How does a "natural argument" proceed?
"Amy went to the shops, so she will get the bread" is typical. No ifs. "Amy went to the shops" is taken to be a proposition that will be immediately accepted as true, and the follow-on is taken for granted without any serious "logic" going through our heads. Yet we remain open to the possibilty that Amy might forget to buy some bread. Why?
Consider what at first looks like a simple cut-and-dried example: "I am pressing the light-switch, so the light will come on". Let's say ""I am pressing the light-switch" is also immediately accepted as true. So the light should come on. But suppose it doesn't. Would the logic (if any) of the statement be wrong? Traditionally, if the light didn't come on, then the switch wasn't pressed. But this is disallowed because the switch was pressed. Of course the reason why the light didn't come on is because one or more of a large number of unmentioned conditions was not met. One would consider them one by one in receding order of probability (of not being met): the light bulb has failed, a fuse has blown or a safety switch tripped, there's a general power failure, we didn't pay the bill so the electricity provider disconnected our supply, the house wiring has been damaged.... everyone's suddenly gone blind, electricity no longer powers anything. The point is, most reasoning works like this - it is not contained in the proposition, so to speak, but comes into play only if needed, from a kind of field which radiates out into the world, in theory ad infinitum, at some point resembling a mini-paradigm-shift. (One of the reasons why the ball didn't move when Johnny kicked it could be the same reason why the New York stock market crashed - or why Amy forgot to get the bread.)
This applies whether or not we formulate our "arguments" in classical terms. But then the basic classical formulation is rendered all but useless (it always was, of course). The light switch example is
illuminating (!) because you can see how pressing the switch is not so much a cause in itself as a gateway for other causes/conditions to operate.
So the typical "natural argument" runs: A (is true) so, all being well, B (is true). Whether we need the "is true" (especially as regards the consequent) is a matter of opinion. But it's becoming increasingly clear that few propositions can carry the truth value "true" as an indelible stamp, yet what they must always carry is the claim to be true, the "purport to be true" stamp. The reason why propositions cannot be conclusively verified is not because of weird Popperisms but because they cannot make that final connection with reality.
So how can a proposition be contradicted? Well, at first sight by offering a proposition with (the equivalent of) a negation sign in it; so, for example "Amy has gone to the shops" is contradicted by "Amy has not gone to the shops" (which of course puports to be true). But I still think we communicate in contexts where the truth of some propositions is taken for granted and cannot be sensibly denied. This is the foundation upon which the structure of "ordinary arguments" should be based. (Funnily enough, it's similar to the dubious foundation on which scientific propositions are based, given a mild degree of deference to "paradigm shifts".) Contexts, fields of knowledge, statement situations - that's where the boundaries of meanings lie.
The bleakness of propositions
Consider the statement: Jill's 21st birthday was about 10 days ago, when in fact it was 11 days ago. Nonetheless it is a true statement, and "just as true as" the statement Jill's 21st birthday was 11 days ago. Other "vague" statements: Violets are a kind of purplish colour, Tahiti is somewhere in the South Pacific, human beings resemble gorillas, swifts tend to fly higher than most other birds ... . These are all true because consistent with the facts. But what does it mean to be consistent with the facts? Presumably only "consistent with other more accurate propositions". But even the most "accurate" propositions are only those that are consistent with the facts, i.e. with other similar or identical propositions. All true material propositions only reflect certain aspects of real situations (or represent extracts from reality). The crucial question is whether there are "facts" or "actualities" which are not propositions yet which are somehow related to propositions (no matter how vague) in a way that makes those propositions true. Propositions are communicative, implying some kind of authorship or positing, and some kind of receivership. If never received, they are simply "dead". But the amount of information communicated by propositions is invariably very small. Consider this: At 8 o'clock one evening a daughter SMSs her mother with the message "Mum, I'm just going to see a movie at the Ritz, might be late home". But in fact the daughter went to her boyfriend's house instead. The mother believes her daughter and forms some kind of impression of where she is and what she's doing. Now suppose her daughter did in fact go to the movie. Would that change the mother's impression? No, it wouldn't make the slightest difference. The "fact" (proposition) of her daughter going to the movie is extremely bleak even though the situational detail in the event that she had gone is entirely different from the detail in the event that she had not gone. The meaning of the proposition is no more than what the mother makes of it. But its truth may be tested by propositions that subsequently transpire, whether admissions of deception or evidential statements, and these propositions are of the same order of bleakness as the original SMS. The truth is pretty thin.
Facts without words (this is also included in a page on "domestic propositions")
"I'm putting some pepper in the soup" is true if I'm putting some pepper in the soup, and that's that. But you cannot understand the unquoted (antecedent) sentence as being a sentence, a proposition or anything else. It ought not to be said at all. Language may be the only way to express something, at least in print! But I intend the unquoted sentence to be redundant, to be replaced by an activity: "I'm putting some pepper in the soup" is true if [present action of me putting pepper in soup]. We seem to lack the means of talking about something without talking! The "something" is either a non-verbal experience or a real-world object/activity. (Notice that “is true” can be harmlessly omitted from these examples.)
But now I'd like to say that the utterance itself is part of the same situation as the activity which it describes. Moreover in an actual "Putting pepper in the soup" situation (assuming the meaning of the phrase is understood) we hardly needed even the first (quoted) statement, let alone the unquoted version. It would be odd if we ever needed to say: " 'I'm putting some pepper in the soup" is true because that's what I'm doing. Can't you see what I'm doing, you idiot?" Obviously a deaf person could follow the procedure perfectly well without needing any talk at all. But in that case there would be no statement to be true or false. Nonetheless the statement "I'm putting some pepper in the soup" would be true if I uttered it. So would a proposition such as "At [such & such a time and place] Dave Robinson was putting pepper in some soup". (Not to mention: “A while ago somewhere or other some lousy excuse-for-a-cook was putting some stuff in a concoction” - true but unhelpful.)