# What truth-functions of elementary propositions can be consired to form a picture?

In Tractatus Logico-Philosophicus Ludwig Wittgenstein says that every elementary proposition is a picture. It is clear that we must make a distinction between elementary propositions and other propositions, because we cannot consider a negation of an elementary proposition to be a picture.

For example the proposition "This house is not red" would be true if "This house is blue" or "This house is gray" is true but they can`t both be in same picture, because they are contradictory claims. But if we think about a finite conjunction of elementary propositions it seems possible to consider it to be a picture.

So would a solution be those truth functions that are true only in one row in a truth table?

• First your definition of contradictory is off. The statements "this house is blue" and "this house is gray" are INCONSISTENT with each other but NOT CONTRADICTIONS. Contradiction has a precise meaning. All inconsistencies are not contradictions. There are other types besides that one. Perhaps what the message is by a proposition & "picture" is that the proposition should be as descriptive as humanly possible. The error of your examples are the alleged propositions end in adjectives. That is vague & misleading. All sentences are not propositions. You seem to think they are equivalent. Commented Sep 16, 2019 at 18:01
• I said contradictory not (logical) contradictions. Inconsistent claim is exactly the same as logically contradictory claim. Colours have precise meanings in physics. I didn`t say all sentences are propositions. Commented Sep 16, 2019 at 18:10
• You are wrong as I stated. All inconsistent claims are not identical with contradictory claims. You are writing in such a way that is consistent with people thinking every sentence can be expressed as a proposition. I never said you literally stated such a claim. The proper term here is YOU EXPRESSED. I am not nit picking nor literal about your expression. Since you seem to be unfamiliar with some philosophy concepts & context I take it you are in math or science? You cant use contradictory however you like especially in a philosophy site. You should use proper terms to get you ideas across. Commented Sep 16, 2019 at 18:31
• Any inconsistent claim is logically equivalent to "A and not-A". Any inconsistent theory has only one model - the empty set. Commented Sep 16, 2019 at 18:44
• I am not sure this is so straightforward: a conjuction of propositions that turn out to be mutually exclusive does not form a "picture", for example. I think only small subset of conjunctions will be picturable, when we can take it all in at once, so to speak, and it probably has more to do with our imagination capabilities than with logic. @Logikal Please be more polite with new users, that reminder is there for a reason. Commented Sep 16, 2019 at 20:57

Propositions associated with facts or states of affair are pictures of those facts or states of affairs. In contrast to tautologies and contradictions they have sense and because of that they have true-false poles. Anat Biletzki and Anat Matar provide this description:

Tautologies and contradictions, the propositions of logic, are the limits of language and thought, and thereby the limits of the world. Obviously, then, they do not picture anything and do not, therefore, have sense. They are, in Wittgenstein’s terms, senseless (sinnlos). Propositions which do have sense are bipolar; they range within the truth-conditions drawn by the truth-tables. But the propositions of logic themselves are “not pictures of the reality … for the one allows every possible state of affairs, the other none” (TLP 4.462).

Consider the OP's example:

For example the proposition "This house is not red" would be true if "This house is blue" or "This house is gray" is true but they can`t both be in same picture, because they are contradictory claims.

A picture of either a gray house or a blue house would also be a picture of a house that is not red. Propositions associated with a state of affairs have true-false poles. They are "bipolar". They may be either true or false. If the proposition is "This house is not red" and the picture is of a blue house then the proposition would be true and associated with the picture of a blue house.

However, a proposition that is a tautology such as "This house is red or this house is not red" would not be a state of affairs or a fact. It does not have true-false poles because it is always true. A proposition that is a contradiction such as "This house is red and this house is not red" would also not have true-false poles because it is always false.

Here is the question:

So would a solution be those truth functions that are true only in one row in a truth table?

Propositions that are neither tautologies nor contradictions would have at least one row in a truth table that is true and at least one row in a truth table that is false. These propositions would have true-false poles. They are contingent. They would have sense and be pictures of reality. From those pictures one could tell if the propositions actually represent the state of affairs (they are true) or they do not (they are false).

Biletzki, Anat and Matar, Anat, "Ludwig Wittgenstein", The Stanford Encyclopedia of Philosophy (Summer 2018 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/sum2018/entries/wittgenstein/.

• The point is that many pictures are true with respect to the truth conditions of "This house is not red". For example a picture of a moon made of cheese. Commented Nov 20, 2019 at 20:04

In Tractatus Logico-Philosophicus Ludwig Wittgenstein says that every elementary proposition is a picture.

Clearly, propositions are not visual pictures.

Dictionaries provide apt definitions of the meaning of the word "picture" as it was used by Wittgenstein:

Picture

1. The main circumstances of an event or a time; the situation.

This is a generalisation of the notion of picture. Pictures in the ordinary sense also fit this definition.

A picture, broadly considered, is a representation which is not expected to be complete. It only has to bring together a few snippets of truth.

Different kinds of pictures may show different kinds of things. Photographs are not painting are not drawings.

It is clear that we must make a distinction between elementary propositions and other propositions, because we cannot consider a negation of an elementary proposition to be a picture.

I fail to see why we should make this distinction. A novel may be considered, broadly, as a very large conjunction of many elementary propositions, some negations, some disjunctions, and a novel seems indeed like a tableau about life, hence, a picture.

A painting does not explicitly use negations while propositions, at least as described using words, can. But this difference can be attributed to the various means you can use to express a proposition and propositions need not include negations.

If we insist that propositions can include negations, then perhaps we may just as well give up the notion that they are pictures. For example, it may be enough to take propositions to be logically dignified ideas or beliefs.

For example the proposition "This house is not red" would be true if "This house is blue" or "This house is gray" is true but they don`t both can be in same picture, because they are contradictory claims.

We could represent the same house twice in one picture, once blue, once gray, and therefore ... not red. The house would be represented as not red. In statements using words, "blue" does not imply "not red". In a picture, blue implies not red. And maybe that makes propositions not pictures after all.

Strictly speaking, we consider propositions and pictures without any identification of the things represented outside the propositions or pictures themselves. Whatever extraneous identification we may consider will not be in the proposition or in the picture itself.

Thus, propositions and pictures both can be true not only of what we choose to think of as being represented by them, but of other things as well as long as they fit the description. The painting of a twin will often be true of the other twin.

For the same reason, the same proposition or the same picture will be false of many things beside the one we may have in mind.

Thus, if we represent the same house twice in one picture, once blue, once gray, the two parts of the picture will be false of any red house, as indeed of mountains, people and neutrons.

The two parts of this picture may each be true of what we think of as the same house but at different times, once when it was blue, once when it was gray.

But if we think about finite conjuction of elementary propositions it seems possible to consider it to be a picture. So a solution would be those truth functions that are true only in one row in a truth table?

It is possible but rather limiting. Why not use disjunctions and negations? Or indeed implications? A truth table looks indeed somewhat like a kind of picture, although they are generally used to prove validity, not to present a picture of the factual truth.

Not very practical, but we could use a truth table, without any implication in it, to paint the picture of Mona Lisa. It would be a proposition. Aren't all forms of expression logically equivalent? I would hope so.

• You have an interesting example of a picture of my example proposition, but I claim it does not represent the conjuction of the propositions "This house is blue" and "This house is gray", because you cannot consider the picture for example to be a single photograph, so that the houses are the same. IMO the word "this" includes the same timeness. One valid use of that word would be to point your finger on a house and say "This house is not red". Your example could be considered to be an example of a house being painted. I don`t know can propositions be really considered to be pictures. Commented Sep 18, 2019 at 6:22
• @JohanAspegren They can in the generalised sense of the word "picture" (see my edit, copied from a dictionary). They cannot in the narrow sense of visual representation. Wittgenstein must have been talking about the generalised sense of "picture". - 2. Visual pictures are not necessarily "single photographs". You won't have a sensible conversation if you redefine the vocabulary to fit your preconceptions. Wittgenstein talked of "pictures", not "photographs". The same picture of Marilyn Monroe by Andy Warhol represents her several times in false colours. Same Marilyn. Commented Sep 18, 2019 at 16:18