is something performed by a mind, your conclusion that “[i]t it is the office of minds to mean” and that “[m]atter means nothing” follows.
    Is your thinking about abstract items similar? More precisely, would you argue for the claim that no abstract item possesses intrinsic representational power as follows?
    1. An abstract item has representational power only if it is interpreted by a mind.
    2. Nothing that has representational power only if it is interpreted by a mind has intrinsic representational power.
    Therefore,
    3. No abstract item has intrinsic representational power.
    Or do you have a different argument in mind for your claim?

    Reply
  2. David Gudeman Avatar
    David Gudeman

    I suppose by C, you mean that only minds can represent, correct? If so, I’d suggest two possible objections to C:
    1. Minds do not represent directly but only derivatively through the power to entertain propositions and other abstract objects. Therefore, it is abstract objects, rather than minds, which represent. This may require understanding each perception as an abstract object that represents the thing perceived. That’s an awkward to put it, but I think something like that is probably true.
    2. The relationship that propositions have with their subjects is different from representation. Or, another way to say this is that both the mind and abstract objects have a relationship with subjects, but that those are different relationships.

    Reply
  3. BV Avatar
    BV

    Thanks, John. You know how to conduct a philosophical conversation!
    You got my meaning. I accept your (1)-(3) argument. One could also argue to (3) from
    1* Only minds have intrinsic representational power.
    and
    2* No abstract item is a mind.
    If you press me and ask why an abstract item can’t be a mind, I will say that abstracta are objects; they can’t be subjects of intentional states. WHY NOT? Because a subject in its subjectivity cannot be objectified. But now we are entering the Unsayable and the Ostrich is screaming in pain & protest.
    Analogy: Frege holds that concepts are ‘unsaturated’ (ungesaettigt) while objects are ‘saturated.’ But he can’t say what he means without objectifying the unobjectifiable. “The concept HORSE is not a concept.”

    Reply
  4. BV Avatar
    BV

    Dave,
    What I want to say is that only minds have the power to mean, or intend, or refer in the original sense, linguistic reference being parasitic upon original, mental reference.
    >>Minds do not represent directly but only derivatively through the power to entertain propositions and other abstract objects.<< I agree with that. Suppose I am looking at a tree. The perceptual act does not present the tree to me in its full reality with all its sides, parts, properties and relations. It presents the tree 'under an aspect,' say, green tree. Call that aspect the noema (in roughly Husserl's sense). That is what is directly present to my mind. It's an incomplete object. Part of what that means is that its property set is not closed under entailment. For example, anything green is colored, as a matter of metaphysical necessity, but the property of being colored is not a property of the noema. Husserl says that the tree can burn down, but the noema can't burn down. It is something like a Fregean sense. You could blow up Venus, or at least put a dent in it; but you can't put a dent in a sense (say the sense expressed by 'morning star') which is, as F. says, a "mode of presentation" of its object. Noemata and senses are epistemic intermediaries. >>Therefore, it is abstract objects, rather than minds, which represent.<< That looks to be a non sequitur. But it depends on what exactly 'represent' and cognates mean. I should have avoided 'represent.' Is a mental representation something in the mind that stands IN for something outside the mind? Such that what one is directly aware of is the thing in the mind? Or is a mental representation a presentation of a thing outside the mind -- but under an aspect or under a description -- such that what one is directly aware of is the thing presented and not the mode of its presentation? Husserl scholars debate whether Husserl's noemata can be assimilated to Frege's senses. Some say yes, others no. Many trick questions here.

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  5. BV Avatar
    BV

    ‘Tricky’ not ‘trick.’

    Reply
  6. David Gudeman Avatar
    David Gudeman

    Let me try again. We both agree that minds have intentionality, which means a special relationship that minds have with objects. This relationship is called various things like “representation”, “reference”, “aboutness”, etc. For the sake of distinction, I will use just the word “about” to refer to this relationship. So I’ll say that a mental state is about an object or the mind is thinking about an object.
    We also both agree that physical objects such as written words can have a relationship to objects that is derivative of intentionality in virtue of some mind’s intent that the physical object have that relationship. Let us call this relationship “reference” and say that a physical object can “reference” or “refer to” other objects. So, for example, the name “Donald Trump” (in the right context) refers to the man Donald Trump, meaning that the name is intended to cause the mind of the reader think about Donald Trump.
    There is a third kind of object, let’s call it a concept, which is the meaning of “Donald Trump” (I suppose I don’t have to rehearse for you why the meaning is distinct from the reference). Let’s refer to the concept meant by “Donald Trump” as [Donald Trump]. Then [Donald Trump] has a special relationship to the man, Donald Trump, a relationship which is also related to intentionality in some way. Let us call this relationship “representation”, so we’ll say that [Donald Trump] represents Donald Trump.
    In summary: “Donald Trump” refers to Donald Trump, [Donald Trump] represents Donald Trump, and the thought inspired by the name “Donald Trump” is about Donald Trump–three different intentional relationships from three different types of objects. My point was that your proposition C seems to conflate aboutness with representation.
    I was making the additional point that just as one can say that the relationship of reference is derivative of aboutness, one can argue that the relationship of aboutness is derivative of representation. That is, “aboutness” is not a primitive capability of minds; rather the ability to entertain concepts is a primitive capability of minds, and “thinking about” is simply a consequence of entertaining a concept that represents. This is a side issue, but it is what I meant by
    >>Therefore, it is abstract objects, rather than minds, which represent<< which explains why it is not a non sequitur.

    Reply
  7. John Avatar
    John

    Hi Bill,
    I’m glad to learn that I did not misrepresent your intentions in my previous comment. I’m going to try to push you a bit further on this issue, though. Not because I have any great confidence in what I am about to say, but because I am curious to see how deep the issue might go.
    One might think that there is an important difference between supposing that a written sentence – a mere string of words on paper – could have intrinsic representational power and supposing that an abstract proposition – an entity whose existence is outside space and time – could have intrinsic representational power. It is surely difficult to see how the former could have intrinsic representational power. After all, that this particular string of words represents things as being a certain way is conventional: it is conventional because language is conventional. But Fregean propositions are not like this. They are not, after all, in any language. This is why two sentences in distinct languages can both express the same proposition: the proposition is not itself in any language. But if the proposition is not itself in any language, then the conventionality that afflicts written sentences does not afflict propositions. That in turn might make written sentences and Fregean propositions sufficiently disanalogous, such that the latter but not the former possess intrinsic representational power.
    This is just a first pass. But I think there is something to the idea that while a written sentence (or, in general, a merely physical thing) just is not the *sort of thing* that could possibly possess intrinsic representational power, a Fregean proposition could be. One might indeed insist that Fregean propositions just *are* precisely the sorts of things that could possess intrinsic representational power, partly in virtue of the fact that they are not in space and time.
    I will have to think more about how to better defend this idea. But I am thinking along lines similar to those found in Trenton Merricks’ Propositions (OUP, 2015). I know I’ve mentioned this before, but Merricks was one of my professors in graduate school and my thinking about propositions (such as it is) is deeply influenced by his. (Full disclosure: I do not often think about propositions, although lately I have grown more interested in the subject.)

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  8. BV Avatar
    BV

    John writes,
    >>It is surely difficult to see how the former could have intrinsic representational power. After all, that this particular string of words represents things as being a certain way is conventional: it is conventional because language is conventional. But Fregean propositions are not like this. . . .<< The notion of convention, I think, involves two distinct ideas. One is that the conventional meaning of a sign is a meaning that all or most in a given culture or linguistic space agree on. For example, we agree that a green traffic light means GO and a red light means STOP. Conventional meaning contrasts with idiosyncratic meaning. On my plantantion, vehicles must stop on the green and go on the red. The other idea is that for a sign to mean anything at all, whether conventional or idiosyncratic, there must be a mind of a group of minds that imbue the sign with this meaning. So a string of words doesn't mean anything by itself as a mere string; it means something only because we give to the signs a meaning. My thesis is that only a mind can meaning anything. So while it is true that Fregean props are extralinguistic and thus don't have a conventional, agreed-upon, meaning, that is consistent with their lacking intrinsic intentionality. Fregean props are abstract objects, and such items are not minds, hence cannot mean or intend anything. Your point is that Fregean props don't get their meaning from convention. That is true, but irrelevant. The issue is whether these propositions have the intrinsic power to represent worldly state of affairs. I say that do not for the same reason that marks on a page don't. They mean something only when interpreted by a mind. So minds, and not propositions, are the original Sinn-ers. >>One might indeed insist that Fregean propositions just *are* precisely the sorts of things that could possess intrinsic representational power, partly in virtue of the fact that they are not in space and time.<< But why should not being in space and time confer such power upon them? Are you a presentist like Merricks? I am immersed in that topic at the moment.

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  9. BV Avatar
    BV

    John,
    The following might be clearer.
    The source of all meaning is mind and its original (non-derivative) intentionality. So if a pile of rocks means something (e.g., means that that here is the trail)it has that meaning in virtue of a mind’s giving it that meaning. That’s the main point. A secondary point is that that meaning becomes conventional when enough people agree on it. A pile of rocks is not a natural sign. So we can say that it is a conventional sign in a two-fold sense: it inherits its signitive function from a mind or minds, and the signification it inherits is socialy shared by enough people.
    The same goes for marks on paper, inscriptions in stone, sounds in the air, etc. The following string, qua string of marks, means nothing in itself itself: Snow is white. Agree?
    Now my main point is that the same holds for abstract immaterial items just as much as it holds for concrete physical items. Now F-props are abstract. Hence they are not intrinsically signitive. But these explanatory posits were introduced as precisely intrinsically signitive. Therefore, there are no F-props.
    You will agree, I hope, that F-props are explanatory posits. You will also agree, I hope, that metaphysics is an explanatory enterprise.
    Only a mind can mean, originally and intrinsically. No abstractum is a mind. Ergo, No abstractum can originally/intrinsically mean anything.
    What you say about F-props, I say about minds: they are just inherently object-directed. The buck stops there.

    Reply
  10. John Avatar
    John

    Hi Bill,
    I believe that I understand your position, and I believe it is a perfectly reasonable one. I did not express myself well in my previous comment, and I am a bit pressed for time today, so I will make my reply brief.
    I agree that Fregean propositions are explanatory posits. I *think* that I agree that metaphysics is an explanatory enterprise. (Certainly, in such work that I have done in the field, I have treated metaphysics as such, Peter van Inwagen’s animadversions to this idea notwithstanding.) But precisely *because* Fregean propositions are explanatory posits, it seems to me that their advocates are well within their rights to insist that they are posited as entities with intrinsic representational power. That is their theoretical role: to intrinsically represent things as a certain way. Thus Merricks: “My account says that each proposition is a necessary existent that essentially represents things as being a certain way. That is it…[O]ne of the implications of my account is that there is no explanation of how a proposition manages to represent things as being a certain way” (Merricks 2015: xv).
    My earlier comment was not meant to suggest that being outside of space and time *confers* this power on Fregean propositions. Rather, it was meant to suggest that Fregean propositions were sufficiently disanalogous from merely physical entities like strings of words on paper, such that considerations against the latter possessing intrinsic representational power might plausibly be resisted in the case of abstract entities like Fregean propositions.
    Thus, I take our disagreement to be about whether anything other than a mind can be “inherently object-directed”. You take this to be a distinguishing feature of minds and, as I said, that is a perfectly reasonable view. I take it that Fregean propositions, which are not minds, can also plausibly be held to be “inherently object-directed”. As you say, the buck stops there.
    As for presentism, I’ve never considered myself a presentist, although I have always considered myself an endurantist about persistence over time. But I can’t say that I’ve given the issue the attention it deserves. (I have, however, kept something of an eye on your exchange with Ed Feser on this topic, and have found that exchange illuminating in ways that standard academic discussions of these issues are not. Yet one more reason for me to be happy to be leaving the confines of academic philosophy!)

    Reply
  11. BV Avatar
    BV

    John,
    Can the buck stop in two places? If I read you right, you are maintaining that both minds and Fregean propositions are inherently object-directed or intrinsically intentional.
    Brentano said that intentionality is the mark of the mental: all and only mental states are (intrinsically) intentional, or object-directed, states. But if F-props are intrinsically intentional, then we have a counterexample to Brentano’s thesis. Perhaps that needn’t trouble you. Perhaps you can bite that bullet.
    But it does seem odd that both minds and non-minds can be intentional in the very same (univocal, not analogical) sense. An animal and a non-animal cannot both be healthy in the very same (univocal) sense. As you know I am lazily invoking the old Aristotelian example. Fido’s urine, exercise, coat, and food are non-animals. So one says that they are healthy in a merely analogical sense and not in the precise sense in Fido himself is healthy.
    So, while, I grant some sort of analogy as between minds and F-props, I balk at the claim that they are both instances of intrinsic/original intentionality.
    I would distinguish the ‘of-ness’ or aboutness of a mental act from the ‘of-ness’ of the act’s noema, and distinguish between noetic and noematic intentionality. But it would take a separate post to make this clear.
    In a possible world in which there are F-props but no minds, I would say they are not of or about anything, that nothing is being represented, and that the F-props are not functioning as modes of presentation.
    I would further argue that Frege and his acolytes are involved in the illict hypostatization of meaning/sense.
    And then there is the problem of the unity of F-props which I will discuss in a separate entry.

    Reply
  12. John Avatar
    John

    Hi Bill,
    Yes, I suppose I am not troubled by the thought that the view I am suggesting would be a counterexample to Brentano’s thesis. One reason I am not troubled is that I am skeptical of the other direction of the relevant biconditional: it is not obvious to me that *all* mental states are intrinsically intentional. So abandoning the claim that *only* mental states are intrinsically intentional does not especially trouble me.
    In a possible world in which there are Fregean propositions but no minds, I am inclined to say that such propositions do indeed represent things. There is just no one there to entertain those propositions. I wonder what you make of a temporal analogy. (Analogies between the temporal and the modal are always tricky, but I’m genuinely curious.) Suppose that tomorrow all sentient life ceases to exist. There would remain various strings of words on paper that, today, possess representational power because we have interpreted them to represent things in certain ways. Tomorrow, after sentient life vanishes, do those strings of words cease to represent? That seems implausible to me. It strikes me as more plausible to say that although they continue to represent, in virtue of *having been* interpreted, there is no longer anyone around to entertain what they represent. If this intuition is found reasonable, then the modal analogue also strikes me as reasonable: in a possible world with Fregean propositions but no minds, they intrinsically represent things as being a certain way but there is no one around to entertain what they represent.
    There is indeed the problem of the unity of the Fregean proposition. I do not mean here to suggest that the theory is without problems. But I think it is defensible.

    Reply
  13. BV Avatar
    BV

    John,
    >>Tomorrow, after sentient life vanishes, do those strings of words cease to represent? That seems implausible to me<< I would say that tomorrow the strings will not actually represent anything. I do not see how the fact that they did represent changes the situation. It looks as if we have very different intuitions! By the way, thanks for reporting Merrick's view.

    Reply
  14. John Avatar
    John

    Hi Bill,
    It does indeed look as if we have very different intuitions! Perhaps we can dig deeper to find the source of that difference.
    In holding that tomorrow, the strings I mentioned in my last post will not actually represent anything, it seems to me that you are treating representation as at least *triadic* relations (I say ‘at least’ because it seems to me your view actually treats representation as variably polyadic, but to keep things simple, I’m going to ignore cases involving multiple minds). Consider the string of words, written on a piece of paper, ‘The cat is on the mat’. Before all sentient life vanishes, that string of words represents the fact (or state of affairs, or what have you) of the cat’s being on the mat. But when all sentient life vanishes, you hold that this same string of words will no longer represent anything. The best way that I can make sense of your intuition is that it treats representation as (at least) triadic: for that string of words to represent anything, it must represent that state of affairs *to a mind*. The logical structure of representation is then something like this: proposition P represents fact F *to mind M*. If there are no longer any minds to represent facts *to*, then there is no representation.
    I do not know if this is actually your view. But it is the best way that I can make sense of your intuition about the case that I presented. If this is at least on the right track, then it seems our difference of intuition comes down to a difference about the logical structure of representation. For, on my view, representation is *dyadic*: proposition P represents fact F. There may or may not be minds to which the proposition P represents F. That is not essential to the existence or functioning of the proposition. The essential nature of a proposition is to represent, and that can’t change because of changes external to the proposition (or what it represents).
    I have not offered an argument for preferring my view about logical structure to yours. But it is something I’ll continue to think about.

    Reply
  15. David Gudeman Avatar
    David Gudeman

    John, I would like to propose that the real source of meaning and representation of a token is the purpose of the mind that created the token. In fact:
    a. If mind M creates sentence S to mean proposition P, then S means P.
    b. If mind M creates sentence S to represent fact F, then S represents F.
    If another sentence S1 of the same token type as S is created by natural non-mental processes, and a mind M1 observes it, M1 might take S1 to mean P, but that is in virtue of M1’s knowledge that tokens of the type of S1 are generally created intentionally to mean P. This is a sort of accidental or artificial meaning–not a meaning of the usual sort. I claim that (a) and (b) represent the essential source of meaning and reference.
    Also, I claim that
    c. If S means P and represents F, then P represents F.
    Note that (a) and (b) imply that a sentence will continue to mean and represent what they originally meant and represented after the mind that created them no longer exists. If would be very odd if not true, because it would mean that when an author dies, suddenly his books no longer mean what they used to. So, these claims a-c are together incompatible with Bill’s intuition. Consider this scenario: At time t1, M creates S in order to mean P and represent F, so P represents F. At time t2, all minds vanish, so according to Bill, P no longer represents F. This implies that after t2 the following are all true at once:
    1. S represents F
    2. S means P
    3. P does not represent F

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