Post by Eugene 2.0 on Mar 6, 2023 18:03:14 GMT
Usually logic is dealing with propositions as p, q, r... which symbolizes sentences or completed thoughts. So, a proposition represents our thoughts or ideas in language or any kind of symbolic structures. However, there are two more types of sentences in language we may find: questions, and imperatives. Well, the questions also may be called as interogatives. In any case, logic is able to deal not only with declarative types of sentences. So, here's a piece of example how can interogatives can circulate in logic.
Such sentences as 'x is an elephant', or 'the sun is either x, or y' can be easily transformed into question as like 'what an elephant is?' , and 'is it true that the sun is x, not y?'. So, mostly the questions can have these forms:
'x is y' = 'what x is?'
'x is y, or z' = 'is x y, or it is z?'
The most important is to answer the question, but from a logical point of view there are many other features that should be aimed, as these ones:
'what x is?' <-- 'there is an y such that x is y'
'is x y, or it is z?' <-- 'x is y'
So, the important thing is that for a question it is important to know if there is an answer. If there's an answer means that such a question (can be/is) completed. We may compare it to propositions saying that if a question can be completed, then it is quite the same as for the proposition to be true.
Okay, so the question is what can be inferred from what? Is it possible to infer 'what is y?' from 'what is x?'? (Must say that there's a paradox: to answer this question means that we have to answer it firstly by our present or current talk.) The most general rule for the inference is:
p can be inferred from q iff if p is completed, then q is also completed.
Let's draw an example: 'what is a triangle?' --> 'what is an irregular triangle?'
Okay, so here's a tip we can go with it doing some epistemological attempts. Assuming this interogative logic we want to know can we know everything? or is it possible to know everything?
Let's find out:
if p --> q, then if not-q, then not-p.
In other words if one of sub-questions (or a smaller, or a tinier questions) cannot be completed (answered), then the greater cannot be answered. And it doesn't seem to be wrond. Again: if we cannot answer on at least one small question this means we cannot answer on all questions.
But here's something additional: where is the limit to p? I guess it can be interpreted as in this kind of thing:
if there is no r such that r doesn't belongs to p, and for any q if p --> q, then p is the most ultimate question
The most dramatic thing is - there's no way to find this out, until r is known, but we cannot perform it. If this logic works, then the skeptic axiom works too.
Such sentences as 'x is an elephant', or 'the sun is either x, or y' can be easily transformed into question as like 'what an elephant is?' , and 'is it true that the sun is x, not y?'. So, mostly the questions can have these forms:
'x is y' = 'what x is?'
'x is y, or z' = 'is x y, or it is z?'
The most important is to answer the question, but from a logical point of view there are many other features that should be aimed, as these ones:
'what x is?' <-- 'there is an y such that x is y'
'is x y, or it is z?' <-- 'x is y'
So, the important thing is that for a question it is important to know if there is an answer. If there's an answer means that such a question (can be/is) completed. We may compare it to propositions saying that if a question can be completed, then it is quite the same as for the proposition to be true.
Okay, so the question is what can be inferred from what? Is it possible to infer 'what is y?' from 'what is x?'? (Must say that there's a paradox: to answer this question means that we have to answer it firstly by our present or current talk.) The most general rule for the inference is:
p can be inferred from q iff if p is completed, then q is also completed.
Let's draw an example: 'what is a triangle?' --> 'what is an irregular triangle?'
Okay, so here's a tip we can go with it doing some epistemological attempts. Assuming this interogative logic we want to know can we know everything? or is it possible to know everything?
Let's find out:
if p --> q, then if not-q, then not-p.
In other words if one of sub-questions (or a smaller, or a tinier questions) cannot be completed (answered), then the greater cannot be answered. And it doesn't seem to be wrond. Again: if we cannot answer on at least one small question this means we cannot answer on all questions.
But here's something additional: where is the limit to p? I guess it can be interpreted as in this kind of thing:
if there is no r such that r doesn't belongs to p, and for any q if p --> q, then p is the most ultimate question
The most dramatic thing is - there's no way to find this out, until r is known, but we cannot perform it. If this logic works, then the skeptic axiom works too.