Logical Sentences

[Arjen]

Say, I am trying to explain the working of (at first) propositional logic to someone. We have arrived at forming (prop) logical sentences out of normal sentences. A question that ariso was if all sentences can be translated by the use of logic. I think so, albeit by different logical systems at times. I am wondering though, can every sentence be translated into every logical system (with some imagination) or are there definate guidelines for that; such as that sentences with a certain construction should be translated into predicate logic (or would best be?) or perhaps that certain sentences cannot be translated into modal logic?

[jgweed]

However grotesque the result, any sentence can be translated into any particular kind of logic, because each kind reflects the universal rules of validity. Which kind is used will, it would seem, depend upon which best and most clearly expresses not only the proposition at hand, but allows the analysis of the entire deduction as a whole.

[Arjen]

Thats what I thought, but I figured that since I was going to relay the information I'd best get a second opinion.

[VideCorSpoon]

You ask the question whether or not all sentences can be translated by the use of logic? It depends. Anything and any sentence can be broken down into logical syntax. However, this depends on whether or not the sentence you are translating is logically correct.

Logic (well… propositional logic) depends (mostly)on Wff. Wff stands for “well formed formula.” Within this formula, the logical syntax must be correct, precise, and following. This is perhaps the greatest skill anyone can get out of logic because understanding the foundations of a well formed formula is a sure way of constructing a good argument in everyday use. Understanding well formed formula’s can also discern which arguments are bad, nonsense, irrelevant, etc. It’s a very useful thing to know.

So to answer the question, any sentence can be broken down into logic… however, it must be in the form of a well formed formula. Now the questions arises “what if the sentence is not a well formed formula?” This is almost always the case, as many people just don’t know how to make well formed arguments. The answer is that you have to make it into a well formed formula. You basically have to correct the argument so that it can be looked at in a logical way and examined.

So you are right in thinking that most sentences can be translated using logic. Also, your concern about guidelines is well founded, and I stated that well formed formulas are the key to correct interpretation to address that concern. That it would have to be translated into a more abstract form of logic is not necessary…. Unless you want a more abstract answer.

[Arjen]

I'll keep that in mind. Thanks VideCorSpoon!

[Holiday20310401]

Originally Posted by VideCorSpoon

however, it must be in the form of a well formed formula. Now the questions arises “what if the sentence is not a well formed formula?” This is almost always the case, as many people just don’t know how to make well formed arguments. The answer is that you have to make it into a well formed formula. You basically have to correct the argument so that it can be looked at in a logical way and examined.

I know this isn't what you're trying to say but the thought came across while reading this, can I form a thesis or argument based on the interconnectedness of several logical statements.

I was wondering if this is possible by means of thematically connecting statements, even if they happen to be opinions that also need proving.

And even the way of connected the statements would be a pattern.

[Arjen]

That would depend on the thesis. If you would research why the statements are incorrect for instance, that would be possible. By incorrect reasoning nothing can be proved though, so it cannot show anything other then its own incorrectness. To prove anything it would need at least one correct reasoning.

[Holiday20310401]

Yeah so there are I guess you could say two levels. There are the reasons and then the premises. And then what if the premise is the thesis and we don't know what it is yet.

I mean I read the logic stuff and all the time it deals with finding truth and false from 'premises' and 'therefores'. (braindead, can't think of the right words)


And we must have the two it seems. Its like finding the angle of a triangle. We seem to need the angle and a length in the logic scenarios. Why can't we use the method of finding the angle by knowing all 3 lengths. If we knew all the reasons or all the premises, can we not work out the other as a single statement. I mean, a premise could be a premise for one thing and a conclusion for another.

If I wanted to develop a theme statement that interconnected all the themes I had decided mingle together because they are all of an influence on the same system, then I just need either the reasons or the premises, which end up meaning the same thing. All in all, I just need how the themes connect, then the statement can become clear.

[jgweed]

An argument can be composed of more than one premise and each premise can be expressed as a WFF, and then a conclusion (thesis) correctly drawn from the series of premises, although in most cases, these premises are not stated as WFFs or in a formal manner. Few people would enjoy reading a series of premises and conclusions stated in logical form, so generally translation is required for analysis.

One needs, in argumentation, to provide warrants for accepting the truth of each premise. These warrants range from appeals to the veracity of matters of fact to additional chains of premises leading to accepting the original premise as true (which would mean that the first premise in the series was a conclusion of other premises).
Quite often these argumentative chains can be quite long, contain many terms (not all of which are explicitly stated), and require some de-rhetorical reading to bring the argument itself to the forefront. One is reminded of some of those "brain-teasers" where one person never lies and the other never tells the truth, and the reader is presented with a string of statements that will lead to knowing which person is which.

Understanding logic and the various methods and requirements of argumentation, and then making the all premises and conclusions explicit and linked to one another in a logical chain more often then not is enough to show humbug for what it is.