How do radical skeptics address the following knowledge "Something may be or may not be"? The proposition "Something may be or may not be" covers all possibilities and therefore is absolute knowledge. A = B or A != B. How do they address this proposition and do they think this is knowledge or their definition of what is knowledge differs from mine?

  • I don't know about radical skeptics, but Buddhist thinkers long ago broke up that statement by arguing that a thing might both be and not be, or that a thing might *neither be nor not be. We might think about the peculiarities of quantum superposition in this regard, so it's not mere word-play... Jun 12 at 15:04
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    No, it is not knowledge at all. It is a tautology, i.e. a statement that does not exclude any truth-condition. See W's Tractatus, 4.46 Jun 12 at 15:35
  • I would like to watch the arguments of such a skeptic, something that it and its existence and non-existence don't exist. (Binary thinking is infused in us). Jun 12 at 15:49

Please bear in mind there's a difference between law of non-contradiction (LNC) and law of excluded middle (LEM). LNC essentially says any proposition and its negation cannot both be true at the same time, while LEM essentially says any proposition is either true or false and there's no middle case. And as we know both laws can be violated in non-classic logic such as paraconsistent logic and intuitionistic logic, respectively.

It seems your question can be paraphrased as "the proposition A=B is either true or false is knowledge or not". If we accept knowledge as justified true belief in most philosophy references, then your question is essentially that is the proposition LEM is qualified as JTB knowledge true? It's a tautology which is a justified true belief under most logics such as classic propositional or predicate logic, thus it's a knowledge. But for the more cautious intuitionists such as some constructive or intuitionistic mathematician like Brouwer, LEM as stated in usual form is not justified as referenced here:

In general, intuitionists allow the use of the law of excluded middle when it is confined to discourse over finite collections (sets), but not when it is used in discourse over infinite sets (e.g. the natural numbers). Thus intuitionists absolutely disallow the blanket assertion: "For all propositions P concerning infinite sets D: P or ~P" (Kleene 1952:48). For more about the conflict between the intuitionists (e.g. Brouwer) and the formalists (Hilbert) see Foundations of mathematics and Intuitionism.

So for intuitionists at least your question can be answered in the negative as the above paraphrased proposition is false. By the way, intuitionists care called radical constructivists, not radical skeptics though since they still agree with most other laws and inference rules with classic logicians.


The most obvious remark is that if we have no knowledge as to whether some proposition is or is not the case, then we have no knowledge at all. Might-or-might-not is a state of ignorance not a state of knowledge.

Since you have not proffered your definition of "knowledge", how can the poor sceptic judge whether it is the same as theirs or not? They cannot even know what your question means. (But of course, once you do offer a definition, expect the radical sceptic to immediately shred it to ribbons).

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