In preparation for the print edition of Veriphysics, which has been requested by a few intrepid minds and is obviously necessary for the long run, I’ve updated The Treatise to include an appendix to demonstrate the legitimacy and utility of the Triveritas, which consists of the paper on the two trilemmas and begins thusly:
The Agrippan Trilemma is one of the oldest and deepest problems in epistemology. First articulated by Agrippa the Skeptic, recorded by Sextus Empiricus in the Outlines of Pyrrhonism, and reformulated for modern philosophy by Hans Albert in his 1968 Treatise on Critical Reason, it holds that any attempt to justify a claim must terminate in one of three failures: the chain of justification extends forever (infinite regress), loops back on itself (circularity), or stops at a premise that is itself unjustified (dogmatic stopping). Since these three options appear to exhaust the logical possibilities, and since none of them constitutes genuine justification, the Trilemma concludes that justified knowledge is impossible.
The major epistemological traditions of the modern era have each responded by conceding one horn. Foundationalism accepts dogmatic stopping, identifying certain beliefs as properly basic and terminating the chain there. Coherentism accepts circularity, holding that beliefs are justified by mutual support within a web. Infinitism accepts the regress, arguing that an infinite chain of reasons is not inherently defective. Each of these frameworks treats one horn as a feature rather than a defect. None defeats the Trilemma. Each surrenders to it.
This paper solves the Agrippan Trilemma. The solution is not a trick, not a reframing, and not a claim that the problem is somehow misconceived. The Trilemma is a legitimate argument. Its conclusion follows from its premises. The solution is to show that one of its premises is false: specifically, that the third horn, dogmatic stopping, is built on an amphiboly that, once identified, breaks the horn entirely.
The amphiboly is this: the Trilemma treats “terminates” as equivalent to “terminates arbitrarily.” It assumes that any stopping point is an unjustified stopping point, that all termination is epistemically equal, that there is no distinction between stopping because you have run out of reasons and stopping because you have run out of unchecked dimensions. This conflation is not argued for in the Trilemma. It is assumed. And it is false.
The Triveritas demonstrates that it is false. The Triveritas holds that warranted assent requires the simultaneous satisfaction of three independently necessary conditions: logical validity (L), mathematical coherence (M), and empirical anchoring (E). Each dimension terminates at its own bedrock: L at logical axioms, M at mathematical axioms, E at observation. The Triveritas takes the third horn. It terminates. But it terminates at three independent stopping points of fundamentally different kinds, each constraining the others. The probability of all three stopping points being wrong in a way that produces a coherent false positive is strictly lower than the probability of any single stopping point being wrong. This is proved mathematically and confirmed empirically across twelve historical cases spanning four centuries and seven fields.
Checked termination is not dogmatic stopping. The third horn breaks.
So the print edition will consist of The Treatise and The Refutation of Kant, and includes the three following appendices:
- Solving the Agrippan Trilemma: Triveritas and the Third Horn
- The Sophistic Foundation of Reason: A Fundamental Flaw in Enlightenment Epistemology
- Kant Against Kant
It should be available in hardcover and paperback sometime next week. I already have plans for second, third, and possibly fourth volumes, but only the second is likely to be out this year. In the meantime, it should be interesting to see if anyone comes up with any substantive criticisms, or if, as with Probability Zero, no one will be able to do so.