Notes on Truth and Knowledge

Truth is just a label that we assign to propositions (deflationary theory). We can do this in any way we desire (we can conceive of truth in any way we desire), but some methods are more useful than others.

Most people accept that a very useful conception of truth is to divide propositions into analytic and synthetic, and to say that for analytic truths, a proposition is “true” if it can be derived from brute definitions and/or axioms and/or synthetic truths; and that for synthetic truths, a proposition is “true” if it corresponds with reality (correspondence theory). Some propositions aren’t neatly categorized until they are broken down into more atomic propositions or further explicated, because language is imperfect at latching onto clean propositional structure. Normative propositions are either not truth-apt or (mostly) analytic, I haven’t decided which yet. Leaning toward analytic due to Frege-Geach-type reasoning.

For example, the proposition “2+2=4” is analytic and derivable from Peano axioms. The proposition “all bachelors aren’t married” is analytic and derivable from the definition of a bachelor. The derivation process itself is theory-laden but also based on axioms of logic.

The proposition “all swans are white” is synthetic. It is true if all swans are, in fact, white. Can we know this without seeing all the swans in the world? No. Can we still assign a truth value to this proposition with limited information? Absolutely. As a side note, we can’t technically know with 100% certainty anything at all about the external world because of the limits of our perception and cognition, which blends nicely into these points.

We can perform this synthetic truth assignment in any way we desire, but some methods are more useful than others. For the swan conjecture, if all swans I’ve seen look white, I can make the conjecture that all swans are white. This is an inductive hypothesis. I then make the empirical prediction that the next swan I see will look white. The problem of induction disappears once one considers the concept of falsification. We assign the truth label to “all swans are white” and rest happy until we see a non-white swan, in which case we declare our original conjecture false and we can come up with a new conjecture.

The scientific method is basically an elaborate, sophisticated version of this assignment method. This is why we consider empirically unfalsifiable theories “unscientific” (or “pseudoscience” if they masquerade as scientific). The elaborate version does indeed work in Bayesian inference and probability and can use information-theoretic heuristics to come up with optimal strategies for developing robust inductive conjectures that are likely to stick around for a while. For example, if we were to assign “0” to white swans and “1” to non-white swans and graph this in R2 with “time” or “observation” on the horizontal axis, the MDL-optimal conjecture assuming all known data is white would be the line x2=0 which posits that all swans are white. We didn’t have to choose this conjecture; we could have modeled with a step function that would step up to 1 from now onward, but this is a worse conjecture according to MDL.

What if the synthetic proposition is unfalsifiable, like “God exists” or “consciousness is fundamental” or “the MWI is correct”? Then the scientific method does not apply, and we have to appeal to different truth assignment functions. This is the most contentious part of epistemology and there’s no great guide for what to do here. Some may reject pretty much all unfalsifiable synthetic propositions — I think this is technically a valid approach, but not very satisfying. It does away with pretty much the entirety of metaphysics and teleology. It also does away with much of history — the way we weave a thread of historical interpretation by connecting together bits and pieces of evidence/information is not a scientific endeavor unless we conceive of the possibility of uncovering new evidence, like through archaeology or something; without this in the historian’s consciousness, historical analysis primarily works with empirically unfalsifiable propositions.

It is also undeniable that the assigned truth values of unfalsifiable synthetic propositions do impact the world. They give us purpose and meaning in our lives. They establish virtues and ethics. They power communities, cultures, nations, ideologies, and historical zeitgeists. Some propositions are also clearly more truthful than others, and some are just self-evidently axiomatic and can be declared true by rote fiat (the external world exists, I exist, some conception of causality exists, etc). The axioms and definitions from which analytic truths are derived could perhaps be considered unfalsifiable synthetic propositions as well (law of identity, stability of language, non-contradiction, axioms of abstract systems of mathematics, suffering is bad, etc). Some of these might even be controversial, and that’s part of the point! We clearly argue over such things because their truth value is meaningful. I think a lot of positivist STEM types either refuse to acknowledge this, pretend science can somehow solve it, or treat it as unimportant, which I believe is a mistake as a physics/compsci student and former example of this archetype :)

So in my opinion, we must do our best to assign truth to synthetic propositions that are unfalsifiable from an empirical standpoint. A good start is logical consistency. The tensions inherent within an omnipresent, omnipotent, omniscient, and omnibenevolent God pose a challenge of logical consistency.

Another criterion is parsimony, and this comes down to raw pragmatism. If I say that we live in a matrix-like simulation, I’m not really offering any explanatory power and am needlessly complicating our view of reality as it wouldn’t matter. The simulation hypothesis worked well in fiction because it was possible to break out of it. In reality, it takes less mental effort to simply reject that premise and move on.

The God question is a bit different, because many religions will claim that we have access to the divine through the written word of God or through something like the Holy Spirit. While still unfalsifiable (discrepancies can be made to fit into the framework by appealing to the mysterious/mercurial nature of God), the truth of this is tremendously important and we can’t just reject it on grounds of parsimony. What we can do is constrain our conception of God — if I say that God is “male” (whatever that means), I can reject this particular proposition while maintaining all explanatory power of God, so I strip it from the “theory” i.e. the overall working conception at present. Polytheism to monotheism was in some sense an exercise in parsimony optimization as well.

Another metric that goes with explanatory power is brute fact presence. We want to reduce the number of brute facts, which I define to be true synthetic propositions that have no specified causal, structural, and/or teleological explanation (this has room for improvement, I know). The beginning of the universe and the values of fundamental physical constants are examples of what many point to as brute facts that are removed with the presence of God. Extremely high correspondence between mental and physical states is a brute fact (or quasi-infinite set of brute facts) under a naïve dualist disposition. Et cetera.

The proposition should further be abductively accurate — it should be consistent with what is already known. If I claim that millions of people died during a particular war many centuries ago, but only have records for several hundred, I’d better have a compelling reason for why my figure is so high when a lower value is an orders-of-magnitude closer fit to known evidence. If I claim that all that exists is physical, I better have a compelling reason for why the Hard Problem either isn’t a real/coherent problem or can be resolved in physical terms.

And finally, the proposition should be coherent. I’m not well-versed with coherence as it has been discussed in analytic philosophy, but my version of coherence judges propositions in part regarding how interpretable they are and how well they fit into existing frameworks to construct more cohesive wholes. I place some value in clarity, holism, and unity beyond mere optimization of the previous criteria. Right now I view it as kind of an aesthetic preference, I’ll admit, and it’s the one I have most trouble thinking about myself.

The ultimate purpose of all of these criteria regarding unfalsifiable synthetic propositions is to arrive at a cohesive conception of reality that makes sense. To that end, the relative importance of the various criteria might differ depending on the specific analysis involved (history, metaphysics, normative propositions, etc). But the key point is that all of these strategies apply to a separate category of propositions than the one covered by the scientific method/information theory.