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How can we create problems out of nothing (our imagination) ?

Example 0: The absolute truth is that "I know that I don't know". True or false

Example 1: A cat has 20 legs , after walking 10 km it reaches its destination with only 3 legs . How many legs did the cat lost after walking 10 km ?

Example 2: Is the total length of the universe unknown? true or false?

Example 3 A car has 1000 doors. t True or false ?

Example 4 On an island there are 3 people ,person A is saying that 1 + 1 = 3,person B is saying that 1 + 1 = 3 , person C is saying that 1 + 1 = 2 . Does person C has the correct answer ? True or false ?

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    Language : our "language engine" has an ulimited capability to produce syntactical correct expressions. And our brain has the capability to select among them those that has a sense, i.e. are capable of expressing a correct semantical content. – Mauro ALLEGRANZA Feb 22 at 9:45
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I'll try to have a stab at this. Let us break down the examples.

Example 0: Proposition A that B (where A = {I know}, B= {I don't know}}

Example 1: A cat has 20 legs

Example 2: That D is either True or False. Where D={ Total Length of the Universe is Unknown }

Example 3: That E is either True or False. Where E={ A Car has 1000 doors }

It has been argued that the human brain has different modules for different cognitive processes. Let's consider three modules - visual, linguistic, logical and apply them to your examples:

Example 0: The language module processes and creates linguistic propositions: example 0 is fine because it is a purely syntactic arrangement. The visual module helps you imagine and you cannot visualize what you don't know. With logic module which processes logic, you find that Token A =/= B

Obviously, this is a conflict in modules that creates circularity.

Similar applies to Example 1: A cat has 20 legs is perfectly fine by the linguistic module. But your visual memory says you've only seen cats with 4 legs. Then your logical module can prioritize your visual memory, over your linguistic propositions and identify that it is a problem.

Example 3: A car has 1000 doors. This is similar to example 1, except that your linguistic module can identify with the logic that something that has 1000 doors cannot be a car but it could be a train. Or a car could have 1000 doors but your visual memory says you've only seen cars with far fewer doors.

Example 2: The sub-tokens Total length and universe are semi-visualizable. It means you compare them to shapes or concepts you know, such as a scale or a sphere. But combine it with unknown then you have a proposition that is linguistically processable, but visually cannot be accounted for, because you cannot imagine how long the universe is, thus, you can logically come to the conclusion that the proposition D is true.

Example 4: Example 4 is a bit different because here you have mathematical axioms and linguistic expressions. If by One plus one equals Two means 1+1 =2 Then this proposition is a mathematical axiom that is expressed linguistically. If by One plus One equals Three means 1+1 =3 Then this proposition is not a mathematical axiom that can be expressed linguistically.

However, imagine the persons A and B are from a different country (or planet) and when they say One plus one equals Three they really mean 1+1= 2, then maybe this proposition is a mathematical axiom but linguistically misrepresented to person C.

But we, as the spectator, know the mathematical axiom 1+1=2 is always true therefore we can employ our logical faculties to analyze the linguistic propositions and find the conflicts accordingly.

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Knowledge has systemic properties (c.f. systems theory). Knowledge is not only a set of atomic elements (Kant's concepts), each one related to an idea or mental concept (e.g. war, a rock, the number nine, a particle, a song, hunger, etc.), but it is a set of interconnected elements by what we call relationships (e.g. think on Monica Lewinski, now, think on the person she's related to; think on an electron, now think what other entities is it related to; etc...; you will find probably the same relations that anyone finds).

But the problem is that we're not gods. We only have a small set of elements of knowledge, quasi-integrated with relationships. But we don't know a lot of things. This means that we don't have the mental relationships to connect a huge amount of concepts with others. For example, a car has 1000 doors, true or false? is a system that you are trying to relate to another system, the truth. You just don't know the relationship. Perhaps you find the answer one day, perhaps you don't. If you find it, you will create the mental relationship between both systems. If you don't, you will continue to survive, with that missing mental link, which is something completely natural.

So, your issue, expressed within this understanding, is just related to finding relationships between concepts we already know. That's it.

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