Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

Atomic Sentences, Negation, and Direct Reference

Edward argues:

Now I claim that in systems where there is no distinction between predicate and sentence negation, we have ‘direct reference’. This is easily shown. Direct reference in a singular sentence is when the sentence is meaningless when the singular subject fails to refer. Assume that ‘a is F’ is not meaningless. If it is true, then there is a referent for ‘a’. If it is not true, the sentential negation ‘It is not the case that a is F’ is true. If sentential negation is equivalent to predicate negation, it follows that ‘a is non-F’ is true, and so a exists, and so, there is a referent for ‘a’. But (by excluded middle) either ‘a is F’ is true, or its contradictory (the sentential negation) is true. In either case, ‘a’ has a referent. Thus if ‘a is F’ is not meaningless, ‘a’ has a referent. Conversely if ‘a’ does not have a referent, ‘a is F’ is meaningless. But that is Direct Reference, as I have defined it.

This reasoning strikes me as correct.  The notion of an atomic sentence is foundational for modern predicate logic (MPL).  For such sentences there is no distinction between predicate and sentence negation.  And given Edward's definition of 'direct reference,' I am persuaded that MPL entails direct refence for the subject terms of atomic sentences.

Note that I am substituting 'atomic sentence' for Edward's  'singular sentence.'  Every atomic sentence (whether monadic or relational) is singular, but not every grammatically singular sentence is atomic.  Or at least that is not obviously the case.  Thus it is far from obvious that 'Peter smokes,' which is grammatically singular, is logically atomic.  If one holds, with Russell, that grammatically proper names are definite descriptions in disguise, then the grammatically singular 'Peter smokes' will have an analysis that is existentially general.

Correct me if I'm wrong, but the subject term of an atomic sentence is what Russell called a logically proper name and distinguished from a grammatically proper name.  So what Edward has shown is that Direct Reference holds for logically proper names.  But this does not show that Direct Reference holds for ordinary names, grammatically proper names, such as 'Edward'  in 'Edward is English' or 'Peter' in 'Peter smokes.' 

Direct Reference for grammatically proper names, whether nonvacuous or vacuous (e.g. 'Vulcan') is false.  But as far as I can see MPL is not committed to Direct Reference for such names.  So while I am persuaded by Edward's reasoning above, I am not sure what its relevance is.

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Bill Vallicella

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10 responses to “Atomic Sentences, Negation, and Direct Reference”

  1. Edward Ockham Avatar
    Edward Ockham

    >>So while I am persuaded by Edward’s reasoning above, I am not sure what its relevance is.
    The relevance is that there are also very strong arguments against proper names being translatable into the ‘predicates’ of MPL. I summarise them here http://ocham.blogspot.com/2011/08/translating-ordinary-language-into.html.
    How do you reply to these arguments? Otherwise, if you accept them, and if at the same time you accept the argument above that ordinary language proper names cannot be translated into the logical constants of MPL you have the problem that ordinary language cannot be translated into MPL at all. Do you see that as a problem?
    Note that I have given replies to three of the arguments linked to. But this requires buying the idea of singular concepts, which you don’t.

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  2. Edward Ockham Avatar
    Edward Ockham

    Sorry, the link is here http://ocham.blogspot.com/2011/08/translating-ordinary-language-into.html (WordPress doesn’t like full stops after a URL).

    Reply
  3. Bill Vallicella Avatar
    Bill Vallicella

    This is TypePad, not WordPress. I tried the latter but didn’t like it.
    I hope to look at your arguments later in the day.
    We may be beginning to make some progress after many years of wrangling.
    Suppose OL cannot be translated into MPL. One could ‘go draconian’ and say,”So much the worse for OL!” I shrink back from that extremism, however.
    I once encountered a fanatic who said, “If it can’t be said in the language of PM (Principia Mathematica), it can’t be said!”

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  4. Edward Ockham Avatar
    Edward Ockham

    I think there are essentially three positions
    (A) It is possible to resolve philosophical arguments (as expressed in ordinary language) by an agreed formalisation in a language with a determinate proof procedure.
    (B) It is possible to carry out such a formalisation project using MPL as the agreed formal language (as per your fanatic)
    (C) The formalisation project is fundamentally unachievable.
    I incline to (A). It is possible to resolve philosophical argumentation by a regimentation or formalisation of ordinary language, but ‘the language of principia mathematica’ is the wrong vehicle. I wonder if you incline to (C). But then, what would that mean? Does it mean that ordinary language is fundamentally incoherent? But then what are we talking about, when we talk about philosophical matters? Or is it that there are truths which are somehow unexpressible? But then, again, what are we talking about, when we try to talk about such truths?

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  5. Bill Vallicella Avatar
    Bill Vallicella

    I take it that by ‘argument’ in (A) you mean ‘disagreement.’ Consider a typical philosophical disagreement. One guy says that the redness of a red tomato is a universal. Another denies this and says that the redness is a particular (a trope). How could their agreement on MPL as the vehicle of formalization help resolve this question?

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  6. Edward Ockham Avatar
    Edward Ockham

    The disagreement could be resolved (not necessarily by MPL, but by some agreed means of formalisation) in exactly the way that Ockham resolves it. Ockham argues that ‘X is a universal’ really means ‘the word for X is a universal term’. His whole project (largely in the middle chapters of part I of the Summa) is to show how all talk about universals, if it is to make any sense at all, is really about items of language, and not Platonic entities. By this means he also resolves the question of whether the universal is in some sense particular. He says that the word itself is particular. But its meaning is universal, in that, used in the same sense, it can apply to many things.

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  7. Bill Vallicella Avatar
    Bill Vallicella

    I don’t follow you. No logical formalization can resolve this substantive dispute. No doubt ‘red’ is a univrsal term. But that triviality does not dispose of the question whether redness is a universal.

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  8. Edward Ockham Avatar
    Edward Ockham

    >>I don’t follow you. No logical formalization can resolve this substantive dispute. No doubt ‘red’ is a univrsal term. But that triviality does not dispose of the question whether redness is a universal.
    Ockham would say that ‘red’ is a universal term. And ‘redness’ is simply an abstract noun formed from the adjective ‘red’, such that ‘Mars has redness’ is simply another way of saying ‘Mars is red’. So formalisation, which includes specifying the true meaning of ordinary language statements, does indeed resolve this substantive issue.
    Ockham argues in chapter 5 http://www.logicmuseum.com/wiki/Authors/Ockham/Summa_Logicae/Book_I/Chapter_5 and subsequent chapters for that abstract nouns are simply derivative of concrete nouns. And he argues here http://www.logicmuseum.com/wiki/Authors/Ockham/Summa_Logicae/Book_I/Chapter_15 against the idea that a universal is some thing outside the mind.

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  9. Edward Ockham Avatar
    Edward Ockham

    The key part of Ockham’s argument is chapter 7 http://www.logicmuseum.com/wiki/Authors/Ockham/Summa_Logicae/Book_I/Chapter_7 .
    “I say that Aristotle’s opinion was that no imaginable thing is conveyed by the name ‘man’, unless it is conveyed by the name ‘humanity’ in the same way, and conversely. The reason of this is that according to him no thing exists in the world below except material and form, or composite or accident. But none of these, as is clear by example [inductive] is more conveyed by one of these names than by the other. And assuming this, it is clear that ‘an intellective soul is a humanity’ is false.”
    His whole argument is that a proper understanding (i.e. a regimentation or formalisation) of language is necessary in order to argue against those who hold that a universal is something external to the mind. Once we understand that ‘redness’ is not a name for some individual Platonic object, and that no imaginable thing is conveyed by the name ‘red’, unless it is conveyed by the name ‘redness’, then we have resolved the problem of universals.

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  10. David Brightly Avatar
    David Brightly

    Ed, if I spoiled your Saturday evening Pimms please accept my apologies. I hope you had another!
    Ed allows here that there are two senses of ‘reference’ in play: a strong sense which is external object dependent, and a weak sense in which we are merely told who or what is being talked about. Which sense is operative in the quoted passage? It seems it can’t be the strong sense because the concept of logical consistency applies to any set of sentences. {Fa, Ga, ~∃x.Fx&Gx} is an inconsistent set independently of the meanings, if any, of ‘a’, ‘F’, etc. Consistency places a requirement on the ‘patterning’ of the sentences. This can be explained independently of any intended meanings for the letters. One just needs the ideas of individual, concept, individual instantiating a concept, plus the logical constants. On the other hand, if the weak sense is intended then DR is trivially satisfied, regardless of the flavour of logic in play.

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