Q
Question
Identify the philosophical problem precisely — and see why it matters

If someone told you they had an argument with a friend, you would picture raised voices, frustration, perhaps a slammed door. When someone tells you they have an argument for a position, you picture something else entirely — a set of reasons, a case being made, a chain of thought leading somewhere. These are not the same thing, and philosophy is only interested in the second.

But what exactly makes a chain of thought into an argument, in the philosophical sense? Why do some collections of sentences qualify and others do not? And why does the distinction matter so much that it is the very first thing a philosophy student needs to learn?

What is an argument — in the precise, technical sense that makes it the primary tool of philosophical inquiry?

This is not a trivial question. Philosophy is sometimes described as the discipline of asking questions. That is half right. Philosophy is the discipline of asking questions and then giving and evaluating arguments in response to them. Arguments are how philosophy makes progress — or at least, how it tries to. A philosophical claim without an argument behind it is not philosophy; it is opinion. A philosophical argument that has never been examined for weaknesses is not good philosophy; it is dogma.

The distinction between arguments and non-arguments — and the skill of identifying which is which — is foundational. Every other article in this package builds on it. Article A2 on deductive and inductive reasoning assumes you can already recognise an argument. Article A3 on validity and soundness assumes you can identify premises and conclusions. Article A4 on fallacies assumes you understand what a well-formed argument looks like — so you can recognise when one goes wrong.

Before any of that, you need this. Let us begin.

U
Unpack
Map the key concepts, distinctions, and vocabulary needed to engage with arguments philosophically

Arguments are not disagreements

The word "argument" in ordinary English usually refers to a dispute — a heated exchange between people who disagree. Philosophical usage is entirely different. In philosophy, an argument is a structured set of statements in which some statements — called premises — are offered as reasons for accepting another statement — called the conclusion. There is no requirement for disagreement, dispute, or even two people. A single person working through a problem in their notebook is doing philosophy when they construct an argument.

This technical meaning is not arbitrary. It captures something important: an argument is an attempt to provide rational support for a claim. The premises are meant to give you a reason to believe the conclusion. If they succeed, you have a good argument. If they fail, you have a bad one — but it is still an argument. The key thing is the attempted rational connection between premises and conclusion.

What arguments are made of: propositions

Arguments are made of propositions. A proposition is a statement that is either true or false. "The Earth orbits the Sun" is a proposition. "Killing for pleasure is wrong" is a proposition. "Paris" is not a proposition — it is just a name. "Close the window" is not a proposition — it is a command. "Is it raining?" is not a proposition — it is a question.

This matters because only propositions can function as premises or conclusions in an argument. An argument can only work by presenting truth-apt claims and asserting that some of them support others. Commands and questions cannot play that role.

P
Proposition
A statement capable of being true or false. Propositions are the building blocks of arguments. "The cat is on the mat" is a proposition. "Sit down!" and "Is it cold?" are not. In formal logic, propositions are often represented by letters: P, Q, R.

The structure of an argument

Every argument has at least two parts: one or more premises and a conclusion. The premises are the reasons given. The conclusion is the claim that those reasons are supposed to support. The relationship between them is called an inference: the argument asks you to infer, or conclude, the conclusion from the premises.

Here is the simplest possible argument — one that has been used in philosophy classrooms for two and a half thousand years:

Argument in Standard Form — A Classic Syllogism Deductive
P1 All humans are mortal.
P2 Socrates is a human.
∴ C Therefore, Socrates is mortal.
The symbol ∴ means "therefore" — it marks the conclusion. Notice that the conclusion does not just repeat the premises; it follows from them. If P1 and P2 are both true, the conclusion must also be true.

This argument has two premises (P1 and P2) and one conclusion (C). The premises provide a reason for the conclusion. If you accept that all humans are mortal, and you accept that Socrates is human, you are committed — by logic alone — to accepting that Socrates is mortal. You cannot coherently accept both premises and deny the conclusion.

Assertions, explanations, and arguments: the crucial distinctions

One of the most common mistakes beginning philosophy students make is treating every passage of reasoning as an argument. Not every passage is. There are three things that are often confused:

An assertion is simply a claim made without any supporting reasons. "God exists" is an assertion. "Euthanasia is wrong" is an assertion. Assertions can be true or false, but they are not arguments — there is no support offered, no inference from premises to conclusion. In philosophy, bare assertions carry no weight. You can assert any position you like; what matters is whether you can argue for it.

An explanation offers reasons, but those reasons explain why something happened rather than establishing that it is true. "The window broke because a stone was thrown at it" is an explanation. Both speaker and listener already accept that the window broke; the explanation accounts for it. An argument, by contrast, attempts to convince someone that the conclusion is true — or at least, gives them reasons to accept it.

An argument offers propositions as reasons to believe a conclusion. The conclusion is the claim the argument is trying to establish. The premises are the evidence or reasoning offered in its support.

Indicator words: how to find premises and conclusions

In practice, philosophical passages are rarely laid out in the tidy P1/P2/∴C format shown above. Arguments are embedded in prose, mixed with descriptions, qualifications, and examples. Learning to identify them requires knowing what to look for. Philosophers and logicians call these indicator words.

Conclusion indicators signal that what follows is a conclusion: therefore, thus, hence, so, it follows that, we can conclude that, consequently, which shows that, this proves that. When you see these words, the statement they introduce is almost certainly the conclusion of an argument.

Premise indicators signal that what follows is a reason being offered for something: because, since, for, given that, as, the reason is that, this is supported by, after all, in view of the fact that. When you see these words, the statement they introduce is almost certainly a premise.

E
Examine
Analyse arguments from the philosophical tradition — and practise identifying what is and is not an argument

Aristotle and the invention of logic

The formal study of arguments — what we now call logic — begins with Aristotle in the fourth century BCE. Aristotle noticed something remarkable: there are forms of argument that are guaranteed to produce true conclusions, provided the premises are true. The argument about Socrates above is one of them. The specific form — "all A are B; x is an A; therefore x is a B" — is called a syllogism.

What Aristotle grasped is that the guarantee of the Socrates argument comes not from the specific content — not from Socrates, or humans, or mortality — but from the form of the argument. You can substitute any terms you like and the argument will still work, as long as the form is preserved. This insight was the beginning of formal logic, and it remains central to philosophy today.

AR
Philosopher
Aristotle
384–322 BCE
Founder of formal logic  ·  Metaphysics  ·  Ethics  ·  Political philosophy
Aristotle's logical works — collected under the title Organon ("instrument") — represent the first systematic attempt to identify the conditions under which an argument is guaranteed to preserve truth from premises to conclusion. His theory of the syllogism dominated Western logic for two millennia. More fundamentally, Aristotle established the idea that good reasoning has a structure — that there are rules of inference that apply independently of content.
Relevant works: Prior Analytics (formal syllogistic logic); Posterior Analytics (the logic of scientific demonstration); Topics (dialectical reasoning). For senior secondary students, the clearest entry point is a good introduction to Aristotelian syllogisms before approaching the primary texts.

Descartes' cogito: an argument hiding in a sentence

One of the most famous sentences in the history of philosophy is René Descartes' "I think, therefore I am" — in Latin, cogito ergo sum. Generations of students encounter it and treat it as a profound, self-evident insight. But look more carefully: therefore is a conclusion indicator. The cogito is an argument. Its premise is "I think." Its conclusion is "I am" — I exist.

When we lay it out in standard form, the hidden structure becomes visible:

Descartes' Cogito — Reconstructed Deductive
P1 I am thinking (this very moment).
P2 [Implied] Whatever is thinking must exist.
∴ C Therefore, I exist.
Notice P2 is in brackets — it is a hidden premise. Descartes does not state it explicitly; it is assumed. These implicit premises are called enthymemes. Identifying them is one of the most important skills in philosophical argument analysis.

Seeing the cogito as an argument rather than a slogan opens it to scrutiny. Now we can ask: is the inference valid? Are the premises true? Does the argument actually establish what Descartes thinks it establishes — that there is an "I" doing the thinking, rather than merely that thinking is occurring? The philosopher Georg Lichtenberg raised exactly this objection in the eighteenth century, suggesting the most the argument proves is not "I think" but "there is thinking going on." Reconstructing the argument in standard form is what makes that objection visible.

Does this passage contain an argument? A worked example

One of the most practically important skills in philosophy is recognising whether a passage actually contains an argument — or whether it is an assertion, an explanation, or something else entirely. Here is a passage for analysis:

Passage for Analysis
"The death penalty is a cruel and unusual punishment and therefore should be abolished. Capital punishment brutalises the state by making it a killer, and it has not been shown to deter crime any more effectively than imprisonment."
Is there an argument here?
Yes. The word "therefore" is a conclusion indicator. The passage is not merely asserting that capital punishment should be abolished — it is offering reasons for that conclusion.
What is the conclusion?
The death penalty should be abolished. This is the claim the passage is trying to establish.
What are the premises?
P1: The death penalty is a cruel and unusual punishment. P2: It brutalises the state. P3: It does not deter crime more effectively than imprisonment.
What questions does this raise?
Is P1 true by definition, or does it need argument? Does P3 follow even if P2 and P1 are granted? Are there hidden premises? Does the argument actually entail the conclusion — or only make it more plausible?

Notice what happens when we lay the argument out this way: it becomes possible to evaluate it. We can agree or disagree with individual premises. We can ask whether the conclusion really follows from the premises stated. We can ask what is being assumed but not said. This is what philosophical analysis of arguments looks like — and it all begins with recognising the structure.

The hidden premise: the enthymeme

One of the most important and most common features of arguments in the wild is the enthymeme: an argument in which one or more premises are left unstated because they are assumed to be obvious. The Descartes example above has an enthymeme. The capital punishment passage arguably has one too: embedded in the argument is the unstated premise that the state should not brutalise itself — a normative claim that the argument assumes without defending.

Identifying enthymemes is philosophically important for two reasons. First, hidden premises are often where the real philosophical weight of an argument lies — making them explicit reveals what the argument is actually committed to. Second, unstated premises are often more controversial than stated ones; they may be the weakest point of the argument, and they are easy to miss precisely because they are not on the page.

S
Synthesise
Master argument reconstruction — the core skill of philosophical analysis

The most important practical skill in this entire package is argument reconstruction: taking a philosophical passage — a paragraph from Plato, a sentence from Kant, a paragraph of contemporary ethical argument — and laying it out in the clear P1/P2/∴C format you have seen in this article. This is the skill your examinations will test. It is also the skill that actually changes how you read.

Argument reconstruction is harder than it looks, for several reasons. Philosophical prose does not announce "here comes an argument." Premises are scattered through paragraphs. Conclusions sometimes appear before premises. Hidden premises lurk unstated. Authors use rhetorical language that sounds like an argument but may not be one. The method below will guide you through this process systematically.

Five Steps for Reconstructing a Philosophical Argument
1
Find the conclusion first
Always start with the conclusion, never the premises. Ask: what is this passage ultimately trying to get you to accept or believe? Look for conclusion indicators (therefore, thus, hence, so, it follows that). The conclusion is the target; the premises are the path to it.
2
Identify the stated premises
Once you have the conclusion, ask: what reasons are being given for it? Look for premise indicators (because, since, given that, in view of the fact that). List each reason as a separate, numbered premise.
3
Uncover hidden premises
Ask whether the stated premises actually entail the conclusion, or whether there are gaps. If the argument does not quite work as stated, there is likely a hidden premise filling the gap. Make it explicit. Ask: what would have to be true for these premises to produce this conclusion?
4
Write it in standard form
Write each premise on a separate numbered line (P1, P2, P3…). Draw a line. Write the conclusion below, preceded by ∴. Each statement should be a single, clear proposition — no compound sentences, no ambiguities if you can help it.
5
Check the structure
Read the reconstruction aloud. Does it sound like the original argument? Does the conclusion follow from the premises? Have you been fair to the original author — neither overstating their claims nor understating them? Reconstruction should be charitable: give the argument its best possible form before evaluating it.

Practise: Plato's argument from opposites

Here is a passage adapted from Plato's dialogue Phaedo, in which Socrates argues for the immortality of the soul on the day of his execution. Your task is to apply the five steps above before reading the reconstruction that follows.

Primary text — Adapted from Plato, Phaedo (c. 360 BCE)
"Consider: do not all things which have an opposite come to be from their opposite? The living, for instance, come from the dead, and the dead from the living. Sleep and waking are opposites — and we pass from sleep to waking and back. If all things come to be from their opposites, then death too must give way to life. Therefore, the souls of the dead must exist somewhere, since it is from them that the living come."
Conclusion
The souls of the dead must exist somewhere — i.e., the soul survives death.
Premise indicators
"since it is from them" is a premise indicator for the last sentence. "Consider" signals that supporting reasons are coming.
Stated premises
P1: All things that have an opposite come to be from their opposite. P2: Life and death are opposites. P3: The living come from the dead (as the dead come from the living).
Hidden premise
If the living come from the dead, the souls of the dead must exist in some form in order to generate new life — i.e., existence between death and rebirth is assumed.
Plato's Argument from Opposites — Reconstructed Deductive
P1 All things with an opposite come to be from their opposite — hot from cold, sleeping from waking.
P2 Life and death are opposites of one another.
P3 The living come to be from the dead (as the dead come from the living).
P4 [hidden] For the living to come from the dead, something of the dead must persist between death and rebirth.
∴ C Therefore, the souls of the dead exist somewhere — the soul survives death.
Now that you have the argument in standard form, you can ask: is P1 true? Does the analogy with sleep and waking actually hold for death? Does P4 follow? Is P3 an empirical claim — and if so, how would Plato support it? The reconstruction has not told you whether the argument is good — that is the task of Articles A2 and A3 — but it has made it possible to find out.

Notice what the reconstruction reveals. Plato's argument depends on an analogy — that death and rebirth are like sleep and waking. Once you see that, you can ask whether the analogy is a strong one. Sleep and waking are reversible processes for a single continuous organism. Death followed by rebirth, if it occurs at all, may be an entirely different kind of process. The hidden premise P4 does a great deal of work — and it is precisely the premise that needs the most support. You would never have seen this if you had not reconstructed the argument.

T
Transfer
Apply the concept of argument to new contexts — and see why it matters beyond philosophy

Arguments everywhere — and why recognising them matters

The concept of argument you have learned in this article is not confined to philosophy seminars. Arguments — in the precise sense — appear wherever human reasoning appears: in courtrooms, in scientific papers, in newspaper opinion columns, in political speeches, in your own thinking when you try to decide what to believe.

In a courtroom, a barrister does not simply assert that their client is innocent. They construct an argument: premises drawn from evidence, testimony, and law, leading to the conclusion that guilt has not been established beyond reasonable doubt. The legal standard of proof is, at its core, a demand for a well-constructed argument — one whose premises are reliable enough to warrant a conclusion of such consequence.

In science, a research paper's Results section contains data; its Discussion section contains an argument — from the data, to conclusions about what the data shows. The philosopher of science Karl Popper argued that what distinguishes science from non-science is the logical structure of its arguments: good scientific arguments are constructed in such a way that they could, in principle, be shown to be wrong. This is the concept of falsifiability, and it depends entirely on understanding what an argument is and how it works. (We return to this in Package I: Philosophy of Science.)

The IB Theory of Knowledge connection

If you are studying IB Theory of Knowledge, you will recognise that the concept of argument connects directly to some of TOK's central questions. What counts as a "knowledge claim"? What is the difference between claiming to know something and merely believing it? How do we evaluate competing claims in different Areas of Knowledge?

The answer, in every case, involves argument. A knowledge claim in history is one supported by historical argument from evidence. A knowledge claim in science is one supported by experimental argument from data. A knowledge claim in ethics is one supported by philosophical argument from moral principles. The concept of argument — premises, conclusions, valid inference — is the thread that connects all of TOK's Areas of Knowledge to one another. The better you understand argument, the better equipped you are for TOK.

Bertrand Russell on philosophical method

BR
Philosopher
Bertrand Russell
1872–1970
Mathematical logic  ·  Epistemology  ·  Political philosophy
Russell, who co-authored Principia Mathematica with Alfred North Whitehead and transformed the foundations of mathematical logic, argued that the great contribution of logical analysis to philosophy was precisely the ability to reveal the hidden structure of arguments — including arguments that looked plausible but concealed contradictions, or arguments that looked weak but concealed genuine insight. Russell believed that most philosophical disputes persisted not because the questions were unanswerable, but because philosophers had failed to analyse the arguments precisely enough.
"Philosophy, if it cannot answer so many questions as we could wish, has at least the power of asking questions which increase the interest of the world, and show the strangeness and wonder lying just below the surface even in the commonest things of daily life." — The Problems of Philosophy (1912)

Connecting to the rest of Package A

You have now established the foundation: you know what an argument is, how to identify its parts, and how to reconstruct arguments from philosophical prose. Everything that follows in this package depends on this foundation.

In Article A2, you will ask a new and harder question: not what an argument is, but what makes one good. The first great distinction you will encounter is between deductive arguments — where the conclusion is guaranteed by the premises — and inductive arguments — where the premises provide support but not certainty. These are two fundamentally different ways of drawing conclusions, with different strengths and different vulnerabilities. Much of the most important philosophy of the last four hundred years turns on understanding the difference.

In Article A3, you will learn the three concepts that allow you to evaluate any argument: validity (does the conclusion follow from the premises?), soundness (are the premises actually true, as well as the argument being valid?), and cogency (for inductive arguments). Together, A1, A2, and A3 give you a complete toolkit for philosophical argument analysis — the same toolkit that professional philosophers use.

The question to carry with you into Article A2
You now know what an argument is. But knowing that Socrates is mortal because all humans are mortal — are you as certain of that as you are certain that the next stone you drop will fall? Both feel like solid conclusions. Are they the same kind of reasoning?
Article A2 answers this question by drawing the most important distinction in all of logic. Take your uncertainty into it. It is exactly the right frame of mind with which to begin.