An Introduction to Philosophical Thinking, Part II

Content notes: This series is intentionally opinionated and exploratory in nature. It is not intended as an academic treatment of philosophy, nor as a rigorous defence of particular positions. Instead, it serves as an accessible introduction to a handful of philosophical ideas and ways of thinking, aimed at casual readers who are curious about philosophy but may not wish to engage with formal proofs, technical debates, or scholarly conventions.

In Part I, we outlined the goals of this series and briefly discussed what philosophy is, from a deliberately opinionated standpoint.

To recap, we argued that philosophy is useful in our day-to-day lives because it offers tools for examining how conclusions are reached, how assumptions enter our thinking, and how certain patterns of reasoning quietly shape our decisions.

In other words, philosophy teaches us how to identify the structure of an argument: what is being assumed and where a conclusion actually comes from.

I also used an analogy, comparing a mode of thinking we should avoid to “read-only” electronic components, to highlight the importance of how we think and reason, as opposed to merely what we already know.

In a similar vein, Aristotle argued that emotional discipline is necessary for rational debate, noting that “someone whose life follows his feelings would not listen to an argument turning him away or even understand it.”

In this text, we compare mathematics and science as preparation for comparing philosophy to both in Part III. This should help clarify what philosophy is and how one might think like a philosopher. Before doing so, however, we need to clarify two concepts.

The first is the meaning of Epistemology in the context of this series, and the second is the difference between Epistemic Truth and Pragmatic Utility.

Epistemology

Epistemology is a world of its own, covering many schools of thought and centuries of debate. For the purposes of this series, however, we will adopt a deliberately simplified view in service of our broader goal: learning how to think like a philosopher.

In order to do that I would suggest simplifying Epistemology to three questions:

1. What do we know?
2. How do we know what we know?
3. How reliable is what we know?

I would also suggest we follow an Sceptic’s^[1] point-of-view when thinking about epistemology as in my opinion it is the most useful outlook for our purposes here. We will adopt what is known as methodological scepticism, a stance most famously associated with René Descartes and his claim, “I think, therefore I am.”^[2]

As we will see, these three questions also challenge us on what can we know and perhaps force us to think more deeply about the nature of knowledge itself.

Truth and Utility

Rather unsurprisingly, these two topics are also more complex than we can tackle in a relatively short essay. In order to advance our series, I suggest we make the following simplifications by treating them as two distinct questions:

Epistemic Truth: Is the claim true in a fundamental sense—independent of context or usefulness?

Pragmatic Utility: Does the claim reliably work for practical purposes when applied or tested?

Consider the claim: “Ocean tides are primarily caused by the Moon.”

In principle, one could try to establish this as an epistemic truth by imagining a decisive test: removing the Moon, or altering its course or speed, and observing the resulting changes in Earth’s tides. If the effects matched our expectations, the claim would seem epistemically secure.^[3]

In practice, however, the strength of this claim lies less in such hypothetical tests and more in its pragmatic reliability. We can repeatedly observe how the Moon’s position correlates with tidal behaviour, measure these effects with high precision, and integrate them into a broader framework of physical theory. The claim works—it allows us to predict and explain phenomena consistently.

Seen from this perspective, philosophical scepticism exposes a useful contrast. A sceptic might argue that it is impossible to prove, in an absolute sense, that the Sun we see and benefit from truly exists. Epistemically, this may be correct. Yet this uncertainty has little practical consequence: the Sun behaves with remarkable consistency within our experience, and we organise vast parts of daily life around that reliability.

This tension between what can be known with certainty and what is trusted because it works points toward a broader distinction—one that becomes clearer when we briefly examine mathematics and science, both of which play a central role in how philosophy approaches knowledge.

Mathematics and Science

Mathematics and science operate in fundamentally different epistemic modes. In mathematics, proof is absolute and universal, meaning it must account for every possible case defined by a statement. Demonstrating that a concept works for one or even many examples does not constitute a formal proof.

If we were to accept a mathematical argument that is not universal, we would fall into what is known as proof by example, which is invalid.^[4] In mathematics, evidence is not the same as proof.

Equally, once proven, the statement is true forever, unless the axioms themselves change. It would be logical, then, to claim that maths aims at certainty.

In science, however, theories are not proven in the mathematical sense. In fact, scientific theories are never proven—they are corroborated.

More than anything else, a scientific theory must be falsifiable, meaning it must make predictions that could be shown false.

Before Karl Popper introduced the idea of falsifiability in the 1930s as an explicit condition of a scientific theory, science was usually associated with verification and confirmation. This meant testing hypotheses and rejecting theories when they failed, so falsification was an implicit practice, not a formal rule.

Employing Popper’s idea, we can assume two useful statements:
A) A theory that cannot be falsified is not scientific, even if it sounds plausible.
B) A theory that cannot be disproved is not meaningful scientifically.

Although these two statements appear similar, they are neither identical nor contradictory. Let us unpack them.

Statement A tells us what could be counted as science.^[5] It sets the boundaries of what can be considered scientific and what cannot be. In other words: what distinguishes science from non-science?

Here, “not scientific” means it does not belong to the scientific method; thus, it should not be evaluated using scientific standards. Crucially, “not scientific” does not mean false, useless, or irrational.

Take the following statement as an example: “The universe exists to teach us moral lessons.”

This statement is not scientific because it is not falsifiable. No one can prove or disprove it unless, for example, a creator of the universe were to demonstrate that this was indeed its purpose.

Note that the claim is not “We can learn moral lessons from the universe.” Rather, it claims that the universe exists for that single purpose.

In this example, whilst this statement is not scientific per se, it could be considered within the realms of philosophy, metaphysics, or theology. Being non-scientific does not inherently mean a claim is false.

Whilst Statement A is about classification and the question of what belongs to science, Statement B is about the usefulness of a claim or what science can do with it.^[6]

Here, “not meaningful scientifically” means that a claim cannot be tested; therefore, it cannot be challenged, improved, or eliminated. Consequently, it cannot participate in scientific progress, as no observation can count for or against it.

So, even if it sounds like it explains something, it fails to be useful in scientific terms—or, in Popper’s words criticising certain theories: “They explain everything and therefore explain nothing.”

Another example could help us here. Consider this statement: “An invisible, undetectable force guides every human decision.”

This statement is not falsifiable; therefore, it is not scientific. It is also not meaningfully scientific because no observation could ever disprove it: it is an invisible force that is also undetectable. So, in the scientific world, this statement is totally useless as it cannot be challenged, redefined, or corrected.

However, this doesn’t mean it is meaningless. This statement could be considered in fields like theology, as they do not rely on scientific methods.

All of this is to say that science aims at the best explanation so far, under the constant threat of revision.

But why wouldn’t science seek universal truth like in maths?

The answer is that maths is a man-made construct, whilst science needs to explain the universe—which is rather unlikely to be man-made. Like anything else, this distinction between maths and science is a contested topic, but for our purposes here, I would like to give you a few examples to make this more clear.

Consider this simple equation: 2 - 5 = -3

Do you agree with it? Now, let me ask you a question: Suppose you have two apples and I take five of them. How many apples do you have?

The answer is that I can’t. There is no way that I can take five apples if you only have two. Maybe I can come back and take another three later, but that action simply cannot be completed in the real world. Mathematics allows negative numbers because it operates within an abstract system governed by defined rules, not physical constraints.

The reason we can have universal proofs in maths but not science is that we wrote the rules for maths. We can prove three is a prime number, not because we have divine knowledge, but because we defined what a prime number is—and we defined it exactly in a way that would describe numbers like three.

In philosophy, this is often described as the distinction between a priori knowledge—typically associated with mathematics and logic—and a posteriori knowledge, which characterises empirical sciences. As with much of philosophy, this distinction itself is debated, but it serves as a useful lens here.

In Part III, we will contrast philosophy with both mathematics and science.

Footnotes

1. Skepticism in American English. ↩︎

2. René Descartes-1637. Originally “je pense, donc je suis” in French. Later on “Cogito, ergo sum” in Latin. ↩︎

3. This is an example of Interventionism or Manipulationism. The underlying idea is “X causes Y if intervening on X changes Y, whilst holding other factors fixed.” ↩︎

4. Also known by its technical name Enumerative Induction. ↩︎

5. A demarcation claim. ↩︎

6. An epistemic claim. ↩︎