Contemporary Developments
Some (such as dialetheists) argue The law of non-contradiction is denied by paraconsistent logic, however, “negation” in paraconsistent logic is not really negation in the formal sense; it is merely a subcontrary-forming operator.
The law of the excluded middle is not part of the execution of intuitionistic logic, but neither is it negated. Intuitionistic logic merely forbids the use of the operation as part of what it defines as a "constructive proof", which is not the same as demonstrating it invalid (this is comparable to the use of a particular building style in which only nails are allowed, and screws are forbidden- it does not necessarily disprove or even question the existence or usefulness of screws, but merely demonstrates what can be built without them).
As such, while some doubt these principles, to this day they have yet to be successfully challenged or had any coherent alternatives presented.
Read more about this topic: Law Of Thought
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