Are There Logically Simple Propositions?

Leo Carton Mollica e-mails:

 

Your most recent post (for which many thanks) inspired the below-expressed argument, and I was curious as to your opinion of it . . . . I think it has something behind it, but right now I feel uncertain about my examples in (2).

 

0. There is something curious about the relation between a proposition or declarative sentence and the terms or words that compose it: the list L ("Christ," "Judas," "betrays") clearly differs, at the very least in not having a truth value, from the sentence "Judas betrays Christ," yet nothing immediately presents itself as the ground G of this difference. One plausible candidate for G is some kind of union or togetherness amongst the members of L present in "Judas betrays Christ" and not in L itself, but this proposal is open to a serious challenge.

 

1. Suppose we accept Barry Miller's thesis, from "Logically Simple Propositions," that some declarative sentences have only one semantic element. His favorite such sentence is the Romanian "Fulgura," whose only constituent word translates (if I remember aright) the English "brightens," and which is interesting in requiring no actual or implied subject to form a complete sentence (like "It's raining" in English, but without the dummy subject).

 

2. Now, the lone word in "Fulgura" seemingly can occur outside any proposition. If, for example, someone were to ask me to recite my favorite Romanian word, or to translate "brightens" into Romanian, it would be strange to take me as telling them something false, or to have them respond "No, it isn't," upon my replying with "fulgura." There would, however, be nothing strange about the sentence "Fulgura" being false and someone telling me as much. [. . .]

 

3. Even in such simple sentences, therefore, there is a distinction between the sentence and the words contained therein, for one can be had without the other. But the ground of this distinction cannot be any union or togetherness among the words that enter into the sentence for the simple reason that no union or togetherness amongst items can be had without distinct items to unify or bind together. It can, therefore, be at least plausibly argued that the general ground of the difference between a sentence and its constituent words is no kind of union or togetherness.

 

I take Mr Mollica's basic argument to be this:

 

a. If there are logically simple sentences/propositions, then the problem of the unity of the sentence/proposition is not one that arises for every sentence/proposition.
b. There are logically simple sentences/propositions.
Therefore

c. The problem of the unity of the proposition is not one that arises for every sentence/proposition.

 

My response is to reject (b) while granting (a).  I discussed the question of logically simple sentences/propositions with Barry Miller back in the '90s in the pages of Faith and Philosophy.  My "Divine Simplicity: A New Defense (Faith and Philosophy, vol. 9, no. 4, October 1992, pp. 508-525) has an appendix entitled "Divine Simplicity and Logically Simple Propositions."  Miller responded and I counter-responded in the July 1994 issue, pp. 474-481.  It is with pleasure that I take another look at this issue. I will borrow freely from what I have published.  (Whether this counts as plagairism, depends, I suppose, on one's views on diachronic personal identity.)

 

A.  A logically simple proposition (LSP) is one that lacks not only propositional components, but also sub-propositional components.Thus atomic propositions are not logically simple in Miller's sense, since they contain sub-propositional parts.  A proposition of the form a is F, though atomic, exhibits subject-predicate complexity.

 

B. Miller's examples of LSPs are inconclusive.  Consider the German Es regnet ('It is raining').  As Miller correctly notes, the es is grammatical filler, and so the sentence can be pared down to Regnet, which is no doubt grammatically simple.  He then argues:

 

Now there is no question of Regnet being a predicate; for as a proposition it has a complete sense, whereas as a predicate it could have only incomplete sense. Hence, Regnet and propositions like it seem logically simple. (Barry Miller, "Logically Simple Propositions," Analysis, vol. 34, no. 4, March 1974, p. 125.)

 

I find it hard to avoid the conclusion that Miller is confusing propositions with the sentences used to express them.  Regnet and fulgura are grammatically simple.  But it scarcely follows that the propositions they express are logically simple.  What makes them one-word sentences is the fact that they express propositions; otherwise, they would be mere words.  So we need a sentence-proposition distinction.  But once that distinction is in place then it becomes clear that grammatical simplicity of sentence does not entail logical simplicity of the corresponding proposition.

 

C.  It is also unclear how any intellect like ours could grasp a proposition devoid of logical parts, let alone believe or know such a proposition.  To believe that it is snowing, for example, is to believe something logically complex, albeit unified, something formulatable by some such sentence as 'Snow is falling.'  So even if there were logically simple propositions, they could not be accusatives of minds like ours.  And if propositions are defined as the possible accusatives of propositional attitudes such as belief and knowledge, then the point is stronger still: there cannot be any logically sinple propositions.

 

D.  So it seems to me that 'the problem of the list' or the problem of the unity of the sentence/proposition is one that pertains to every sentence/proposition.  It is a problem as ancient as it is  tough, and, I suspect, absolutely intractable.  For a glimpse into the state of the art, I shamelessly recommend my June 2010 Dialectica article, "Gaskin on the Unity of the Proposition."

Comments

[Leo Carton Mollica]

Thanks for the post! I'm deeply honoured.

I'll put up a more detailed response later, but I wonder whether your move in (D) doesn't require you take the meaning of the verb "to snow" (which presumably refers to a certain activity in nature) as logically dependent upon the meaning of the noun "snow" (which presumably refers to a certain kind of ice crystal). This seems suspicious: shouldn't the latter be defined in terms of the former, as in "Snow is the ice crystal that descends when it is snowing"? What else could distinguish snow from all other kinds of ice crystal? Or is this just obscuring matters?

By the way, I had just ordered your and Dr. Miller's exchange from Faith and Philosophy before reading your post on copulae. Sadly, I doubt I'll be seeing it any time soon.

[Bill Vallicella]

The pleasure is all mine.

I don't understand your point. I can believe that snow is falling but I can't believe that snow. Now suppose we introduce the word 'shnow' to mean 'snow is falling.' Then I can believe that shnow. But although 'shnow' is gammatically simple, that does not show that the proposition it expresses is logically simple.

[arash]

Bill,
could you please comment more on point C? What could explain that "if there were logically simple propositions, they could not be accusatives of minds like ours"? Thanks.

[Steven]

Hi BV and Leo,

I am not sure how much this helps, but I will try to provide some input. There are a lot of single word complete (i.e., grammatically acceptable) sentences in Romanian: Fulgera/fulgura (lightning is striking); ninge (it is snowing); ploua (it is raining).

Now, these are third person singular verbs in the indicative mood, so that it seems to me clear they express a complex proposition, since there is an implied subject, although it is not expressed in any words.

[Bill Vallicella]

Steven,

We agree then. It is very interesting, though, that there are single words that can function both as nonsentences and as declarative sentences.

A related phenomenon is the one-letter word which can function both as a letter and as a word. An example is 'I' which can function both as letter and as word (first-person pronoun). It can also be construed as a Roman numeral. 'A' is another example as is 'O.' Any others?

[Bill Vallicella]

arash,

Well, isn't it obvious that in every decl. sentence, judgment, proposition, there has to be a distinction between what is being talked about and what is being said of what is being talked about?

[arash]

FYI,

In Italian too, there are one word sentences: "piove" ("it's raining"),"nevica" ("it's snowing"), "tuona" ("it's thundering")

[Leo Carton Mollica]

Dr. Vallicella,

Forget the argument in the first post; I've thought it over, and I am inclined to judge it unsalvageable.

I think, however, that you are too liberal in assessing the gap between sentences and the propositions they express. If the structure of natural-language sentences were not a good guide to the structure of their corresponding propositions, then how could the study of the former assist in the understanding of the latter? But if the structure of sentences like "Fulgura" and "Regnet" is a guide to the structure of the propositions they express, doesn't it give some grounds for thinking those propositions simple?

Steven,

Now, these are third person singular verbs in the indicative mood, so that it seems to me clear they express a complex proposition, since there is an implied subject, although it is not expressed in any words.

Why would that follow? Remember that to count against the sentence's logical simplicity, the third-person subject must be the real thing, not grammatical filler like the "it" of "It's snowing." So, what would the implied subject of such a sentence be?

[Bill Vallicella]

Leo,

How do you know that 'Regnet' is a sentence and not a verb? To know that it is a sentence you have to know that it expresses a complete thought and has a truth value. What is the complete thought that 'Regnet' expresses? It is that the weather is rainy, or the sky is raining, or rain is falling, or rain is occurring. And so the proposition expressed is not simple even though 'Regnet' is grammatically simple.

In general sentence structure is a guide to the logical structure of the corresponding proposition. 'Fulgura' is just an exception that proves the rule.

To me the clincher is that the discursive intellect cannot grasp a proposition that has no logical articulation.

[Bill Vallicella]

Leo,

Did you already pay F & P? I have an extra copy I could send you for free.

[Leo Carton Mollica]

Dr. Vallicella,

Let me see if I can summarise our dispute thus far:

1. As Barry Miller and others have argued at length, some proposition-expressing sentences (such as "Regnet") are grammatically simple. Since grammatical sentence-structure is generally a safe guide to logical proposition-structure, the simplicity of these sentences gives a prima facie reason for supposing the propositions they express to be logically simple. If, therefore, you deny them to be so simple, you must have some grounds for your denial that overrides the general analogy between grammar and logic.

2. One such line of evidence seems to be that the proposition expressed by "Regnet" is a logically complex proposition like that the weather is rainy, or that rain falls from the heavens. But I don't see any reason to prefer these complex propositions as candidates for what "Regnet" expresses, unless we already know that this proposition must be logically complex. So your grounds for anti-simplicism (to coin an ugly phrase) must lie elsewhere.

3. This "elsewhere" would seem to be your contention that "the discursive intellect cannot grasp a proposition that has no logical articulation," so the dispute hinges on this point. I do not, however, think I understand it, so could you please elaborate? What is it to say that a proposition has a logical articulation, why couldn't a simple proposition have one, and why can the discursive intellect not grasp a propisition lacking one?

And no, I have not yet payed Faith and Philosophy, so I'll gladly take you up on the offer. Many thanks.

P.S.
Is your Dialectica article the same as this post?

[Leo Carton Mollica]

Whoops, the link in the last sentence didn't work. I was referring to
http://maverickphilosopher.typepad.com/maverick_philosopher/2009/10/gaskin-on-the-unity-of-the-proposition.html

[Account Deleted]

Leo,

The pivotal dispute between you and Bill on this issue has to do with the following contention you made in this last post:

"Since grammatical sentence-structure is generally a safe guide to logical proposition-structure, the simplicity of these sentences gives a prima facie reason for supposing the propositions they express to be logically simple."

The above quoted statement features several problems that are relevant to the dispute. Consider the antecedent first. What do you mean by the "grammatical sentence-structure"?

In modern (post Chomskian) Linguistics they distinguish between surface-structure vs. deep-structure. The surface-structure of a sentence does not even give its true grammatical deep-structure. So if by that phrase you mean the *surface-structure*, then it is trivially true since the antecedent is false.

If, on the other hand, by that phrase in the antecedent you mean *deep-structure*, then while it may be true that deep structure is "generally a safe guide to logical proposition-structure", the consequent is false. For the deep structure of a sentence with a one word surface structure may feature a complex grammatical deep structure and I bet in all the examples discussed it does.

Bill's point can also be stated (as he did) in terms of truth conditions or logical form. Consider the following pair of sentences:

1) Jill kicked Joe;
2) Joe was kicked by Jill.

These two sentences have different (surface) grammatical structure, but the same logical form; i.e., the conditions under which they are true are the same. Thus, once again, the superficial grammatical structure is not a reliable guide to their logical form (or truth-conditions). These are just a few examples that show that surface grammatical structure is not a reliable guide to grammatical or propositional structure. It is merely the point were we begin to analyze what the sentence expresses. Therefore, one word sentences are just the starting point for propositional structure.

Conclusion: There is no one-to-one isomorphism between surface structure and propositional structure.

[Bill Vallicella]

Leo,

For me, the simplest conceivable proposition has the form *a is F,* which has three subpropositional components. The Fregeans would say there are two components since they import the copula into the predicate -- a mistake if you want my opinion. Either way, there are subpropositional components -- which implies that the proposition is not simple in Miller's sense.

Can I argue for this? I don't think so, at least not noncircularly -- the point is too basic. I just don't understand what one would be grasping or understanding or having before one's mind if one had a Miller-simple proposition before one's mind.

So I simply invoke that (to me) self-evident point, then I go on to explain how Miller's examples are not compelling. And then my work is done.

Suppose someone in the kitchen glances toward the stove and says, 'Hot.' That word could be construed as a sentence. What thought does it express? The complex thought that the stove is hot.

Send me your physical address in an e-mail and I'll mail you the journal.

Yes, that link is basically the Dialectica article.

[Leo Carton Mollica]

Peter,

Unless the deep-structure of a sentence is entirely inaccessible, however (in which case the study of natural-language sentences could not be of assistance in the study of logic), I do not see that your criticism holds water. First, most of the examples Barry Miller gives do have a superficial grammatical complexity, since they involve a pseudo-subject like the "it" of "It's snowing" or the "es" of "Es klappert." What makes them simple sentences is not that they consist of only one word, but that any words or components beside the verb are mere grammatical filler, that only the one word or component plays any role in determining the sentence's sense. And if that does not qualify them as "deeply" simple sentences, I do not know what would.

However, my acquaintance with modern linguistics is passing, so tell me if I'm misunderstanding something.

BTW, have you read "Logically Simple Propositions"?

[Bill Vallicella]

Peter,

Thanks for that. But we will have to ask whether the only way to specify logical form (logical syntax) is via a specification of truth conditions.

[Leo Carton Mollica]

Dr. Vallicella,

For me, the simplest conceivable proposition has the form *a is F,* which has three subpropositional components. The Fregeans would say there are two components since they import the copula into the predicate -- a mistake if you want my opinion. Either way, there are subpropositional components -- which implies that the proposition is not simple in Miller's sense.

I suppose, then, that we might be at something of an impasse. The simplest proposition I can conceive is of the form F, where F is a zero-place predicable not constructed out of an n-place predicable where n≥1. Just as we don't need three subjects for a two-place predicable, or two subjects for a one-place predicable, to play its role in a proposition, so we don't need even one subject for a zero-place predicable to play its role in a proposition.

Suppose someone in the kitchen glances toward the stove and says, 'Hot.' That word could be construed as a sentence.

Could it, though? In modern English, the most I could see it properly construed as would be an abbreviation of a sentence. In what person and tense is it? As a sentence, it would be ill-formed in a way "Fulgura" or "It's snowing" would not.

[Account Deleted]

Leo,

First, the deep structure is certainly accessible; that is what modern post Chomskian linguistic with its transformation rules all about.

Second: "only the one word or component plays any role in determining the sentence's sense."

Perhaps! But the sense it determines must be itself complex and not a one component sense. I do not see how a one component sense can convey a proposition that has a truth value. This is not an unusual situation at all.

Consider the English word 'bachelor'. It has a two word sense; namely, unmarried male. We can imagine a language in which they do not have *one* word that expresses the sense *unmarried male*; perhaps they have two or more words that express the same sense.

Again all the linguistic data that is available to us indicates that there is no one-to-one isomorphism between surface word/sentence structure and sense/propositional structure. This holds at the level of words/sense and all the available evidence suggests that it also holds in the case of sentence/proposition level.

A grammatical construction, "simple" or otherwise, qualifies as having a propositional sense inly if it expresses something that can have a truth value (or at the least it exhibits the logical form of constructions that typically have a truth-value. This qualification is necessary in order to account for sentences including empty names; a contested topic around here).

Unlike Bill, I consider this point to be convincingly arguable. No, I did not have the opportunity to read the aforementioned article. Where does it appear?

[Leo Carton Mollica]

Peter,

Again all the linguistic data that is available to us indicates that there is no one-to-one isomorphism between surface word/sentence structure and sense/propositional structure. This holds at the level of words/sense and all the available evidence suggests that it also holds in the case of sentence/proposition level.

I am confused as to why you think I am here interested in the surface-structure of sentences like "Es klappert" and "It's snowing," since superficially most such sentences exhibit a subject-predicate structure. (Unless, of course, I am misinterpreting "surface-structure," in which case I welcome correction.)

Perhaps! But the sense it determines must be itself complex and not a one component sense. I do not see how a one component sense can convey a proposition that has a truth value. This is not an unusual situation at all.

I do not, however, see why we should prefer a many-word-sense interpretation of the verb "regnet" or "fulgura" over a one-word-sense interpretation unless we assume that nothing can be a proposition or have a truth-value if it have no internal components, i.e. if it be simple. But to so assume is surely to beg the question.

The article appears in Analysis, Vol. 34, No. 4 (Mar., 1974), pp. 123-128, and is available from JSTOR: http://www.jstor.org/stable/3328014

[Account Deleted]

Leo,

Thanks for the link.

"I am confused as to why you think I am here interested in the surface-structure of sentences like "Es klappert" and "It's snowing," since superficially most such sentences exhibit a subject-predicate structure."

Because o/w I do not see why one would think that a one word sentence expresses a one component proposition unless one assumes a one-to-one isomorphism. So, for instance, you have been discussing one-word examples of sentences such as 'fulgura' or 'regnet'. One asks: Do these sentences correspond to one-component propositions or to complex propositions? The only reason I can think of to opt for the former is to assume that a one-word sentence corresponds to a one component proposition and a multiple word sentence to a multiple word proposition. (I wonder whether the proponents of simple propositions also maintain that there are cases where a complex sentence corresponds to a simple proposition? If not, why such a possibility is ignored or excluded?)

"I do not, however, see why we should prefer a many-word-sense interpretation of the verb "regnet" or "fulgura" over a one-word-sense interpretation unless we assume that nothing can be a proposition or have a truth-value if it have no internal components, i.e. if it be simple."

That is just what I maintained in my previous post. So now it is up to the proponents of simple propositions to show how the truth conditions of an alleged unstructured proposition are given. So could you give an example of how the truth conditions of such a simple proposition are to be stated? For instance, what are the truth conditions for the alleged simple proposition that is expressed by the utterance of "regnet"?

So I do not see this as a mere assumption in the sense that it is begging the question arbitrarily. There are reasons behind making the assumption and these reasons are linked to the manner we think about assigning truth conditions to sentences. We of course also assume that the truth conditions so assigned frequently reveal the structure of the propositions expressed by these sentences.

[Bill Vallicella]

Leo,

I'd say we are at an impasse. No proposition my mind can grasp is logically simple.