List,
maybe I have found an easy way to explain an aspect of intuitionalistic logic: Read first "supplement" and then "suppsupplement":
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Suppsupplement about intuitionalistic logic:
Maybe I have found an easy way to explain an aspect of intuitionalistic logic:
Negation (single or double) is an event (operation), and implication is a state. An event creates a state, but a state does not create an event. So, reflecting about the relationship between implication and double negation:
If you have a state, the event that has created it, is in the past. The past is definite, it can be analysed by deduction. So from an implication you can infer to a double negation.
If you have an event, you cannot conclude to the state it will create, because from your point of view this is in the future, and the future is unclear. Things may happen, that may change everything. So you cannot infer from a double negation to an implication.
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Supplement:
I wrote, that the concept of negation doesn´t have an extension. But now I think, that a negation is not a state (of something to not exist), but an event: A reaction, repulsion, disappointment, reflection denying something. This should have occured to me earlier, just by looking at the ending "-tion". The extension of "negation" is the whole of these events, and the intension is their common quality, which is privative, depriving.
This means, that "No A with no B" does not contain any negation. Only "If you have sorted out all As, and look for Bs in the residue, you will find none", contains a negation, resp. two of them.
This again means, than we both may be right, in a way: "Not B" may be more primitive that "If-Then", but it is not a negation. "I can find no Bs anymore" is less primitive, and is a negation. But that is just a guess, I have lost the thread about primitivity-ranking, now that it has become so complicated.
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