Category Archives: Foundations

On Valuing Truth

Following on from my ninth axiom, I wanted to make two brief points about what I mean by valuing truth:

  • I value absolute truth, although it might be slightly more accurate to say that I value strong and weak knowledge of the truth.
  • I implicitly value consistency, since reality (absolute truth) is consistent (axiom 3).

 

 

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The Ninth Axiom

At the very beginning of this blog, I laid out a set of eight axioms with which I was to derive my philosophy. Since they were spread out across several posts, I will collect them here for convenience:

Axiom 1: Axioms are valid starting points.

Axiom 2: The fewer axioms you need, the better.

Axiom 3: There is some underlying consistent reality that is made up of things.

Axiom 4: I (or the thing that I think of as “me”) exist in some form in that reality.

Axiom 5: Things in reality interact, forming temporal and causal relationships.

Axiom 6: My senses provide me with information that is functionally determined by the underlying reality.

Axiom 7: My memory is usually a reliable and valid guide to my past experiences.

Axiom 8: Logic is a valid form of reasoning.

Although I would probably word them differently now, and there are certainly quibbles to be had, I still think the general intent of these eight form a solid foundation for truth-seeking and philosophy.

However, they are incomplete in terms of actually determining how to live your life. I sort of already came to this conclusion in my previous post based on the Charles Taylor essay, but I want to draw some more explicit conclusions from that:

  • My core eight axioms provide sufficient grounding for determining reality and truth, but not for values or decisions.
  • I currently live my life by a so-far-unexpressed set of values which includes truth, consistency, and something akin to secular-humanist values (though that needs much more elaboration).
  • Arguing one set of value axioms over another is impossible as long as they are all reasonably simple and compatible with the core eight.
  • Adhering rigidly to any single declarable value seems to be a recipe for disaster.

With all that said, I present my ninth axiom:

Axiom 9: I value truth and beauty, not necessarily in that order.

The wonderful thing about “beauty” is that it is deliberately vague. Music can be beautiful and I value that. Human life is beautiful, and I do value that. There is beauty in some efficiencies, and I value that. Truth, though sometimes harsh, is always beautiful. The right lie may also be considered beautiful.

The beauty of beauty is its pragmatism. Plus, who can resist the implicit quark-naming joke?

The Scientific Method

All of this wandering around thinking about rationality, empiricism, truth and knowledge now finally culminates in the scientific method. This is, of course, not the be-all and end-all of truth or knowledge, but it is one of the most useful tools we have for probabilistically determining the shape of reality.

If you’re not familiar with the scientific method (really?) it goes something like this:

  1. Have a question.
  2. Take a guess.
  3. Find something that your guess predicts.
  4. Measure it.
  5. If your measurement doesn’t match your predication, go back to 2. If it does match your prediction, go back to 3.

You will note, of course, that the scientific method never stops. It is an endless loop of trying out new ideas and finding ways to verify or disprove them. Every successfully predicted measurement is another step on the way towards statistical certainty, but of course like any empirical practice we can never get all the way there.

It is also relatively important that your guess (step 2) must be capable of making predictions (step 3). Every so often someone will claim to have solved a great complicated scientific problem by the means of some mysterious new substance. When asked about this substance, they are incapable of predicting its properties other than that it makes their theory magically work. These ideas do not fit in the scientific method – if it doesn’t generate predictions, it’s not science.

Truth and Knowledge

Truth

While empiricism gives us some probabilistic, mediated access to reality, our senses are frequently consistent with each other. However, we have no way of knowing if this input represents what is or simply some high-level abstract interpretation of a transformed version of what is. Both of these could be called “true” however in normal speech, so I will borrow the Buddhist doctrine of Two Truths. In very brief summary:

Absolute Truth: The underlying reality of what is.

Relative Truth: What we consistently and reliably interpret of what we sense.

Absolute truth might, for example, be nothing more than atoms interacting according to physical laws. Regardless, it is exactly the reality accepted in axiom #3. Relative truth is the world that we construct from empiricism, with tables and chairs and clouds and cats and dogs. Even if, fundamentally, there is nothing that is a dog in the underlying reality, the existence of dogs is still a relative truth, a practical concept useful for navigating the world.

Knowledge

The definition of knowledge is another big problem in philosophy, and is more-or-less the defining question of epistemology. Based on our axioms so far and the previous two posts, I use the following three definitions of knowledge:

True Knowledge: This is the definition of knowledge that pedants like to trot out when arguing for epistemic scepticism. “True” knowledge is knowledge of absolute truth (see above) which is impossible because of the circular trap. We have no way of knowing that the axioms we have taken are correct, thus no way of knowing anything else which we might derive from them. However, this meaning is almost never used in non-philosophical debate.

Strong Knowledge: Strong knowledge is knowledge based on “inviolate empiricism”; facts like gravity1 that consistent across a truly enormous number of observations (all relative truths, of course). Logical derivations from axioms (and from inviolate empiricism) also qualifies of course: knowledge of algebra is strong knowledge. This usage occurs outside of philosophy debates, but mostly in scientific and other formal contexts.

Weak Knowledge: Weak knowledge is knowledge based on probabilistic empiricism. It is reasonable, for example, for me to say that I “know” certain things about Shakespeare, but the chain of actual facts and observations between myself and him is quite long and tenuous. Nonetheless, I say I know these facts because they are still far and away the most probable explanation of all the various things I have experienced. This is the most common usage of knowledge in informal conversation.

(1) Yes, I know, quantum theory and relativity etc etc. What goes up must still come down.

Empiricism and Probability

We have a set of tools now for operating on truths, but we lack the raw materials to operate on. Fortunately there is another common epistemic view.

Empiricism is the view that knowledge of reality comes from the senses. As I mentioned in my brief discussion of axiom #6, we are not assuming quite this much, though we are taking at least a partially empirical view. Our senses provide some sort of access to reality, although that access may be mediated, transformed, inconsistent, etc. Due to this caveat, we cannot simply make knowledge-claims based on our senses: “I see _ therefore I know that _.” could be perfectly wrong.

However, we can say “I see _ therefore I know that something in reality is causing me to see _”. This is somewhat more accurate though less useful. More importantly, we can appeal to the consistency of reality (axiom #3), the partial consistency of memory (axiom #7), and the validity of logic (axiom #8) to make probabilistic empirical claims, such as the following:

I see _, and I have many memories of seeing the same _, therefore it is probable that I will continue to see _.

Of course sight is not the only possible sense here; one can make similar claims using hearing, smell, touch, etc. By adding an appeal to causality (axiom #5) one can also make probabilistic claims about correlation:

I see X and have a memory of just seeing Y. I have many memories of seeing X shortly after seeing Y, and no memories of not seeing X after seeing Y. Therefore it is probable that if I again see Y, I will shortly see X.

(I use X and Y instead of _ above because I have two blanks to fill in that I wish to distinguish between). Just like any probabilistic claim, the more samples you have (in this case memories) the stronger the claim.

It is these probabilistic claims that we can use as raw materials, feeding them into our rational tools to produce an understanding of reality. Of course we cannot use this to achieve whatever constitutes “real” truth with any certainty, but strong probabilities are better than nothing. With rationalism and empiricism in hand we will use the next post to delve more deeply into the concepts of truth and knowledge.

Rationalism and Certainty

The question of what constitutes or defines knowledge is another big problem in philosophy, and on its own forms what is called epistemology. I leave aside (for now) the central epistemic questions in order to discuss certain common perspectives; I will return to the broader questions in a few days.

Rationalism is, loosely defined, the view that knowledge and truth come from reason, logic, etc. By taking axiom #8 we are inherently taking what is at least a partly rational view, although there is somewhat more to it than that. However, on its own this axiom gives us a whole slew of tools in the category of what I shall call “logical systems”. These include propositional and predicate logic, algebra, set theory, probability and all the other systems that are strictly abstract (despite possible practical applications).

The critical point is that these systems are only tools. While they do produce internal “truths” (such as the statement that two plus two is four), all of these internal truths are at root truths by definition. Even the weirder, hard-to-prove theorems do eventually fall out of starting definitions; that’s how we define a proof. More interestingly, these tools give us methods of “lossless” operation on existing truths. The logical form of modus ponens takes two truths and produces a third truth of the same strength; no certainty is lost in the deduction.

These tools are extremely powerful, but like all tools they are useless on their own; they require raw materials to operate on. There are perhaps certain interesting facts that can be derived from our core set of eight axioms, but I would be very surprised if you could get very far (I have not even bothered to try). Instead, we need some other system to generate facts for us to operate on. Next time I will look at where we can get raw materials to feed our rational tools.

Building Reality, Part Two: The Mind

Five axioms down, three to go. I’ve titled these three “The Mind” because they’re more to do with that kind of concept, but I don’t mean to imply that the mind is necessarily distinct from metaphysics (which was the title I gave the previous three axioms). As I mentioned in the discussion of axiom #4, that’s not true by definition.

Axiom 6: My senses provide me with information that is functionally determined by the underlying reality.

Reliability of the senses is a big question in empiricism, philosophy of science, etc. This axiom doesn’t go quite that far; all it gives us is the fact that our senses are somehow determined by the underlying reality. Maybe we only have access to a subset of reality, or maybe there’s some random transform in place between reality and what we sense. Regardless, we have some sort of access, however mediated or probabilistic.

Axiom 7: My memory is usually a reliable and valid guide to my past experiences.

Reliability of memory is another big question in a lot of disciplines, and there are obviously cases where it doesn’t hold. Amnesia and memory implantation both seem to be real phenomena after all. As with reliability of the senses, I’ve chosen to split the difference. We assume our memory is usually reliable, for some definition of “usually”.

Axiom 8: Logic is a valid form of reasoning.

This one is kind of cheating since I’m explicitly leaving the definition of “logic” so vague. I am intending it here to include forms such as propositional and predicate logic, and all the other weird mental constructs without which it’s hard to make sense of things like mathematics. Perhaps this would be better phrased as something more to do with thought processes in general than pure logic. Hmm…

Regardless, we now have our eight core axioms from which we can start to build up an understanding of the world. I expect to revisit these occasionally as I think up better wordings, or discover missing concepts, but as per axiom #2 I hope not to add to them unless absolutely necessary. Let’s at least see how far we get with just these eight!