ellauri096.html on line 112: Agnostics overestimate how easy it is to identify what cannot be known. To know, one need only find a single proof. To know that there is no way to know, one must prove the negative generalization that there is no proof. After all, inability to imagine a proof is commonly due to a failure of ingenuity rather than the non-existence of a proof. In addition to being a more general proposition, a proof of unknowability requires epistemological premises about what constitutes proof. Consequently, meta-proof (proof about proofs) is even more demanding than proof.
ellauri096.html on line 114: The agnostic might be tempted to avoid presumptuousness by converting to meta-agnosticism. But this “retreats” in the wrong direction. Meta-meta-proof is, in turn, even more demanding than meta-proof. Meta-meta-proof requires both the epistemological premises about what constitutes proof that meta-proof needs and, in addition, meta-meta-proof needs epistemological premises about what constitutes meta-proof.
ellauri096.html on line 136: Foundationalists reject (1). They take some propositions to be self-evident. Coherentists reject (2). They tolerate some forms of circular reasoning. For instance, Nelson Goodman (1965) has characterized the method of reflective equilibrium as virtuously circular. Charles Peirce (1933–35, 5.250) rejected (3), an approach later refined by Peter Klein (2007) and championed at book-length by Scott F. Aikin (2011). Infinitists believe that infinitely long chains of justification are no more impossible than infinitely long chains of causation. Finally, the epistemological anarchist rejects (4). As Paul Feyerabend refrains in Against Method, “Anything goes” (1988, vii, 5, 14, 19, 159).
3