Propositions and hypotheses

A look in some considerable detail at why I use these two different terms for apparently very similar concepts, and precisely how the concepts apply to several different kinds of utterance.

In My World View I say:

But there are several questions that may arise in the mind of anyone reading this: Why do I need two terms? That is, when is a proposition a hypothesis, and when isn't it? Come to that, why do I talk about “propositions”? Why don’t I just say “statement”?

The answer is that it is only a usage, but it is the normal usage in science and philosophy.
A statement conveys something, or perhaps a lot of things.
A proposition is an unambiguous, normally simple (as opposed to complex) statement, because it is useful to us to break statements down so that each proposition says only one thing for us to evaluate.
Finally, we refer to a proposition as a hypothesis when we are chiefly interested in the credibility rating that we are assigning to that proposition.

That may seem clear to you or it may make you ask: “How does this work in practice?” Let us go back a little way and work up, using a few examples.

The utterance

We define an utterance as anything a person says, that is, any use of the voice. For the purpose of this discussion, it is extended so as to refer also to any text written or displayed in any medium.

All of the following, picked more or less at random, are utterances:

  1. Hello.
  2. How are you?
  3. The cat sat on the mat.
  4. I hate vinegar.
  5. Aaarrrghhh!!!
  6. At the very end of the only book-length work of his that was published in his lifetime, the Tractatus Logico-Philosophicus, the philosopher Ludwig Wittgenstein borrows an analogy from Arthur Schopenhauer, comparing the book to a ladder that must be thrown away after one has climbed it. {adapted from Wikipedia]

Of these utterancess, it would appear that only numbers 3, 4, and 6 are statements that something is the case; and of these, only numbers 3 and 4 are directly readable as propositions.

Greetings

What of the other utterances listed above? Well, as is well known, utterance 1 is a greeting. Greetings are often conventional, and one might think thay have no intrinsic meaning, or that “Hello” is just an empty utterance-word. If that were true, we could simply ignore them; but it isn't. The implied meaning of “hello” is “I am here; I recognize that you are there.” plus also quite often “I wish you well.” Considered structurally, greetings take several forms. However “Good day” implies (because it is an elliptical form of) the statement “I wish you a good day” , which really means the same as “I hope that you have a good day”, so it can be regarded as a proposition, namely that it is the case that the speaker has benevolent sentiments towards the hearer.

Utterance 2 is also in a way a form of greeting, but strictly speaking it is a direct question (even apart from the fact that people very often say “Hello; how are you?” so that the second utterance is heard after the greeting part).

Questions

In ordinary grammar terms, one might or might not consider a direct question to be a special sort of statement (with an interrogative syntactical structure); but in the philosophical context, as far as I am concerned a direct question is not a proposition. However, it is an utterance that has the purpose of expressing a desire for information, and a simple rewording converts this interrogative form, this apparent non-proposition, into a proposition! If instead of “How are you?” I say “I wish to know how you are”, my new utterance is quite clearly a proposition, expressing that it is the case that I am interested in the hearer’s health.

This latter syntactical form, expressing a question but doing so within a sentence that has a main verb that is not an interrogative, is called an indirect question. Other examples of the indirect question are:
"John wanted to know why Mary had sold her car." (John said: "Mary, why did you sell your car?")
"You’ll wonder where the yellow went when you brush your teeth with Pepsodent." (The jingle promises that you will ask yourself: "where did the yellow go?")

Note that no question mark is required — or, indeed, allowed — when writing an indirect question. Actually, many writers or editors use or tolerate a question mark after an indirect question, but such marks are always wrong. This error is particularly common after “wonder” — there are even examples of this error in Tolkien (LotR)! It is nevertheless quite wrong.

In summary, a direct question is (by my stipulation in this definition) not a proposition, but an indirect question is a proposition asserting the existence of a wish or need for additional information in somebody’s mind or within some system.

Exclamations as propositions

Utterance 5 is not a proposition, although some linguisticians might well say that it is an implied stamement. I say it is not a proposition because although it appears to be a coded expression of some emotion, and so quite probably also implies that its utterer is undergoing some sort of experience causing that emotion, we cannot be certain even when we hear it exactly what the emotion is, and we certainly can’t tell anything by reading it when it is written down.

Because of the lack of explicitness, I classify such utterances as signs rather than propositions. The study of signs, semiotics, is closely related philosophically to linguistics and thus to this branch of thought. Utterance 5 is a sign, just as a high-emotion reading on a polygraph or voice stress analyser would be a sign, that an individual or organism was experiencing some form of emotion or stress.

From my analysis of utterance 5, you will have gathered that I don’t consider an utterance to constitute or represent a statement that can be classified as a proposition unless the content of the proposition is explicit in some way. But you need to be aware that this does not require that the statement be as explicit as it could possibly be! If instead of “Aaarrrghhh!!!” a person said “I am experiencing an emotion” , that is a perfectly good proposition. I do not require that the person say “I am experiencing a feeling of elation” or “I am experiencing a feeling of apprehension” ; these are more explicit, and a psychoanalyst or a detective investigating a murder might well ask for the person who made the vague statement in my example to be more explicit. Whether such a vague statement would be of any interest to anyone is another matter; but the vague statement qualifies technically here as a proposition.

Propositions and hypotheses

What is the difference?

And which of the above propositions are hypotheses? Or, under what conditions would or could each be treated as a hypothesis?

We talk of a proposition being a hypothesis when it is important to us that the credibility rating we are giving to it is significantly different from the extreme values 0 and 1. One example of such an occasion is when the credibility rating is under review, including when the proposition (hypothesis) is being compared with alternative propositions (hypotheses).

Utterance 1

Utterance 1 is a greeting, not an explicit proposition, but one could argue that it carries the meaning “I am here and I recognize that you are here” making the real burden of this single word two propositions.

Taking these two propositions separately, we have “I am here” and “I recognize that you are here”. The first of these is in the first category to which I give, by definition, a credibility or reliability rating of 1.0, namely direct experiences of myself. For me, I am always here; and I define this, for the purpose of discussions such as the present analysis, as absolutely true. I choose not to entertain the doubts expressed by certain philosophers and mystics, who question their own existence — supposing, perhaps, that they themselves are merely figments of somebody else’s imagination. No! I assert that I am not merely a figment of anybody else’s imagination, and to all propositions asserting what is to my senses or consciousness unambiguously the case about myself I give the rating 1.0, “absolutely true”.

Note: this does not include all propositions about myself; examples follow. In normal wakefulness, I can say “I am wearing a blue shirt” . That sort of proposition is normally beyond question and I wouldn’t waste time worrying about its credibility. However, although I’d never deliberately take one myself, if I were somehow to be given covertly by somebody else a mind-altering drug, or to suffer some other experience which led to doubt the reliability of my own perceptions, I might well begin to give significantly-less-than-1 credibility ratings to almost any observations that I made while in that condition. Leaving such rather unlikely situations aside, however, I am not usually concerned about the credibility of simple observations about myself, nor do I consider it necessary to treat such propositions as hypotheses about which I need worry about the reliability.

But are there less obvious propositions about myself with importantly less-than-1 credibility ratings? Yes! A great many. Anything about my health, for example. Or if I was kidnapped — or even just fell asleep on a train — and woke up in a strange place, I might easily not know where I was when I looked out of the window, and might have to entertain several competing hypotheses as to where I was before enough information became available to me to settle the question of my exact whereabouts.

So much for statements like “I am here” . What about “I recognize that you are there” ?

Well, in fact this, a sentence containing an indirect statement, is a complex statement, an outer direct statement and an inner clause which implicitly states that the hearer is wherever (s)he is, and that the hearer is somehow or another within hearing range (that is, whether in person or via some audio communications link) of the speeaker.

The component “I am here” was in the first normally-automatically-true category; the component “I recognize ...” in the second normally-automatically-true category, statements about the state of consciousness, knowledge or opinions of the speaker.

When a person makes a statement in this second category, we have two common credibility ratings: 1 (absolutely true) when the speaker is not lying and 0 ((absolutely untrue, false) when the speaker is lying. Mind you, we have in between those all the cases (rating below 0.5) when the person is genuinely unsure of their own state of mind but probably lying and all those (rating above 0.5) also when the person is genuinely unsure of their own state of mind but when they are probably not lying.

However, the rating for any statement that a person knows or recognize something like the simple fact that somebody else is there could only be other than exactly 0 or 1 in very weird circumstances.

All that discussion notwithstanding, a person is usually quite unlikely to utter the word “Hello” addressed to a person unless they either know the person is there, or intend to deceive some third party. (The exception might be a person walking into an apparently empty area where they expected somebody to be, as when walking in an unexpectedly open house front door, when most people would probably call out “Hello! Is anybody there?”) Thus, if Jack knows that Jill is coming into earshot, picks up a telephone and says “Hello!” and starts talking without there being anybody else on the other end, we can regard the “Hello” as false and give the second implied proposition zero rating. (But note that the first implied proposition still gets a rating of 1!) Neither such proposition is a hypothesis for the speaker Jack; the second might be for the secret observer Jill if she suspects that Jack is talking to a phone that is dead at the other end. If on the other hand Jack records his end of a telephone call on a high fidelity voice recording machine and then causes this recording to be played back when he is absent but Jill is able to hear this recording of his voice, but not see whether actually Jack is present, you might like to say that from Jack’s utterance of “Hello” the first proposition “I am here” is false. If Jill was a trained spy, perhaps, or a much-betrayed wife, and knew that there was some possibility that Jack had played such a trick, but on a given occasion was as yet uncertain whether she was hearing Jack in person or a recording prepared beforehand to deceive her, she might entertain the proposition “Jack is here” as a working hypothesis; and if, for example, she thought that the chances were evens that Jack was really there, she could ascribe to the hypothesis the reliability rating 0.5, which means precisely that.

This long, elaborate discussion of an obscure fictitious scenario illustrates how complex can be the analysis of the propositions and hypotheses that can emerge in even a quite simple situation, even those arising from the simple utterance “hello” . However, the fact that the credibility rating scheme is more than adequate to cover the ins and outs of such a moment of drama and potential deception between people illustrates my claim that my rating sceme is good enough to cover all eventualities.

Utterance 2

As a direct question, utterance 2 is not a proposition; but the implied indirect question “I desire to know your state of health” is a proposition and therefore, with the identical (or any similar) meaning, “I desire to know how you are” is a proposition. The even more specific (and demanding) form of words “I wish you to tell me, now, your state of health” is a proposition but obviously with a stronger implication that the hearer should respond by supplying the information requested.

By the way, from this it is clear that the question of which utterances are (within my definition) statements, and which statements are propositions, is only a limited part of the broader view in semantics which is concerned as to the expressed and implied meanings within any given utterance.

So, the simple enquiry “How are you?” , though often a mere formaity of politeness, implies a statement about the speaker, namely that they wish the other person to tell them their state of health. In the form uttered by the speaker, this implied statemnt is a proposition and can be considered by the hearer as a hypothesis with the full scale of values, from 0 (the speaker does not really care in the slightest) to 1 (the speaker does indeed care quite sincerely). To the speaker (who knows his or her mind), the rating of the implication behind his or her own utterance is either 0 or 1, but to a speaker in inner turmoil about whether or not (s)he cares about the other’s health, it could be somewhere in between. And if the hearer is genuinely uncertain about how much the speaker cares, any rating is possible there too.

An important point illustrated by this simple case is that each person has his or her own private rating of each proposition including whether it qualifies as a hypothesis and its corresponding credibility. Jack may feel totally genuinely concerned about Jill’s health especially if she has been ill; but even if he does, Jill might have all possibly degrees of doubt from none (rating 1) to tatal (rating 0) about the proposition from Jack “I care, and wish to know, how you are” .

Utterance 3

Utterance 3 is a very simple proposition, stating that an event occurred: a quadruped of the feline persuasion took up a seated pose on a particular, previously identified small piece of floor covering (unless, perhaps even more likely, its place of repose was a place setting on a dining table).

This being a simple statement of past fact, it is certainly a hypothesis capable of the full range of credibility ratings. It has all the properties of any simple proposition that is uttered in the context of history.

Note that the definite articles in “The cat sat on the mat” imply that it is known from previous utterances or other available information whichcat it was, and which mat the cat sat on.

With the proviso that we know which cat and mat are being referred to, the statement is the paradigm for all simple propositions, from
“In the 1890s, Winston Churchill acted both as a soldier and as a war correspondent”
and
“Hitler invaded Poland in 1939”
(both generally regarded as true),to
“Queen Elixabeth I secretly married Robert Dudley, 1st Earl of Leicester”
and
“William Shakespeare did not really exist; the plays were written by Francis Bacon”
both of which are generally regarded as untrue.

But what about “King Alfred burnt the cakes when left to mind them baking” ?
This is a popularly told legend, to professional historians perhaps of douibtful authenticity, but still it may not be possible to prove it never happened.

This proposition about King Alfred is a perfect example of using credibility ratings in studying history. It illustrates the important point that, in principle, in this discussion every statement about historical events is a proposition of the appropriate type and can be treated as a hypothesis requiring a credibility rating.

An intersting question arises here specifically about holocaust denial. Such action is illegal in a number of countries and there are moves to make this the situation throughout the EU. In such jurisdictions, would it be illegal to assert that the credibility rating of propositions asserting that the holocaust took place should be set not at 1 but at 0.99 (or some other value, say above 0.90)? Or should it only be illegal to say the rating is below some lower value? Theese legislators are unlikely to concern themselves with my quantifiable rating system so this will never be answered.

By the way, if you are still reading this, and wonder what rating I do give to the holocaust assertion, I suppose I would set it around 0.99999999. The problem of referring to the holocaust assertion proposition as a hypothesis must also be recognized: to anyone who has not read and accepted this page, and my related page about the rating scheme, the mere word “hypothesis” might seem to imply doubt, even denial — indeed, any interpretation that in my scheme is a rating below 0.5. There is nothing I can do about this except to emphasize here that a non-zero difference between a rating and 1 does not mean a denial of the assertion given the rating. For an assertion to be treated as a hypothesis and given such a rating is only to recognize that in an empiricist-philosophical context no proposition can be given a rating of 1 by any person who does not have the kind of direct personal experience of what the proposition states is the case. However, all historical events of such major importance as the holocaust or indeed of either World War as a whole are so thoroughly covered by evidence that the broad facts merit such high ratings, so extremely close to 1, that calling any of them a hypothesis is not really required.

Having empasized all that, I should restate the principle that for all minor, tiny details not covered by evidence immediately to hand and directly available to the utterer, every statement about anything historical must have a rating sufficiently below 1 for that (proposition) to be called a hypothesis.

Remembering that the rating of any proposition is assigned by the individual, I should point out here how this works in history. In World War II, my father was in the British Army, stationed for quite a time in Iraq and what is now Iran. What he saw on a particular day during that time could well have been rating=1 to him. However, my father became ill and was brought back in a hospital ship. He was in hospital for a long time once he got back to England. When he came home, anything he told people about his experiences, including what he saw on any particular day, should not necessarily have had a rating of 1 any more even for him. For one thing, his long period of illness would certainly have affected his ability to recall detail, so had he been asked to write his memoirs (he was not) he would have had to be cautious about remembered detail in anything which he claimed was historically accurate.

To take it to the next stage, had some historian interviewed my father, he would have had to take the above considerations into his rating of what my father told him, plus the consideration that my father might embroider his narrative in order (as the phrase goes) to add verisimilitude to an otherwise sparse description. When a historian examines documents, (s)he has to evaluate the authenticity and the likelihood of error or deception (forgery) in each case; the proposition that expresses what any given document tells the historian must be treated as a hypothesis and given a rating distinctly (though not necessarily very far) below 1.

Utterance 4

Utterance 4 is a proposition about the speaker’s dislike of a certain (by me much hated!) condiment. A statement of what a person likes or dislikes is a statement of fact to the person. To me, my statement that I hate vinegar is a simple proposition with a rating of 1. It is not a hypothesis.

Similarly, to almost anybody (such as friends or family) to whom I am likely to make this statement, it is a simple, true one, not requiring the apparatus of a rating. However, if I were in a restaurant with a dish in front of me and was trying to avoid paying for a meal on the grounds that it was inedible through a misleading entry in the menu, or an error on the part of the waiter or the kitchen (and not on my part when ordering), the head waiter or restaurant manager might have to take my assertion as a hypothesis to be rated; that is, of which the rating might be below 0.5 because I was lying to try to save money.

This scenario is unlikely ever to take place because I rarely eat out (largely beacause restaurants put vinegar in so many things) and when I do eat out I am constantly hypercautious never to order anything containing vinegar. Until I get into the above scenario, it is safe for even a waiter to treat my remark as a simple true statement of fact. In fact it is obligatory for the waiter to do so — to believe me — because if (s)he doesn’t and brings something containing vinegar I will send it back the moment I discover the taste I hate!

Did you think the question of when a proposition becomes a hypothesis was of no interest in the outside world? Think again!

Utterance 5

As explained above, utterance 5 is a sign, not a proposition. Any simple cry, shriek or scream, being a sign and not a proposition in my scheme, cannot be treated as a proposition, but obviously a number of hypotheses can be deduced from such an utterance:

All of these are possibilities. Some overlap others; the first includes the next three, for example.

However, the above is an example of the use of ratings with mutually exclusive hypotheses. Let us suppose that we conclude, from the tone of the utterance, that only the first (including the next three) or the last hypotheses are possible. Then the ratings we give to those two must add up to 1. That is, if we reckon something being wrong or someone being excited or thrilled are equally likely, we give each of those two hypotheses ratings of 0.5.

This maps exactly onto elementary probability theory. If it were always possible to evaluate every hypothesis according to the formal definitions of probability and related ideas in mathematics, my credibility rating scheme would collapse into, and become identical to, probability theory. The only reason why it is stated separately here and in slightly different terms is that my scheme only has the purpose of expressing subjective judgements. In most of the cases where an individual applies it, nothing exists resembling the apparatus and context in which probability definitions can be applied.

The second important reason why probability theory cannot correctly be applied where my credibility rating scheme can be is that the rating changes from person to person. Every time a person utters a proposition to a recipient (that is, a hearer or reader), the recipient must assign his or her own ratinginto which they factor the circumstances of the utterance, as well as who the utterer is (or was) and what (s)he (the recipient) knows about the utterer. So, whereas a probability is often constant from one instance to another, each credibility rating is a function of the person deciding on the rating.

There are cases where a number of people will have the same basis for a rating; for example if a group of people in a community hears a statement made by a person from aoutside the community and equally unknown to them all, the bases for all of their ratings of what the outsider says might perhaps be the same; however, they might still all give very different ratings. Despite living close to each other these people may yet well have quite different experiences in their past lives that leave them differently disposed towards what is said; and often, even though they don’t know the speaker, who that person is may yet affect their ratings. For example, if the speaker is from particular occupation, another person of that same occupation might be particularly well or contrariwise particularly badly disposed toward the speaker for reasons that don’t influence anybody else.

Utterance 6

Utterance 6 is a complex statement and, although (if a person issued it to the press as news) most journalists would happily refer to it as a “statement”, for our purposes here it consists of a number of distinct, explicit or implied statements, which would have to be separated out as follows if we wished to examine them as propositions:

As this shows, this utterance is such a complex statement that it has to be construed as a series of nine separate simple propositions. All of these are of a historical, biographical, or literay nature and can in theory need ratings so that we might talk about them all as hypotheses.

That two men existed who had the names mentioned, and what these men did by way of occupation, is a matter of historical record and as hypotheses would only be interesting if some doubt arose (rather unexpectedly, I would imagine, among students of the history of philosophy in the modern era). What works Wittgenstein published is perhaps additionally a matter of bibliography, of the history of publishing and of librarianship, aside from the routes that take us to the man. In all these areas, we do not need to treat the propositions as hypotheses or to worry about credibility ratings, unless some doubt arises as to the accuracy of the statements.

The only proposition that lends itself easily to questioning is the last, which is one almost of literary interpretation. Did Schopenhauer really use the analogy mentioned? If so, where? The statement does not contain a proposition naming the work from which it is claimed the analogy was borrowed. To evaluate the hypothesis with the given data, one considers what one knows about the history of philosophy and the works of the two individuals named, and what one considers likely. If one knows nothing about either of them, one might give the hypothesis a rating of 0.5 just as a starting point because there are two possibilities: either W. borrowed this thing from S. or he didn’t.

On the other hand, one might say “I saw this on Wikipedia, which I trust implicitly as a reliable source of information. I rate it at 0.99.” But another person might say “Well, on some kinds of information, Wikipedia is brilliant; but on such passing remarks as this one, on obscure subjects, it is all too prone to mis-statements and I don’t reckon the fact that this statement is made there lends any additional credibility at all.”

© 2008 Ian P. Hudson