1
The triad is a set of three sentences
Let d say that determinism is true, f that people act freely, and d → ¬f that determinism rules out free action. Together they have no model, since d and d → ¬f give ¬f, which contradicts f.
Lesson · Identity, Modality and Freedom · Freedom
Free Will, Determinism and Compatibility
Hard determinism, libertarianism and compatibilism are usually presented as rival answers. Written as a set of three sentences they are the three ways to delete one, and the consistency lab shows the set has no model. It also shows that a compatibilist set is consistent while keeping determinism, because it defines free will differently.
d: determinism f: free will
incompatibilism: d → ¬f
{d, f, d → ¬f}: no model
drop f, d, or the conditional: a model
compatibilism keeps d, and changes what f is
Three claims, three deletions
Core ideas
What this lesson establishes
The last lesson was a consistency check on a puzzle about identity. The same check applies to the oldest of the freedom debates, and its first result is a map of the positions.
2
The three positions are the three deletions
Hard determinism keeps d and the conditional and drops f. Libertarianism keeps f and the conditional and drops d. Compatibilism keeps d and f and drops the conditional, which is what the word “compatible” says.
3
What f means decides which sets are consistent
A compatibilist does not only reject the conditional. The compatibilist gives f a different meaning, for instance acting on one's own desires, and under that meaning the conditional no longer connects the two claims.
The material
The triad and its exits
The claims, the set that has no model, the models that appear on each deletion, and the definition on which compatibilism turns.
Definition · Determinism
Determinism is the thesis that the state of the world at one time, together with the laws of nature, entails the state at every later time. It is a thesis about entailment, and it says nothing of compulsion or of what anyone feels.
Take free will in its ordinary sense: when I raise my hand it is up to me, and I could have kept it down. The old worry is that these two do not fit. If the past and the laws entail everything that happens, then my raising my hand was already entailed, and it does not look as if it was up to me. Write the worry as a conditional, and put it beside the two claims it threatens.
1. d determinism is true
2. f some people act freely
3. d → ¬f if determinism is true, no one acts freely
Sentence 3 is incompatibilism, and it is the one in dispute. The lab finds no model for the three: from 1 and 3 comes ¬f, and sentence 2 is f. It reports the smallest inconsistent subset as the whole set, so every sentence has to be present for the clash, and each is a place to give way.
Three places, three positions. The hard determinist drops sentence 2 and accepts that no one acts freely. The libertarian drops sentence 1 and holds that some choices are not entailed by the past and the laws. The compatibilist drops sentence 3. Each position can be stated at its strongest, and each pays: the first gives up the practice of praise and blame, or has to reinterpret it; the second needs causes that are not entailed, which the physics may or may not supply; and the third has to say what freedom is, given that it is not the ability to do otherwise whatever the past.
What drops the conditional
The compatibilist cannot simply deny sentence 3. The conditional is plausible on a reading of f, and that reading is what the compatibilist rejects. Suppose free will is acting on one's own desires, without constraint. Write a for “the person acts on her own desires” and o for “she could have done otherwise whatever the past”. The compatibilist set is d, f, f ↔ a and d → ¬o, which says that determinism rules out the strong ability and keeps free will as acting on desires.
The lab finds a model for it, and the model makes d true and f true. The misreading of the position is the thought that compatibilism needs determinism to be false somewhere. It needs no such thing: the compatibilist holds both claims at once, which is why the position is called what it is.
The cost is on the other side of the biconditional. If the incompatibilist insists that free will does require the ability to do otherwise whatever the past, the sentence f ↔ o replaces f ↔ a, and with d → ¬o the set is inconsistent again. The lab shows the clash is back, and it shows that the dispute has moved from the logic to the meaning of f. A consistent set does not tell you that the compatibilist's a is the freedom anyone wanted. It tells you that the position is coherent.
The lab has one limit that matters here. It treats d, f, a and o as unanalysed claims, and it cannot tell you whether determinism is true or what freedom is. It checks the sentences you chose.
Interactive
Consistency and what must go
Every model, and every minimal inconsistent subset
Method
Mapping a debate by its inconsistent set
Five moves for any question that offers a few claims and says they conflict.
1
Write the claims, including the one that says they conflict
The conflict is itself a sentence. Write the bridge as a conditional, as with d → ¬f, and not as a remark.
2
Ask for a model
If the lab finds one, the claims do not conflict as written. If it finds none, read the smallest inconsistent subset.
3
Delete each sentence once
The model that appears each time is a position. Name it, and name who holds it.
4
Look at the letters, not only the sentences
Ask what each letter means. If a position works by giving a letter a different meaning, add the defining sentence to the set, as with f ↔ a, and test again.
5
Say what each position pays
A position is not defended by being consistent. State the cost it accepts, and decide whether you are willing to pay it.
Positions as deletions
Score 0 / 0Choose the answer you can justify.
One table, three positions
The triad d, f, d → ¬f, with each sentence dropped in turn.
all three: no model
drop 2, f: d true, f false
drop 1, d: d false, f true
drop 3, the conditional: d true, f true
drop 2 is hard determinism
drop 1 is libertarianism; drop 3, compatibilism
Each model is the position's picture of the world, and none is argued for by the table. The second preset keeps the conditional for the strong ability o and changes what free will is, so the set has a model and d remains true in it.
Common mistakes
1
Thinking compatibilism denies determinismThe sentence d is in the compatibilist set, and the lab's model makes it true: determinism and free will are both true in it. What the compatibilist denies is the conditional between them, once free will is understood as acting on one's own desires. The position is called compatibilism because it claims the two are compatible, and determinism is the thing that is kept.
2
Treating a determined act as a compelled actDeterminism is a thesis that the past and the laws entail what happens. Compulsion is a fact about a particular act, such as one made under threat or against one's own desires. The compatibilist's a is exactly what compulsion removes, so an act can be determined and uncompelled, and a person acting on a compulsion is not free under any of the definitions in the lab.
3
Believing consistency is a win for the compatibilistA set with a model shows only that the position is coherent. The incompatibilist's reply is that f ↔ a has changed the subject, and the third preset shows what the reply is: give f the other meaning and the clash returns. The argument is about which meaning of f is the one that matters for praise, blame and choice.
Check your understanding
✓
Finish when you can write the triad, name the three positions as deletions, and show how a definition of free will changes the verdict.
You should be able to state the three sentences, report the verdict and the smallest inconsistent subset, give the model that appears on each deletion, and show with a defining sentence how a compatibilist definition of free will makes the set consistent. A position named without the sentence it drops has not been placed.
Note: The next lesson turns to the argument that gives the conditional its best support, and it is the strongest case an incompatibilist can offer.