Logic Reference

A guide to arguments, validity, and fallacies — return here whenever you need it

A blackboard covered in logical notation and diagrams

This page is a reference, not a lecture. You don’t need to read it all at once — open a section when you encounter a concept in the readings that needs unpacking. The content is drawn from W. Russ Payne’s An Introduction to Philosophy (CC BY-NC 4.0). It lives in Start Here but is designed to be useful across all six units.

In everyday speech, “argument” usually means a disagreement or dispute. In philosophy and logic, it means something more specific: an argument is a set of claims, one of which (the conclusion) is supported by the others (the premises).

The premises are offered as reasons for believing the conclusion. The strength of an argument depends on two things: (1) whether the premises are actually true, and (2) whether the premises actually support the conclusion — that is, whether the reasoning is any good.

Here is a simple example:

Premise 1: All human beings are mortal.
Premise 2: Socrates is a human being.
Conclusion: Therefore, Socrates is mortal.

Notice that the conclusion follows necessarily from the premises: if both premises are true, the conclusion must be true. This is what makes it a strong argument. But not all arguments work this way — some give us good reasons to believe a conclusion without guaranteeing it. The distinction between these two types is what the next two sections cover.

Identifying arguments in a text

When reading philosophy, watch for indicator words that signal the structure of an argument:

Conclusion indicators: “therefore,” “thus,” “so,” “hence,” “it follows that,” “consequently”
Premise indicators: “because,” “since,” “for,” “given that,” “as shown by,” “the reason is that”

First used in the course

Unit 1 — Plato’s Euthyphro. Socrates’ entire method consists of drawing out the premises of Euthyphro’s position and showing that they lead to a contradiction. Identifying the argument structure is the key to following the dialogue.

Deductive validity is the strictest standard an argument can meet. A deductively valid argument is one where, if all the premises are true, the conclusion must be true — there is no possible way for the premises to be true and the conclusion false at the same time.

Two equivalent definitions:

— A valid argument is one where if its premises are true, then its conclusion must be true.
— A valid argument is one where it is not possible for all premises to be true and the conclusion false.

Valid example:

If Socrates is human, then Socrates is mortal.
Socrates is human.
Therefore, Socrates is mortal.

Valid but not sound

Crucially, validity does not mean the conclusion is true. It only means the conclusion follows from the premises. A valid argument can have false premises and a false conclusion. Consider:

Valid but unsound:

All cats are reptiles. (false premise)
My pet is a cat.
Therefore, my pet is a reptile. (false conclusion)

The argument is valid (the conclusion follows from the premises), but it is not sound because the first premise is false. A sound argument is one that is both valid and has true premises. In philosophy, we are always looking for sound arguments — but we often have to evaluate validity and the truth of premises separately.

First used in the course

Unit 1 — The Euthyphro. Socrates shows that Euthyphro’s definitions of piety lead to contradictions. Understanding why those arguments are valid (even if their conclusions are uncomfortable) is the key to following the dialogue. Return here when a logical step in the text feels unclear.

Not all good arguments are deductively valid. Many arguments give us strong reasons to believe a conclusion without guaranteeing it. These are called inductively strong arguments.

Two equivalent definitions:

— An inductively strong argument is one where, if its premises are true, its conclusion is probably true.
— An inductively strong argument is one where it is improbable that the conclusion is false given that the premises are true.

Inductively strong example:

Sam is a line cook.
Line cooks generally have good kitchen skills.
Therefore, Sam can probably cook well.

The conclusion is probably true given the premises — but not necessarily. Sam could be the manager’s nephew who just started last week. This is not a flaw in the argument so much as a feature of inductive reasoning: it gives us good grounds for belief without certainty.

The problem of induction

Inductive reasoning underlies all scientific knowledge — we generalize from observed cases to broader conclusions. But this raises a deep puzzle: on what basis can we justify the move from particular observations to general conclusions? This is the problem of induction, and it is the central issue in Unit 3, when Hume argues that our belief in causation cannot be rationally justified — only habituated.

Looking ahead → Unit 3

Hume’s skepticism about induction is one of the most challenging and enduring problems in philosophy. When you encounter it in Unit 3, come back and reread this section. The distinction between deductive and inductive arguments will be essential for understanding exactly what Hume is worried about.

A fallacy is a mistake in reasoning — a pattern of argument that looks compelling but does not actually support its conclusion. Humans are remarkably prone to certain fallacies, which is why philosophers have given them names.

Ad hominem

Ad hominem is Latin for “against the man.” It is the fallacy of attacking the person making an argument rather than the argument itself. The reason it is a fallacy: whether an argument is good or bad has nothing to do with who is making it. A corrupt person can offer a valid argument; a trustworthy person can offer a terrible one.

Example of ad hominem:

“You can’t trust anything Socrates says about justice — he was accused of corrupting the youth.”

This attack on Socrates’ character does nothing to address the quality of his arguments. You will encounter versions of this fallacy in everyday political discourse constantly once you start watching for it.

Straw man

The straw man fallacy involves misrepresenting an opponent’s position — making it weaker, simpler, or more extreme than it actually is — and then attacking the misrepresentation. It is particularly relevant in philosophy because philosophical positions are often nuanced. When you critique a philosopher’s argument, make sure you are attacking the strongest version of it, not the easiest one to dismiss. This commitment to fair-minded interpretation is called the principle of charity.

False dilemma

A false dilemma presents only two options when in fact there are more. “Either you support the law unconditionally, or you are an anarchist” is a false dilemma — it ignores the many positions in between. Watch for this in the political and moral arguments we encounter in Units 4, 5, and 6.

Begging the question

“Begging the question” does not mean “raising a question” (though it is often misused that way). It means assuming what you are trying to prove. An argument begs the question when the conclusion is hidden inside one of the premises. It is circular, and therefore gives no independent reason for believing the conclusion.

Further reading

For a thorough catalogue of named fallacies, see The Fallacy Files. New fallacies will be introduced organically as they become relevant in the course readings.

A quick-reference glossary. Terms are added here as they become relevant across units.

Term Definition
Argument A set of claims (premises) offered as reasons for believing another claim (the conclusion).
Premise A claim offered in support of a conclusion. Most arguments have two or more premises.
Conclusion The claim an argument is trying to establish. Supported by the premises.
Valid argument A deductive argument in which it is impossible for the premises to be true and the conclusion false. The conclusion follows necessarily from the premises.
Sound argument A valid argument whose premises are all actually true. A sound argument guarantees a true conclusion.
Inductively strong An argument in which true premises make the conclusion probable, but do not guarantee it.
Fallacy A mistake in reasoning — a pattern of argument that appears compelling but does not actually support its conclusion.
Ad hominem Attacking the person making an argument rather than the argument itself. A fallacy because the quality of an argument is independent of who is making it.
Straw man Misrepresenting an opponent’s position (making it weaker than it is) and then attacking the misrepresentation.
False dilemma Presenting only two options when more exist. Forces a choice between extremes while ignoring the middle ground.
Begging the question Assuming what you are trying to prove. The conclusion is hidden inside a premise, making the argument circular.
Dialectic The method of philosophical inquiry through argument and response — formulating a position, facing objections, revising, and responding. Sometimes called the Socratic Method.
Principle of charity The commitment to interpret an opponent’s position in its strongest, most reasonable form before critiquing it.
Skepticism The view that knowledge (or some category of knowledge) is impossible or unwarranted. Ranges from local skepticism (about a specific domain) to global skepticism (about everything).
Metaphysics / Epistemology / Ethics The three main branches of philosophy. Metaphysics: what exists and what is its nature. Epistemology: what we can know and how. Ethics: how we ought to live and act.
Is/Ought Distinction (Unit 3) Hume’s observation that you cannot validly derive a normative conclusion (“one ought to do X”) from purely descriptive premises (“X is the case”) without an additional normative premise that bridges the gap. Also called Hume’s Guillotine. Example: “Humans have always gone to war; therefore war is permissible” moves from an “is” to an “ought” without justification. This gap appears in moral arguments drawn from nature, God, history, and economics — and recurs in every remaining unit of the course.
Ideological reasoning (Unit 5) A pattern of argument in which the premises systematically reflect the interests of a particular group or class, without the people making the argument recognizing this. The argument may be internally valid, but its starting assumptions are not neutral — they are products of a social position. Marx’s contribution was to show this can operate at the level of an entire society’s shared assumptions, not just individual bad actors. See Section 6 for fuller treatment.
False consciousness (Unit 5) A structural form of self-deception in which a person’s beliefs about their own interests are systematically shaped by the conditions that exploit them, without their recognizing this. Unlike individual self-deception, false consciousness is social: an entire class holds beliefs that serve another class’s interests, while experiencing those beliefs as their own freely formed conclusions. See Section 6 for fuller treatment.
Bad faith (Unit 6) Sartre’s term for the self-directed act of denying or evading one’s own freedom — pretending to have a fixed nature (like an object) rather than acknowledging the freedom one is always already exercising. Unlike ordinary self-deception (holding a false belief), bad faith involves a simultaneous knowing and disavowal: the person in bad faith knows they are free, but acts and thinks as though they are not. See Section 7 for fuller treatment.

Definitions adapted from W. Russ Payne, An Introduction to Philosophy, Bellevue College (CC BY-NC 4.0). Is/Ought Distinction added from Unit 3 (Hume). Ideological reasoning and false consciousness added from Unit 5 (Marx). Bad faith added from Unit 6 (Sartre).

Two of the most philosophically interesting concepts Marx introduces are not fallacies in the traditional sense — they are not errors individual reasoners commit in individual arguments. They describe something more disturbing: the possibility that the entire framework within which arguments are made, the assumptions everyone takes for granted, can be systematically distorted by the social conditions that produce them.

Ideological reasoning

An argument engages in ideological reasoning when its premises systematically reflect the interests of a particular group or class, without the people making the argument recognizing this. The argument may be internally valid — the conclusion follows correctly from the premises — but the premises themselves are not neutral. They are shaped by, and tend to serve, a specific social position.

This is different from a simple false premise. A premise can be factually false and anyone with enough information can identify and correct it. An ideological premise feels obviously true — it presents itself as common sense, as what any rational person would accept. That is what makes it ideological rather than merely wrong.

Example:

P1: Free markets allocate resources more efficiently than any other system.
P2: Efficiency is the primary criterion for a good economic system.
C: Therefore, free markets are the best economic system.

The argument is valid. But both premises embed assumptions that are contested — and that happen to serve the interests of those who own productive capital. P1 is empirically disputed; P2 privileges a particular value (efficiency) over others (equality, stability, human dignity) without justification. Those who benefit most from free markets are least likely to notice these assumptions, because from inside their position the premises simply seem obviously correct.

Marx’s point is that this is not a matter of individual dishonesty. The people making these arguments sincerely believe their premises are neutral and universal. That sincerity is not evidence of neutrality — it is evidence of how effectively ideology works.

False consciousness

False consciousness is a structural form of self-deception in which a person’s beliefs about their own interests, situation, or values are systematically shaped by the conditions that exploit or oppress them, without their recognizing this.

The key word is structural. Ordinary self-deception is personal: one person misleads themselves about a specific matter, for particular psychological reasons. False consciousness is social: an entire class holds beliefs that serve another class’s interests, while experiencing those beliefs as their own freely formed views. The mechanism is not manipulation from outside but absorption from inside — through education, culture, media, religion, and the ordinary patterns of daily life in a particular kind of society.

This makes false consciousness philosophically interesting and practically challenging. You cannot simply point out to someone that they are in a state of false consciousness and expect them to recognize it immediately. The beliefs feel true precisely because they have been formed in conditions that make them feel that way. The critique has to go deeper than the individual argument — it has to examine the conditions that made those starting assumptions seem obvious.

The self-exemption problem

Both concepts face a serious philosophical objection: if all reasoning is potentially ideological, and if consciousness can be systematically false, how does anyone — including the person diagnosing others’ ideology — achieve a perspective that is not equally distorted? This is sometimes called the self-exemption problem.

If Marx’s own theory is a product of his class position, it has no more claim to objective truth than the bourgeois ideology he critiques. Marx was aware of this problem but his response to it is underdeveloped. Later Marxist thinkers (particularly in the Frankfurt School tradition) worked on this extensively — but it remains one of the genuine open questions the concepts leave behind.

Introduced in Unit 5 — recurs in Unit 6

These concepts appear in the Unit 5 lecture pages on class struggle and on ideology and alienation. In Unit 6, Sartre’s concept of bad faith operates on related terrain — also a form of self-deception, but one located in individual choice rather than social structure. The contrast between Marx’s structural account and Sartre’s existential account is one of the course’s most productive tensions. See Section 7 for the full treatment of bad faith.

Bad faith (mauvaise foi) is Sartre’s name for a particular form of self-deception that arises not from ignorance but from the structure of consciousness itself. It is, in a sense, the deepest version of self-deception the course examines — not the result of social conditioning (as false consciousness is) but of something built into what it means to be a conscious being.

The core structure

Sartre distinguishes between two modes of being: the in-itself (objects, things — fully self-identical, with no gap between what they are and what they are) and the for-itself (consciousness — characterized by freedom, lack, and the perpetual non-coincidence of the self with itself). Human beings are for-itself: they are never simply what they are, always ahead of themselves in their projects, always free to take a stance on their situation.

Bad faith is the attempt to flee this condition by pretending to be an in-itself — to have a fixed, determined nature rather than a freely chosen one. It is the act of saying (or behaving as though) “I cannot help it; this is just who I am,” when in fact who you are is something you are choosing, moment by moment.

Two forms of bad faith

Form What is denied Example
Denial of transcendence One’s freedom to choose otherwise The waiter who performs his role with exaggerated precision, as though being a waiter were a fixed nature rather than a daily choice
Denial of facticity The reality of one’s situation and its demands The woman on a date who lets her hand rest in her companion’s as though it were an object — deferring the moment of choice by treating herself as not present to it

Both forms involve a failure to hold both sides of the human condition in view at once: facticity (the unchosen facts of your situation) and transcendence (your freedom to take a stance on those facts). Authentic existence means acknowledging both — not denying the situation, and not pretending the freedom away.

Why bad faith is puzzling

Ordinary deception requires one person to know the truth and conceal it from another. In bad faith, the deceiver and the deceived are the same person — which seems to require simultaneously knowing the truth and not knowing it. Sartre’s answer is that the non-coincidence of consciousness with itself (the gap between the self that knows and the self that is known) makes this possible. Bad faith exploits the structural gap within consciousness rather than imposing an external falsehood.

This is what distinguishes bad faith from false consciousness. False consciousness is something that happens to a person through their social conditions — it is structurally imposed from without. Bad faith is something a person does to themselves — a choice made in full (if disavowed) awareness of one’s freedom. The self-deception is active, not passive.

The normative problem

Sartre condemns bad faith as a moral failing — not merely an inconvenience or a psychological curiosity. But this creates a tension: if there are no objective moral norms (as Sartre also claims), on what basis is bad faith condemned? The most defensible answer within his own framework is that bad faith is self-undermining — it relies on and simultaneously denies the freedom it requires to perform itself, making it a form of practical contradiction rather than an external moral violation. Whether this fully resolves the tension is one of the course’s open questions.

The self-deception thread — across all six units

Bad faith closes a thread that runs through every unit in the course. Socrates’ interlocutors deceive themselves about what they know. Descartes worries about systematic external deception. Hume reveals that our confidence in causation is a habit mistaken for knowledge. Marx’s ideology and false consciousness describe socially structured self-deception. Sartre’s bad faith is the terminus: self-deception located not in ignorance, not in social structure, but in the very nature of consciousness itself — and therefore inescapable except through the ongoing, difficult work of authenticity.