An explanation of truth

True ideas are those that correspond to a standard. This standard could be a system of axioms, as in mathematics or logic, or it could be, and by default usually is, reality. Let’s look at some claims about the world, and then evaluate their truth. I’m going to look at five types of claim: definition claims, theoretical claims, empirical claims, moral claims and aesthetic claims. I’ll be using Hume’s fact-value distinction to classify them. This is not an exhaustive list; but it should still be insightful because I think it covers the major bases.

Matters of fact

Definition claims

A man is an adult male human

I got this example straight from Wiktionary, because it is a definition. Of course, we know that yes, a man is an adult male human; we as an English-language community define the concept of “man” that way. Definitions are always true — within the community that defines and uses the concept.

To understand how definitions work, a basic understanding of set theory is helpful. Definitions place a concept as either a subset or superset of other concepts. For example, the set “man” is a subset, or element, of the set of “adult male humans”.

Theoretical claims

Three plus five equals eight

This is an example of a mathematical statement, claim, or more formally, expression. We all know that 3 + 5 = 8 is obviously true. But why is it true? Well, as stated above, truth is all about correspondence with a standard. In mathematics, that standard is laid out by a set of axioms. From Wikipedia:

“An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.”

(For the specific case of addition, it’s worth looking at the page on Peano axioms, which discusses the assumptions you need to make before a statement like 3 + 5 = 8 becomes evaluable, let alone true).

In other words, axioms are assumptions, and act as building blocks, with which knowledge can be built using deductive reasoning.

Deductive reasoning is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion.

The “premises” described here are our assumptions. So we use logic to progress from our premises to a conclusion, and the important thing to note is that the truth of the conclusion is certain (that is, assuming no logical errors).


A classic example of deductive logical reasoning is the syllogism. For example;

  • All men are mortal.
  • Socrates is a man.
  • Therefore Socrates is mortal.

Premise + premise = conclusion. It’s just a case of thinking in terms of really basic set theory, as I’ve shown here visually.

Empirical claims

Wood contains carbon

Does it? This is what I’d call an empirical claim; to be judged by the methods of science. To evaluate it, we need to understand empirical evidence.

Empirical evidence is the knowledge or source of knowledge acquired by means of the senses, particularly by observation and experimentation.

The truth of an empirical claim, like all truth, relies on a standard with which to correspond. But what is that standard?

Well, for questions about the natural world, reality is the standard. That is, the sum total of everything that can be observed, in actuality or in principle. Which is why, when reasoning about the natural world, we rely on empirical (sense-based) evidence.

To restate this: if our understanding of the world matches our observations of the world, then that is evidence for our conceptual model. The greater the evidence, the more likely our hypothesis; our understanding; our model. There is a very important consequence of this methodology: due to the nature of inductive reasoning (reasoning from observations, not from axioms) there is no certainty in science; only degrees of certainty.

It is always possible for an existing scientific worldview to be overhauled by improbable and unexpected observations. We call these black swan events; just as the discovery of black swans in Australia shocked English naturalists, so any theory built upon empirical evidence can be overturned by new data.

While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument is probable, based upon the evidence given.

In this particular case we can confidently assert that wood almost certainly does contain carbon, based on various methods of analysis scientists have used to arrive at such a conclusion. But it is always possible (though diminishingly unlikely as we make more observations) that there are things we have not yet observed that could change the result.

So where does that leave mathematics and logic? Are they somehow not a part of reality? Here are two articles on the subject by the astrophysicist Coel Hellier:

The simple explanation is that in both of these systems, the axioms were intuitively chosen based on observations. The concepts of quantity, or of length, or of “therefore” are found in reality. If I have an apple, and then I get another apple, I now have two apples; hence the “rules” of addition (i.e. Peano’s axioms). Mathematics and logic are just a process of formalising those observations, and have proven to be immensely useful tools thereafter, due to the invariant nature of the patterns underlying reality.

Matters of value

Moral claims

One should not eat meat

This is an example of a moral claim. Throughout history, there have been many theories proposed — often by religions — to explain what it is that gives something moral truth, and if such a concept even exists, including deontological and normative, realist and anti-realist stances. Various “-isms”, including consequentialism, utilitarianism, universalism, humanism, nihilism, theism and many more mean that this subject can become confusing and daunting to those studying it for the first time, who, speaking from personal experience, just want to know an algorithmic answer to How and Why To Live Well and not a historical account of the failed attempts to answer that question.

However, the sheer number of competing theories already says something noteworthy: this is not a field of easy answers. People have been asking this question and disagreeing vehemently about the various proposed answers for centuries. Indeed, wars have been fought over these disagreements. That people could want to destroy those who disagree with their opinion points to a fundamental psychological need for a confidence in one’s role, aims, or purpose. People who hold differing views are therefore a threat to the righteousness of one’s own view.

My own opinion on evaluating moral claims is that when phrased in the abstract, as in this example, they are unanswerable. This is because there is no fundamental, observable “shouldness” to reality. They are two things: statements of personal opinion, and the results of our evolutionary heritage and survival instincts. I explore this topic in more depth in another blog post.

Aesthetic claims

Rachmaninov’s music is beautiful

Aesthetic claims are similar to moral claims in that there is no way to “prove” their truth. In this way they are not objective, but subjective statements of what we value. It might be true that I find Rachmaninov’s music beautiful, but there are many who don’t.

When people claim that “x is beautiful”, that should be interpreted as an opinion: “I think x is beautiful,” rather than a statement of fact. If somebody genuinely believes that their opinion on the aesthetic value of some piece of art, or landscape, or city is objectively true, they are probably deluded and possibly egotistical.

However, as with claims of moral value, there is a caveat to claims of aesthetic value: people actually do agree substantially on what is and isn’t beautiful. There is a form of aesthetic univeralism, which arises from the functional aspects of the item of interest. For example, a city with tree-lined avenues and a lively street culture is somewhat more functional as a city – there will be less sunburn and more social activity – than a congested, barren concrete jungle; and will often be perceived as more beautiful. Similarly, I know that I often perceive highly intelligent people as somewhat more “beautiful” than their peers. This prejudice is a result of the way I value critical thinking and intellectual engagement: prejudices are rooted in peoples’ values, such is our nature.

So, to the extent that people actually agree on what is desirable and what is disgusting, that is often a direct result of whether or not they share core values.


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