Philosophy IBEB 2026

Deductive Argument

If the premises are true, the conclusion cannot be false.

Valid Argument

The conclusion necessarily follows from the premises. If all premises are true, the conclusion must be true.

Sound Argument

The argument is valid AND all premises are actually true in the real world.

Inductive Argument

The conclusion follows from premises based on statistics or patterns. Likely but not guaranteed.

Abductive Argument

The conclusion is the most plausible explanation of the premises. Not guaranteed.

Conclusion Indicators

Words that signal a conclusion is coming: therefore, so, hence, thus, it follows that, consequently.

Premise Indicators

Words that signal a premise is coming: because, since, after all, given that, for these reasons.

Modus Ponens

If P then Q. P. Therefore Q. This is valid.

Modus Tollens

If P then Q. Not Q. Therefore not P. This is valid.

Affirming the Consequent

If P then Q. Q. Therefore P. This is INVALID — a fallacy.

Denying the Antecedent

If P then Q. Not P. Therefore not Q. This is INVALID — a fallacy.

Conceptual Analysis

Taking a concept and breaking it down to figure out exactly what it means and what conditions must all be true for it to apply.

Thought Experiment

An imagined scenario used to test, support, refute or clarify a theory or intuition.

Reflective Equilibrium

Going back and forth between moral intuitions and moral principles, adjusting both until they are stable and consistent. Two fixes when they clash: adjust the principle or revise the intuition.

Utilitarian Principle (UP)

You should perform the action which, of all available actions, results in the greatest total sum of individual well-being.

P1 - Consequentialism

Only the outcome of an action determines whether it is morally right. Intentions and rules do not matter.

P2 - Welfarism

Only well-being matters when deciding if one outcome is better than another.

P3 - Weak Pareto

If everyone is strictly better off in X than in Y, then X is the better outcome.

Strong Pareto

If at least one person is strictly better off in X than Y and nobody is worse off, then X is better. Ties are allowed.

P4 - Unit Cardinal Comparability

Well-being can be measured and compared between different people using the same units. Without this the UP breaks down — you cannot calculate a total sum.

P5 - Transitional Equity

Taking a small amount of well-being from a better-off person and giving it to a worse-off person counts as an improvement. More equal distributions are better.

Hedonism

Well-being equals pleasure minus pain. Only the feeling matters, not what causes it.

Positive Hedons

Units of pleasure. They increase well-being under hedonism.

Negative Hedons

Units of pain. They decrease well-being under hedonism.

Experience Machine

A machine that plugs into your brain and gives you a perfect simulated life that feels completely real. Used to challenge the idea that only feelings determine well-being — most people would not plug in.

Preference Satisfaction Theory

Well-being equals getting what you want. It goes up when your preferences are satisfied.

Informed Preference Satisfaction

Well-being equals satisfying the preferences you would have if you were fully informed about the situation.

Remote Preferences Objection

You want your children to be happy after you die. They are not. You never find out. According to PS theory your well-being dropped — but it seems like it should not have. Satisfying preferences alone is too broad.

Changing Preferences Objection

You sacrifice everything to become a lawyer and then realize you hate it. Satisfying your original preference did not actually make your life better.

Objective List Theory

Well-being equals achieving certain things that are good for you regardless of whether you want them or whether they feel good. The same list applies to everyone.

Objection to Objective List Theory

There is no agreed-upon authority to decide what goes on the list. It is arbitrary and forces values on people whether they want them or not.

Ordinal Scale

You can only rank outcomes. You know A is better than B but not by how much.

Cardinal Scale

You can rank outcomes and measure the difference between them. You know A is better than B and by exactly how much.

Ratio Scale

You can rank, measure differences, and there is a meaningful zero point. You can say one outcome is twice as good as another.

Well-being Level

How well off someone is at a specific point in time. Their absolute score.

Well-being Difference

How much someone's well-being changes between two situations.

Intrapersonal Comparison

Comparing one person's well-being across different situations or points in time.

Interpersonal Comparison

Comparing multiple people to one situation

VNM Utilities

A method of measuring well-being using lotteries and 4 axioms: completeness, transitivity, continuity, independence. If a person's preferences satisfy all 4, their well-being can be represented with numbers. Critics say it only captures rational choice under uncertainty, not actual well-being.

Aggregating Well-being

Adding up every individual's well-being into one total number. Requires that well-being is measured in the same units across people. Problem: only looks at the total, ignores how it is distributed.

Arjun Example

Arjun's organs are harvested against his will. His well-being drops to zero but the people who receive his organs gain so much that the total goes up. Shows that maximizing the total sum can lead to deeply unjust results.

Separateness of Persons

Each person is a distinct individual, not a container of utility. You cannot take from person A just because it benefits B, C and D, unless A agrees.

Utilitarianism SWF

Outcomes are ranked by the total sum of everyone's well-being. Requires unit cardinal comparability.

Egalitarianism SWF

Outcomes are ranked by the sum but extra weight is given to equal distributions. Requires cardinal comparability. Can lead to levelling down.

Prioritarianism SWF

Extra moral weight is given to improving the well-being of worse-off people. A unit of well-being matters more the worse off the person receiving it is. Requires ratio scale comparability.

Rawlsian SWF

Outcomes are ranked solely by the well-being of the worst-off person. The option that maximizes the minimum wins. Requires only ordinal comparability. Violates strong Pareto.

Levelling Down

Making everyone equally badly off in order to achieve equality. Technically equal but nobody benefits and everyone suffers. Rejected by most philosophers.

Diminishing Marginal Well-being

Each extra unit of a resource adds less well-being than the previous one. Getting €1 when you have €0 helps more than getting €1 when you already have €1000.

Social Choice Theory

The study of how to combine individual preferences or well-being into a single collective decision or ranking, especially when full interpersonal comparison is not possible.

Social Choice Function (SCF)

Takes everyone's individual rankings as input and outputs the winner or winners only.

Social Welfare Function (SWF)

Takes everyone's individual rankings as input and outputs a full collective ranking of all alternatives from best to worst.

Welfare Economics framing

Alternatives are policy outcomes. Rankings represent how good each outcome is for each person's well-being.

Voting Theory framing

Alternatives are candidates or proposals. Rankings represent voter preferences.

Plurality Rule

Everyone votes for their top choice only. The option with the most votes wins. Completely ignores second and third choices.

Borda Count

Points are assigned based on rank position. With 3 options: 1st place = 2pts, 2nd = 1pt, 3rd = 0pts. The option with the most total points wins.

Copeland Rule

Every pair of alternatives is compared head-to-head. Win = 1 point, loss = 0, tie = 0.5. The option with the most points overall wins.

IRV - Instant Runoff Voting

If an option has a majority of first-place votes it wins immediately. If not, eliminate the option with fewest first-place votes and repeat until a winner emerges.

Condorcet Winner

An alternative that beats every single other alternative in head-to-head pairwise comparisons.

Condorcet Paradox

Individual preferences are all consistent but group majority preferences cycle — A beats B, B beats C, C beats A. No overall winner exists.

Dictator Rule

One specific person's ranking becomes the group ranking regardless of what everyone else prefers.

Axiom (SCT)

A condition or property that we require a fair aggregation rule to satisfy.

Anonymity

Swapping which voter holds which ranking does not change the winner. All voters are treated equally.

Neutrality

Swapping the names of the alternatives everywhere produces a corresponding swap in the winner. No alternative gets special treatment.

Positive Responsiveness

If X was already winning and one or more voters move X up in their ranking, X must still win and be the only winner. Only Borda satisfies this.

IIA - Independence of Irrelevant Alternatives

The ranking between X and Y must depend only on how voters rank X versus Y — not on where any third alternative sits. No standard voting rule satisfies this.

May's Theorem

With exactly 2 alternatives, majority rule is the only rule that satisfies anonymity, neutrality and positive responsiveness simultaneously.

Arrow's Impossibility Theorem

With 3 or more alternatives, no rule can simultaneously satisfy weak Pareto, IIA and non-dictatorship. No perfectly fair collective decision method exists.

Non-dictatorship

No single person's preferences can automatically determine the group's ranking regardless of everyone else.

Local Fairness

Fairness in specific concrete situations involving scarce resources — e.g. who gets a kidney, salary decisions, housing allocation.

Global Fairness / Social Justice

How a society as a whole distributes rights, duties, opportunities and resources across all its members.

The Kidney Case

Ann and Bob both need a kidney to survive. Only one exists. No morally relevant differences between them. The fair answer is a 50/50 lottery. This shows that fairness matters beyond just maximizing utility.

L1 vs L2 Kidney

L1 = fair 50/50 lottery. L2 = give the kidney to Ann with certainty. The UP picks L2 because it has higher expected utility. Most people's intuition says L1 is fairer. Shows the UP misses fairness.

Claim

A reason for giving a resource to someone that is owed to them personally — based on their need or situation — not just because it produces good consequences.

Strength of a Claim

How much a person loses if their claim is denied. The greater the loss, the stronger the claim.

Broome's Formula

Claims must be satisfied in proportion to their strength. If Ann's claim is twice as strong as Bob's she gets a 2/3 chance and Bob gets 1/3.

Types of Fairness - Broome

His theory is: substantive not formal, narrow not broad, local not global, objective not subjective, comparative not absolute, both outcome and procedural.

Formal Fairness

Rules are applied consistently and equally to everyone. Does not guarantee the outcome is morally right.

Substantive Fairness

The actual outcome is morally right, regardless of whether rules were followed consistently.

Procedural Fairness

The process used to reach a decision is fair, regardless of what the outcome turns out to be.

Outcome Fairness

The final result of a distribution is fair.

Integrating Fairness - Give up P1

Drop the idea that only outcomes matter. Fairness becomes a hard constraint — some actions are ruled out even if they produce a higher total utility.

Broome's Solution - Redescription

Redescribe outcomes to include whether the process was fair or unfair. Since being treated unfairly affects a person's well-being, fairness gets built into the calculation and the UP still works.

Primary Goods

Things every person needs to pursue their life goals regardless of their religion, values or lifestyle. Covers four categories: political rights and opportunities, socio-economic rights and opportunities, socio-economic resources, physical and mental abilities.

Social Justice vs Global Justice

Social justice = how primary goods are distributed within one society. Global justice = how primary goods are distributed across countries internationally.

Rawls - Theory is Deontological

Rights and individual autonomy come first. They are not derived from welfare calculations. They are fundamental.

Rawls - Political Equality

Every citizen gets equal political rights and opportunities — right to vote, freedom of speech, right to run for office.

Rawls - Substantive Equality of Opportunity (SEO)

Two people with the same natural talent who put in the same effort must have equal chances at success, regardless of their background or wealth.

Rawls - Difference Principle

Inequalities in society are only allowed if they make the worst-off members of society better off than they would be under full equality.

Rawls - Priority Order

Political Equality comes first, then SEO, then the Difference Principle. You cannot trade political equality for economic gain. Each is a tiebreaker for the one above it.

Incentives Argument

Giving incentives to talented people creates inequality but also raises overall output. This can be justified under the Difference Principle if the worst-off end up better off as a result.

Veil of Ignorance

You design the rules of society without knowing your own race, wealth, gender, talents or position. You cannot design rules that favour yourself.

Original Position

The hypothetical starting point where people choose principles of justice from behind the veil of ignorance.

Rawls vs Harsanyi

Rawls: you cannot assign probabilities to your future position so you protect against the worst outcome — leads to the Difference Principle. Harsanyi: you assign equal probability to every position and maximize expected utility — leads to UP.

Pattern-based Justice

Whether a distribution is just is judged by what the outcome looks like at a given point in time.

Process-based Justice

Whether a distribution is just is judged by how it came about — was every step voluntary and free of theft and fraud?

Nozick - Principle of Just Acquisition

You may take ownership of previously unowned property as long as no theft, force or fraud is involved.

Nozick - Principle of Just Transfer

Property may change hands as long as the exchange is fully voluntary — no theft, force or fraud.

Nozick - Principle of Just Rectification

When a past injustice has occurred, correcting it is permitted. Example: Ann steals Bob's laptop, Bob is entitled to take €300 back from Ann.

Liberty Upsets Patterns

Any attempt to keep a distribution equal requires constantly interfering with voluntary choices people make. This interference violates individual liberty.

Wilt Chamberlain Example

Millions of people freely pay a small amount to watch a great athlete perform. He ends up very rich. Every transaction was voluntary. The resulting inequality cannot be called unjust.