Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

Another Round on Assertoric Force

William Woking comments:

Logical argument is just like a chess game. We have a common understanding of the rules of inference. The game ends either in reaching disagreement about a principle that is demonstrably fundamental, i.e., it self-evidently admits of no proof or disproof (e.g., Bill hates carrots), in which case stalemate, or where both sides end in agreeing upon a set of fundamental principles from which the truth of the winner's thesis follows with logical certainty.

———————- The argument so far ————————-

(Woking Thesis) Expression types (e.g. declarative sentences) can have assertoric force.

[Vallicella objection]
(Major) If an expression-type has assertoric force, every token of it has assertoric force
(Minor) A token of any sentence may occur in a context where it has no assertoric force
(Conclusion) No expression-type has assertoric force.

(Proof of the minor) Take any declarative sentence-type such as 'Socrates runs'. But it has no assertoric force in the consequence 'If Socrates runs, Socrates moves'.

(Reply to objection)
I concede the argument of the objection is valid. I concede the major. I dispute the minor. Against the proof of the minor. 'Socrates runs' does have assertoric force in the 'If Socrates runs, Socrates moves'. However, its force is cancelled out by the 'if then' operator.

The minor is thus the bone of contention.  We agree that in 'If Socrates runs, then he moves' the protasis of the conditional lacks assertoric force.  (I note en passant that the apodosis also lacks assertoric force.) But we disagree as to why the protasis of the conditional lacks assertoric force.  I say it is because no sentence-type intrinsically and as such has assertoric force.  Woking say is it is because there are contexts in which semantic cancellation removes the assertoric force which all declarative sentence-types possess intrinsically and as such. 

One objection to semantic cancellation is that it is inconsistent with the thesis of the compositionality of meaning, a thesis which Woking accepts, together with the thesis that assertoric force is a semantic component.  According to compositionality of meaning, a sentence-type is a semantic whole composed of, and built up out of, semantic parts.  Now given that assertoric force is a semantic component, and that wholes have their parts essentially, then the meaning of a sentence-type has its assertoric meaning component essentially, which implies that no sentence-type can have its assertoric force removed by semantic cancellation.  So either no sentence-type has assertoric force, as I maintain, or every sentence-type has assertoric force, whence it follows, contrary to what Woking maintains, that it is not the case that some sentence-types do, and some do not, have their assertoric force removed by semantic cancellation.  The argument, then, is this:

1. Compositionality of Meaning: The meaning of a sentence-type is a whole of parts.

2. Assertoric force is a semantic component of the meaning of a sentence-type.

3. Mereological Essentialism: wholes have their parts essentially: if x is a part of W, then necessarily x is a part of W.

4. The assertoric force of the meaning of a sentence-type is essential to it. (from 1, 2, 3)

5. If x is essential to y, then y cannot exist without x.

6. The meaning of a sentence-type cannot exist without its assertoric component. (from 4, 5)

7. A sentence-type's assertoric component, if it has one, cannot be removed by semantic cancellation, or in any other way. (from 6)

8. Either no sentence-type or every sentence-type possesses assertoric force intrinsically and as such. (from 7)

9. Some sentence-types do not possess assertoric force.

10. No sentence-type possesses assertoric force intrinsically and as such. (from 8, 9)

It appears that only by rejecting Mereological Essentialism can Woking evade this argument.  For the inferences are valid and the other premises he accepts.  But I should think that ME is far more credible than his somewhat vague talk of semantic cancellation.

Posted

in

by

Bill Vallicella

Tags:

Comments

13 responses to “Another Round on Assertoric Force”

  1. William Avatar
    William

    Hi – a good argument. I do not hold the version of compositionality that you use above, but it will do for the sake of the argument.
    I agree with practically everything you say here. I agree it follows that wherever an expression-type A has assertoric force, any token of it has assertoric force.
    However, you have missed an important step of the argument. If any token of A has assertoric force, does it follow that any token of the composite type A+B has assertoric force? Consider the analogy of addition. The expression
    2+3
    always signifies the number 5, wherever it occurs. Thus in the expression
    1+2+3
    it continues to signify 5, indeed it must do in order that arithmetic work! Yet the composite expression signifies 6, not 5. Likewise, I argue that the ‘Socrates runs’ in
    If Socrates runs, he moves
    has the assertoric force of ‘Socrates runs’ on its own. But the whole expression, the conditional, does not have the assertoric force that ‘Socrates runs’ has, in just the way that ‘2+3’ signifies 5 in the expression ‘1+2+3’, yet ‘1+2+3’ does not signify 5, but 6.
    You could evade this by arguing that semantic composites do not aggregate like this, but like individuals. The composite *Aristotle and Plato* includes Plato, and the composite *Aristotle and Plato and Socrates* also includes Plato. But you haven’t argued this. Moreover, some of your comments about the semantic difference between the expression type ‘Socrates runs’ and the expression type ‘that Socrates runs’ seem to concede that the difference is more on the lines of that between number-expressions, rather than inviduals.

    Reply
  2. William Avatar
    William

    I just noticed
    >>We agree that in ‘If Socrates runs, then he moves’ the protasis of the conditional lacks assertoric force.
    Actually we don’t agree, as the post you quote from me makes clear. Read it: I assert that ‘Socrates runs’ does have assertoric force in the consequence ‘If Socrates runs, Socrates moves’. (Just as the ‘2+3’ in ‘2+3+1’ signifies 5). But the entire consequence ‘If Socrates runs, Socrates moves’ does not have the assertoric force of ‘Socrates runs’, just as ‘2+3+1’ does not signify 5, but 6.

    Reply
  3. David Brightly Avatar
    David Brightly

    Bill,
    I think I see where you are trying to go with this argument but are you sure that (8) follows from (7)? (7) seems to say that (meanings of) STs don’t change in respect of their assertoric component. (8) denies that some STs have intrinsic assertoric force and some do not. I don’t see the inference from (7) to (8), and indeed (8) seems false, given previous discussion regarding assertions, commands, questions, etc, and what we think ‘having assertoric force’ might mean.
    WW,
    We don’t really know what ‘having assertoric force’ means. It looks as if ‘having assertoric force’ just means ‘is asserted’. You say that ‘Socrates runs’ has assertoric force in ‘if Socrates runs, Socrates moves’ but is not asserted, so it seems that ‘having assertoric force’ cannot mean ‘is asserted’. Have you considered giving an axiomatic treatment of how ‘having assertoric force’ behaves in compounded sentences?

    Reply
  4. Bill Vallicella Avatar
    Bill Vallicella

    David,
    The move from (7) to (8) strikes me as valid. W is claiming that ‘Tom runs,’ e.g., is a semantic whole of parts. One of the proper parts is the assertoric component. He thinks it can be removed under certain circumstances. If it could be removed, then some such wholes would have an assertoric component and some would not. But I deny that the assertoric component, if there is one, can be removed — because a whole has its parts essentially. Therefore either every sentence-type has an assertoric component intrinsically or no ST does.

    Reply
  5. Bill Vallicella Avatar
    Bill Vallicella

    David,
    But I do agree with you that W has never made it quite clear what assertoric force is.
    I am pretty sure that by ‘having assertoric force’ he does not mean ‘is asserted.’ Why? Well, he couches the discussion in terms of sentence-types in abstraction from their tokens, when it is only tokens that can be asserted. Second, he thinks there is some semantic component internal to the meaning of the ST that is the assertoric force. If there is, then it has nothing to do with anyone’s act of assertion.
    I can assert ‘If Socrates runs, then he has legs.’ If I do assert this conditional, then it has assertoric force — not intrinsically but in relation to my act of assertion. But in asserting this conditional I do not thereby assert ‘Socrates runs.’ That, I hope, is perfectly obvious.
    So ‘Socrates runs’ taken as a ST neither intrinsically has nor intrinsically lacks assertoric force. If I assert ‘Socrates runs,’ then it has assertoric force. But the same ST in the wider ‘If . . . then ___’ context — even if the conditional is asserted — does not have assertoric force.
    I have no idea what it could mean for there to be a component of the ST’s meaning that is the assertoric force quite independently of the pragmatics of language usage.

    Reply
  6. William Avatar
    William

    >>We don’t really know what ‘having assertoric force’ means.
    In fact I did define this earlier. I define the assertoric component as the difference in meaning between a ‘that’ clause and the corresponding sentence formed by tagging ‘it is true’ onto the ‘that’ clause. Thus if we agree that the meaning of these two expression-types are different
    (1) It is true that Socrates runs
    (2) that Socrates runs
    then we agree with my definition.
    Note that (1) and (2) are expression-types.
    Bill>>W is claiming that ‘Tom runs,’ e.g., is a semantic whole of parts. One of the proper parts is the assertoric component. He thinks it can be removed under certain circumstances.
    No I didn’t say this. I said it could be ‘cancelled’, and the analogy I gave was of Tom and Daisy at opposite side of a seesaw. When Daisy sits there on her own, she forces her end of the seesaw done. When Tom (whose weight equals Daisy’s) sits at the other end, Daisy’s and does not go down. Tom’s weight ‘cancels’ Daisy’s, but does not ‘remove’ it. How could we remove Daisy’s weight, which is an intrinsic and essential component of her, at this point in time?
    Perhaps ‘counteracts’ would be a better term. The point is that Daisy’s weight, the force she exerts on her end of the seesaw, is always there. Her weight is not removed. But it is ‘cancelled’ by the equal and opposite effect of Tom’s weight.
    Another analogy I used above was of number. The expression ‘1+2’ always signifies 3. This is true even when included in the expresion ‘1+2+3’, which signifies not 3, but 6. Similarly
    (A) ‘Socrates runs’, on its own as a complete sentence, states that Socrates runs, just as ‘1+2’ on its own signifies 3
    (B) In the sentence ‘If Socrates runs, Socrates moves’, the expression ‘Socrates runs’ states that Socrates runs, just as ‘1+2’ signifies 3 even when included in ‘1+2+3’.
    (C) But ‘If Socrates runs, Socrates moves’ does not state that Socrates runs, any more than ‘1+2+3’ signifies 3.
    >> But in asserting this conditional I do not thereby assert ‘Socrates runs.’ That, I hope, is perfectly obvious.
    Agree, and surely you also agree that ‘1+2+3′ does not signify 3, even though 1+2’ does signify 3?
    >>I have no idea what it could mean for there to be a component of the ST’s meaning that is the assertoric force quite independently of the pragmatics of language usage.
    Yet you concede that ‘Socrates runs’ and ‘that Socrates runs’ differ in respect of their linguistic meaning i.e. as expression types. I don’t think you are being consistent.
    >>It looks as if ‘having assertoric force’ just means ‘is asserted’.
    I don’t really understand ‘is asserted’. Assertion is just the attaching of an assertion operator to a noun-clause (i.e. a ‘that’ clause). Formally, every declarative sentence is of the form
    |- c
    where c is an expression for the content of the sentence (i.e. corresponding to a ‘that’ clause) and the turnstile is the assertion operator. There is nothing that is really ‘asserted’, since the assertion operator is not a predicate. Semantic cancellation we could express via the sign -|. thus
    -| |- c
    is equivalent to ‘c’ on its own, i.e. formation of a ‘that’ clause. Finally
    |- -| |- c
    uncancels the effect of the ‘that’ operator, to give us the original assertion again. The problem is that natural language includes the assertion operator buried in the main verb, so it is not visible, leading sceptics like Bill to dispute its existence.

    Reply
  7. William Avatar
    William

    >>Have you considered giving an axiomatic treatment of how ‘having assertoric force’ behaves in compounded sentences?
    Well, for a more formalised treatment:
    c1 = ‘that Socrates runs’
    c2 = ‘that Socrates moves’
    c3 = ‘that if Socrates runs, Socrates moves’ = if_then(c1,c2)
    if Socrates runs, Socrates moves = |- if_then(c1,c2) = |- c3
    The point is to take especial care to disinguish content expressions from sentential ones. This is what is confusing Bill. Above, it is clear that the if_then operator operates on content-expressions, not on assertions. However, ordinary English works somewhat differently, as follows:
    English_if_then(s1, s2) = if_then(that s1, that s2)
    It is now apparently open to someone like Bill to object that the English version includes the sentence-type s1 and s2. But the conditional does not assert that s1, ergo &c. This is fallacious. s1 does assert that s1. but ‘that s1’ does not.
    I suppose we could also introduce the following operator into the language, as follows
    asserts(|- c, c)
    which is trivially true in virtue of the meaning of the |- sign.

    Reply
  8. David Brightly Avatar
    David Brightly

    Bill,
    The view of part-whole relations that supports your argument is quite static. Parts must fit together without modification to make a whole, rather as pieces in a jigsaw puzzle. WW’s assertoric force theory can be made coherent, I think, if we see the meaning of a whole as the result of a construction process in which component meanings are themselves partially taken apart (‘content’ and ‘assertoric force’ separated) and re-arranged, much as a house is made of lengths of timber but the builder is allowed to saw them up, assemble the pieces, and discard the offcuts. Granted, this is a step back from the principle that every ST has the same meaning regardless of context, but I don’t yet see why he is reluctant to make this concession.

    Reply
  9. David Brightly Avatar
    David Brightly

    Many thanks, WW, that makes it all very clear. A small point: I see no sign of ‘assertoric cancellation’ in

    if Socrates runs, Socrates moves = |- if_then(c1,c2) = |- c3,

    but we can make it explicit by writing

    c1 = -| Socrates runs
    c2 = -| Socrates moves
    if Socrates runs, Socrates moves = |- if_then(-| Socrates runs, -| Socrates moves)

    We could argue forever as to whether the whole of the meaning of ‘Socrates runs’ was present in the RHS!
    Algebra is better than physics.

    Reply
  10. William Avatar
    William

    David – you have it exactly.

    Reply
  11. Bill Vallicella Avatar
    Bill Vallicella

    W writes:
    >> I define the assertoric component as the difference in meaning between a ‘that’ clause and the corresponding sentence formed by tagging ‘it is true’ onto the ‘that’ clause. Thus if we agree that the meaning of these two expression-types are different
    (1) It is true that Socrates runs
    (2) that Socrates runs
    then we agree with my definition.<< Everyone must grant that there is an important difference between (1) and (2), and I also grant, though it is less obvious, that the difference is a difference in meaning. BUT: this difference has nothing to with assertion. Why then do you speak of an assertoric component? The difference is a difference between an indicative sentence, which is either true or false, and a clause which is not either true or false. The relevant features here are indicativity and having-a-truth-value, not assertion. That's one problem. Another is that it is sloppy to define the assertoric component as the difference in meaning. That literally makes no sense. There is the difference, but the difference is not a component. Presumably, what you want to say is that the difference in meaning as between (1) and (2) is grounded in, or accounted for, by the presence of a special component in the meaning of (1), a component that is absent in (2). If that is what you mean, then that is what you should say. Third (and I have made this point before)why must there be such a component? Why can't the difference be a brute difference? Fourth, what EXACTLY do you mean by 'meaning'? Could it not be that the difference between (1) and (2) is merely syntactic? After all, the same categorematical expressions occur in both (1) and (2). 'It is true' and 'that' add no new meaning-content. Wouldn't you say they are syncategorematical?

    Reply
  12. Bill Vallicella Avatar
    Bill Vallicella

    W writes:
    >>A) ‘Socrates runs’, on its own as a complete sentence, states that Socrates runs, just as ‘1+2’ on its own signifies 3
    (B) In the sentence ‘If Socrates runs, Socrates moves’, the expression ‘Socrates runs’ states that Socrates runs, just as ‘1+2’ signifies 3 even when included in ‘1+2+3’.
    (C) But ‘If Socrates runs, Socrates moves’ does not state that Socrates runs, any more than ‘1+2+3’ signifies 3.<< The only way I can attach sense to (A) is by taking it as elliptical for A* 'Socrates runs' is the appropriate expression for an English speaker to employ should he wish to state that Socrates runs. The ST 'Socrates runs,' however, taken apart from a speaker and his intentions does not literally state anything. Accordingly, I reject (B) as incoherent. An English speaker cannot utter the antecedent of the conditional in that very 'If - then' context in order to state that Socrates runs. Perhaps our difference is this: You think that the assertoric force of a declarative sentence, when it is embedded in a conditional, undergoes semantic cancellation. I deny that there is any assertoric force to be cancelled.

    Reply
  13. William Avatar
    William

    >>what EXACTLY do you mean by ‘meaning’?
    I stopped at this point. One of the first lectures I attended was by a phenomenology professor who wrote ‘what is the meaning of meaning?” on the board. He gravely announced ‘that is one of the deepest and most difficult questions in philosophy.
    But I suppose you are right: the burden of proof is on me to define exactly what I do mean here. Later.

    Reply

Leave a Reply to Bill Vallicella Cancel reply

Your email address will not be published. Required fields are marked *