If we start questioning the validity of logic, will we soon be unable to trust any logical reasoning and witness the downfall of rational discourse?

It's widely accepted that true and false and two distinct things, and that something must be either true or false. But, suppose you're eating your breakfast one morning, and it occurs to you that you do not need to believe that true and false are distinct, just because this is widely accepted.

"In fact," you think, "the only reason I believe true and false are separate and distinct is because I've been conditioned to believe this."

Now, for whatever reason, the rest of the world catches on that true and false could actually be the same thing. Would we witness the end of rational discourse?

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In this question, the suggestion was that the questioning of the validity of logic will inevitably lead to an inability to trust any logical reasoning, which in turn will lead to the downfall of rational discourse. This assumes without sufficient evidence that a minor action (questioning logic) will lead to a series of drastic and undesirable consequences. The flawed thinking is referred to as a slippery slope.

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If we start questioning the validity of logic, will we soon be unable to trust any logical reasoning and witness the downfall of rational discourse?
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