# Can every proposition be written in a subject-verb form?

Is there a proposition, or more concretely some fact about the world, that cannot be written in a subject-verb (or subject-predicate) form? I was wondering if this is a fundamental limitation of our natural language, thought process, or intrinsic structure of knowledge.

On the converse, is there a proposition that can be clearly written in a different structure than subject-predicate form? I am not concerned with some other sentence structure that can be easily mapped back to subject-predicate form. I was trying to find an example in mathematics, and I have failed so far.

I know my thoughts are naive, so I would appreciate any pointers to the literature.

EDIT: I accepted DWA's answer because he pointed out a non-specifiable subject. This partially answers my question.

• Related: A bit of Wikipedia reveals that "[some?/all?] ergative languages [...] do not have subjects". – user3164 Jun 5 '13 at 15:25
• How do you specify a predicate with multiple parameters? Subject-verb-object gives a relation between from one thing, the subject, to the other, the object. But what if there are three things. "It was raining at a rate of 1 in per hour at 9pm on the western slope of the mountain." 'was raining' but there are three 'things' rate, time, location (and surely could be more). There's more to language (and meaning) than subject-verb-object. – Mitch Aug 15 '13 at 15:08

1. If your question is whether there are propositions that get expressed without the use of Subject and Predicate, then the answer is "yes". There are several examples discussed in debates about the semantics/pragmatics distinction concerning the role context plays in linguistic understanding and the expression of propositions. The basic idea is that there are some propositions like don't get fully articulated by linguistic signs but propositions nevertheless get expressed because context fills in the blanks. So, some people contend that "it rains" expresses a relation between times and places, i.e. rains(t,p), but context supplies the required time and place values.
2. If your question is whether there are certain mathematical facts that cannot be expressed by any natural language (I'm not a mathematician), my best guesses is that no natural language could discretely index all of the points between any two points in a continuum. That is, for two arbitrary points on a line x, y, no natural language could discretely specify all of the points on the line in the form, X+1 and Y-1 and X+2 and Y-2 ... are between X and Y.

Edit: While it is possible to express mathematical facts in natural language expressions (by exploiting various neologisms, thanks Mozibur Ullah), since no language can fully specify the composition of continua by enumeration, there are some facts that can only be partially written in subject-predicate form.

• Regarding #2, even the language of mathematics has the same problem because it is enumerable. – Memming Jun 12 '13 at 13:34
• Agreed. Are you looking for something expressible in mathematical languages but not in natural languages? Or does #2 fit the bill? – DWA Jun 12 '13 at 15:20
• If "... is a point between x and y" is the predicate, then we couldn't specify the entire subject of this predicate by enumeration. In a natural language at least, it seems that at best we could index the subject by pointing to the line and saying "all of the points between here [pointing to x] and here [pointing to y] are between x and y." – DWA Jun 12 '13 at 16:39
• I don't understand the point you make about mathematics. Any mathematical fact can be expressed in a natural language which has neolgisms to take account of mathematical structure. In very early mathematics, problems and solutons were expressed in verse. The reason why mathematics has its own nomenclature and diagrams is that sometimes they are more efficient in communicating and not because they cannot be replaced. – Mozibur Ullah Jun 12 '13 at 18:37
• @DWA I accept your proposal as an explicit example of a mathematical fact that cannot be expressed as any enumerable language. Could you update your answer a bit so that it would be clear for everybody else why this is an answer? – Memming Jun 12 '13 at 19:09

Consider an arbitrary language L which has the syntactic categories: subject, predicate, sentence, and a grammar that generates arbitrary expressions P(s) in the sentence category by taking expressions s from the subject category and expressions P from the predicate category. Let's call a language that satisfies this specification: sp-friendly.

Monadic Predicate Calculus. The language of monadic predicate calculus is an example of an sp-language. There you have unary relations (category: predicate), which combine with individual constants (category: subject) to produce sentences (in the eponymous category).

Here's an example formalization done in such a language. The proposition that Gauss was great could be expressed in an sp-friendly language by the string of symbols "G(g)", where g (category: subject) denotes Gauss and G (category: predicate) denotes the property of being great.

Question. Is there a fact p in a certain body of knowledge (e.g., biology, arithmetic, etc.,) such that p cannot be expressed in any sp-friendly language?

I haven't found such a fact, but sometimes one comes across prima facie likely candidates, e.g.,:

(1) 0 < 1.

The proposition that zero is less than one says something about 0 and 1, but it's not immediately of the predicate-subject form, because it's not clear which of the two numerals is the subject, and in which sense is the less-than relation a unary predicate. But it's possible to turn (1) into a subject-predicate form without loss of logical content as follows. First, let's rewrite (1) in a more transparent notation:

(1) < (0, 1)

Here, as above, we have the binary relation < applied to 0 and 1. Now, there is a device invented by Moses Schonfinkel in 1924 (later independently discovered by Haskell Curry) that allows us to transform a relation-subjects form into a predicate-subject form in the following way: instead of applying an n-ary relation R to arguments a_1,…,a_n once, we curry R, and apply the unary predicate P that results from it to argument a_1, then the resulting predicate to argument a_2,…, then the resulting predicate to argument a_n.

I would need to make use of some basic lambda calculus jargon to be able to give an algorithm for currying arbitrary relations, and for demonstrating the general way of transforming relation-subjects form sentences into predicate-subject form sentences. Instead, I will simply give the result of applying this technique to our example sentence (1). Here it is:

(1) <' (0) (1)

Here, unlike above, we have a unary predicate <' (this is the curried version of the original binary relation <) applied to subject 0 and then to subject 1. Which one of them is the subject, you may ask, and if <' is a predicate then isn't the form of this predicate-subject-subject rather than predicate-subject? The answer is that "<' (0)" is the predicate and "0" is the subject. As a result of the trick, we have turned the truth-valued binary relation < into a predicate-valued predicate <', which when 0 is given to it, returns another predicate! It is that predicate that's applied to 1 to yield the truth-value of the whole sentence.

In a similar way, I believe, other seemingly not sp-friendly sentences can be translated into a predicate-subject form. Admittedly, the predicates turn out to look rather weird, but logically-speaking, there is no problem with equipping a generic sp-friendly language, such as the monadic predicate calculus, with the necessary lambda-calculus machinery (for currying and for reducing the lambda terms) that will enable it to handle predicate-valued predicate expressions (of course, care must be taken not to render the combined system inconsistent!).

• Thank you for rephrasing the question clearly, and thank you for reminding me of the currying technique. So, you can transform logical statements (or functions) into unary predicates (or functions) in these cases...I am still curious if all 'statements'/'languages' can be transformed to be sp-friendly. – Memming Aug 12 '13 at 2:55

This is a semi-serious example because its not how real languages work.

Suppose we can identify & list every fact of the world; now, in the past & the future. Then for every fact assign some arbitrary sign. we now have a 'language' which communicates every fact of the world and has no subjects & predicates!

Of course, we only have very very partial knowledge of now, the past & future. So this doesn't really work. Of course if God was allowed in the picture He knows all this stuff - so He certainly can.

On a more serious level I don't think you can - but I can't think of a good reason why.

EDIT

When rain falls there is no subject that causes it. It is a fact of the world that has no subject. You could say that 'Rain happens'. Rain here is not a subject. In french, one instead says 'Il fait pleut'. Here Il is an impersonal subject. It could refer to nature, or to God. Or it could simply have no referent and is used to give the sentence a S-V form.

In mathematical logic, one has propositional and first order logics. (There are higher ones too). It seems 1-logic is the best place to explore the idea of S-V, where we identify a variable in a formula with the subject.

• I am fairly sure that there are more facts than possible symbols, perhaps unless you include universe-sized symbols. – user3164 Jun 5 '13 at 15:47
• it is meant to be an entertaining example - so serious objections like yours don't apply! – Mozibur Ullah Jun 5 '13 at 15:58
• How about "cloud rains"? – Lie Ryan Jun 8 '13 at 0:36
• Isn't cloud the subject, and rains a verb? – Mozibur Ullah Jun 8 '13 at 1:02
• @Mozibur Ullah: so what did you mean when you say that rain falls have no subject? – Lie Ryan Jun 9 '13 at 3:30

My Answer to the Question is:

If there are facts and propositions, then neither of these kinds of things can be written down because they are abstract objects, so if there are facts or propositions then yes there is a proposition or a fact that cannot be written down in SP form, since it can't be written down at all.

But if there aren't any facts or propositions, then no, all facts and propositions can be written down in SP form (trivially because there are none)

Hunan Roystoman's formulation of the question and my answer:

Are there some facts that cannot be expressed by some subject predicate sentence?

Obviously the answer is yes: It is impossible to state the entire oeuvre that is the truths of mathematics with one long conjunction of subject predicate sentences. This is because there are well over an infinite number of mathematical facts making up the mega mathematical fact that is the whole of mathematics, but no sentence can be infinitely long.

Some might disagree and claim that the mega mathematical proposition that is true if and only if every individual mathematical truth is true, could simply be expressed in one short, swift subject predicate sentence, perhaps with the sentence: 'the mega-mathematical proposition is true'. But this confuses the two notions 'expressing a proposition' and 'stating that a proposition is true', consider the following story to demonstrate:

Troy: 'Gary, who is telling the truth?'

Gary: 'Sarah is'

In this story Gary did not express the proposition that [Jim stole the cookie] he expressed the proposition [the proposition expressed by sarah is true]. Likewise 'The mega-mathematical proposition is true' does not express the proposition that [0+0=0 and 0+1=1 and 1+0=1 and 2+0=2 etc......]

Some might also disagree by saying that there is such a thing as an infinitely long sentence. To which i reply - no there is not! There could not possibly be one, there isn't enough time to write one down...

Yes there are such things as infinitary logics which contain ways of expressing in a finite sentence what otherwise would seem to require an infinite sentence,

For example: let {p1..p2..pn...} be a countable and infinite set of propositional variables and also let S abbreviate the sentence that is the conjunction of {p1..p2..pn...} i.e. S = (p1 & p2 & ... pn & ...). One can give perfectly good truth conditions for S, i.e S is true in a model iff all of {p1..p2..pn...} are true in the model. And you can also define perfectly good deduction rules, e.g. from an infinite conjunction derive any of its conjunctions. So we could say: let M be the set that is all the truths of mathematics and let M& abbreviate the conjunction of all of M, then the sentence we need is 'M& is true'.

But this just takes us back to the above confusion because again we have not really expressed the proposition that is all the truths of mathematics, we have merely named it and said that it is true. I therefore maintain that the infinite structure of mathematics demands an infinite sentence to express the structure, but no sentence can be infinite, so no subject predicate sentence can express the mega-mathematical fact.

Discussion of question:

I think this should be how the question is formulated:

Does reality merely consist in objects having properties and bearing relations to one another, or does reality consist in an altogether different structure (perhaps as well as the object/property structure)?

I think you can save Memming's puzzle about SP language by adding the following:

If there were some non object/property structure to reality then arguably we could not express it in subject/predicate language. Even more worryingly is the idea that we couldn't even conceive of this structure and so know that it is there because our entire conceptual machinery is subject/predicate orientated.

If i've understood Memming at all then i'd recommend from the literature: "Individuals" by P.F.Strawson

The IT IS RAINING example:

'It is raining' could be understood in many SP+quantification ways.

The weather is raining........... i.e the weather is of the raining type,

There is rain

Raining is happening .....just like in 'The Olympics is happening'

The sky is raining

Water droplets are falling

etc..

The point being: one can express that proposition which is true, if and only if, it is raining, with ease in an SP language (e,g. the 5 english sentences i've given above and the few in the comments of Memmon's post). Who cares that there exists a non-SP sentence ('it is raining') which also expresses that proposition?

Perhaps the following demonstration will show how boring it is that there is a non SP sentence that expresses some proposition.

This is a new language:

Syntax: 'a'

Sentences: 'a' is a sentence and nothing else is

Semantics: 'a' is true iff it is raining

here is a grammatically well formed sentence that expresses the proposition that is true just when it is raining, but it ain't subject predicate: a

Hunan Roystoman's 0<1**

'zero is less than one' is a perfectly good example of a subject predicate sentence. The subject term is 'zero' the predicate term is 'is less than one'. That there are two subject predicate sentences that express the same proposition is of no bother, so it is no bother that 0<1 can be written as 'one is such that zero is less than it'. The question asked by Memmon (and then clarified by yourself) was to see if there was some fact that cannot be stated in a SP language, and you have answered this by showing that there are some facts that can be expressed by at least two different subject predicate sentences. It's an embarrassment of riches.

• Your answer to my formulation of the question is misguided. First, sp-friendly infinitary logics can be constructed, which will give us infinitely long subject-predicate sentences. Secondly, your beastly proposition of all mathematical truths ("the mega mathematical fact") is still a single proposition, a single fact, so we don't even need infinitely long sentences to express it. – Hunan Rostomyan Aug 13 '13 at 22:45
• I think you are wrong on both of those points. I've edited my post. – eslaf si ecnetnes siht Aug 14 '13 at 1:23
• Here's the problem. You claim, in fact, that there are propositions that cannot be expressed by any sentence (be it subject-predicate or of some other form). Your example is "the mega mathematical fact", which you then either: (i) have managed to nevertheless express with the sentence "0+0=0 and 0+1=1 and 1+0=1 and 2+0=2 etc...", thus contradicting your thesis, or (ii) have failed to define for us. – Hunan Rostomyan Aug 14 '13 at 2:13