Question: do we attain certainty of at least some facts? We are certain, for example, that of two disjunctive propositions, one is true, the other false. We are certain about the truth of the principle of noncontradiction. While there is a trade-off between the utility of justifying informative claims and indubitably, for the principle of noncontradiction does at most say that there are at least some true sentences. Therefore, we know that there are at least some certainties about logic and there exists some true sentences. This is no argument, for it is exists outside the reach of argument: any criticism would, so the argument goes, have to assume the principle of noncontradiction, making it immune from argument. Therefore, the skeptical position is wrong about some state of affairs.
Is this true?
Two skeptical responses:
- We might note that a great deal of theory-laden cognition takes place when considering the principle of contradiction. We might, although it sounds silly at first blush, have made a simple mistake in our reasoning. Purported past cognitive state p is to person S actually a memory of past cognitive state p. We might misremember p, no matter how certain we are that we remembered p correctly; or be unaware that we have an improper justifier for p; or the justifier for p may be proper, but we may not be aware of it.
- The principle of noncontradiction is wholly supported on the structure of the argument itself, opening itself to the criticism that, while it is assumed as an axiom, logicians and mathematicians that one thought some axioms were obvious or indubitable have turned out to be, upon further reflection, far from obvious or indubitable. Just as Euclid’s fifth axiom could be rejected and still provide consistent non-Euclidean systems, the principle of noncontradiction can be rejected, producing paraconsistent logics.
Are we then certain of at least some facts?