Hume's Criteria

1. Hume's argument:
2. P1: All the objects of human reason or enquiry can be divided into 2 CATEGORIES: relations of ideas (CATEGORY 1) and matters of fact (CATEGORY 2).
3. P2: There is a causal relationship between EVENT 1 and EVENT 2.
4. P3: This causal relationship is an object of human reason or enquiry.
5. P4: This causal relationship is not a relation of ideas (CATEGORY 1).
6. C: ∴ This causal relationship is a matter of fact (CATEGORY 2).
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9. Matters of fact are known a posteriori from impressions rather than ideas
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11. Our impressions may be:
1. External impressions — through our use of our traditional five senses; or
2. Internal impressions — through custom or habit of mind

According to our external impressions: The effect temporally follows from the cause (temporal succession) Cause and effect are spatiotemporally contiguous or close to each other (continguity) Causes are regularly followed by effects (constant conjunction) According to our internal impressions: We get into the habit of mind of expecting an effect after observing cause Custom or habit of mind is the source of our belief that: i) The future will be like the past ii) There is a necessary connection between causes and effects

1. STEP 1: From our external impressions, we have observed regularities between EVENT 1 and EVENT 2 (i.e. sufficiently many EVENT 1-tokens followed by EVENT 2-tokens) in the past
2. STEP 2: From our internal impressions, we form the idea of a necessary connection between EVENT 1 and EVENT 2
3. STEP 3: On observing EVENT 1 (cause), we make the causal inference that EVENT 2 (effect) will follow

1. CRITERION 1 (Contiguity) — A cause and its effect must be nearby each other in time and space
2. CRITERION 2 (Temporal Priority) — A cause must precede its effect in time
3. CRITERION 3 (Necessary Connection) — The cause always produces the effect and the effect is not produced without the cause
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5. NOTE:
6. In the empirical definition, CRITERION 3 (Necessary connection) is replaced with CRITERION 3^′ (Constant Conjunction)
7. CRITERION 3^′ (Constant Conjunction) — A cause is regularly followed by (i.e. conjoined with) its effect

Regularity Theory of Causation

1. According to the regularity theory of causation (Hume, 1748, Mill, 1843, Koch, 1932, Hill, 1965, Susser, 1973, Mackie, 1974, Naranjo et al, 1981):
2. C causes E if every event of type C is followed by an event of type E

1. X₁ causes Y₁ at token level
2. X₂ causes Y₂ at token level
3. X₃ causes Y₃ at token level
4.   ⋮
1. ∴ X causes Y at type level

1. A cause is an INUS (viz. insufficient but non-redundant part of an unnecessary but sufficient) condition
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3. C is an INUS condition of E iff:
1. (C ∧ X) is sufficient for E;
2. (C ∧ X) is not necessary, since Y could also cause E;
3. C alone may be insufficient for E;
4. C is a non-redundant part of (C ∧ X)

1. C is a cause of E on a particular occasion (this is known as token or singular causality) iff:
2. C is at least an INUS condition of E;
3. C is present;
4. The components of X (if there are any) were present;
5. Every disjunct in Y not containing C as a conjunct was absent

1. C — A lit match (present)
2. X — Oxygen, flammable material, other conditions needed for a lit match to cause a fire
3. Y — Lightning strike, faulty electrical wiring, other factors that cause fires in the absence of lit matches
4. E — House in fire
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7. ((C ∧ X) ∨ Y) ⟷ E
8. TRANSLATION: ((C ∧ X) ∨ Y) is necessary and sufficient for E
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11. Analysis:
12. A lit match (C) may be the cause of the house fire
13. However, if conditions needed for a lit match to cause a fire are absent (∼X), then C may not cause the fire
14. In addition, there are some circumstances (Y) in which a fire occurs without C

PROBLEMS with the regularity theory of causation
Problem	Description
	X (common cause) causes both Y and Z ∴ Y, although a leading indicator of Z, would have a spurious (noncausal) correlation with Z X: The spinning of the earth around its own axis Y: Day Z: Night There is a noncausal regularity between day and night ∴ Observed regularities are not sufficient for us to recognize relationships as causal relationships
	Certain causal relata are one-off: the Big Bang is a one-off cause, the murder of a specific individual is a one-off effect, etc ∴ Observed regularities are not necessary for us to recognize relationships as causal relationships In addition, some causal relationships are anomalous: a drug that normally cures a disease could cause death in a small fraction of the patient population that takes the drug
PROBLEM 3: Specific challenges to each of Hume's criteria	OBJECTIONS to CRITERION 1 (Contiguity): OBJECTION 1: The absence of an event (rather than the presence of it) can lead to an effect OBJECTION 2: An event could occur in one part of the world and cause an event elsewhere at a later time
	OBJECTIONS to CRITERION 2 (Temporal Priority): OBJECTION 1: There is simultaneous causal influence in physics
	OBJECTIONS to CRITERION 3 (Necessary Connection): OBJECTION 1: When there are multiple causes of an effect, each cause is no longer individually necessary
PROBLEM 4: Selection problem	There is no method for distinguishing between causally relevant parts of a regular sequence of events and causally irrelevant parts (e.g. mere background conditions, spurious correlations, etc)
PROBLEM 5: No guidelines for establishing degree of causal influence	Any event that has a small influence on the timing or manner of the effect can be said to be a cause However, there is no discussion in the regularity theory of causation of the degree to which a cause influences an effect

Counterfactual Theory of Causation

1. Def 1 — for the regularity theory of causation
2. Def 2 — for the counterfactual theory of causation

1. According to the counterfactual theory of causation (Lewis, 1973, 1986, 2000, Ganeri, Noordhof & Ramachandran, 1996, Ramachandran, 1997):
2. C causes E iff:
   1. E is causally dependent on C; or
   2. There is a chain of causal dependence between C and E

X ☐⟶ Y — If X were true, then Y would be true 'X ☐⟶ Y' is true in the actual world @ iff: i) There are no possible worlds in which X is true (i.e. 'X ☐⟶ Y' would be vacuously true); ii) A possible world w1 in which both X and Y are true is closer to the actual world @ than any other possible world (w2, w3, etc) in which X is true and Y is false (i.e. 'X ☐⟶ Y' would be non-vacuously true); iii) Both X and Y are true in the actual world @ (a special case of (ii))

1. To say that 'X ☐⟶ Y' is true is to that Y depends counterfactually on X

1. C ☐⟶ E — If C had occurred, then E would have occurred too
2. ∼C ☐⟶ ∼E — If C had not occurred, then E would not have occurred too

1. In the actual world @:
2. If Z causally depends on Y, then Y causes Z
3. If Y causally depends on X, then X causes Y
4. X causes Y and Y causes Z
5. There is a chain of causal dependence between X and Z
6. ∴ By the transitivity of causation, X causes Z
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8. However, Z does not causally depend on X
9. In possible world w₁, Z depends causally and counterfactually on W
10. ∴ There can be causation without causal dependence

PROBLEMS with the counterfactual theory of causation
Problem	Description
	EXAMPLE: I give Jones a chest massage (C), without which he would have died Jones recovers and flies to New York (F), where he eventually has a violent death (D) C is the cause of F F is the cause of D However, C is not the cause of D: whether or not C occurred, Jones would still have died
	C causes E in the actual world @ However, it is not true that if C had not occurred, then E would not have occurred C and D are independent: neither C nor D cause the other If C had not occurred, then D would still have caused E: D is causally sufficient on its own If D had not occurred, then C would still have caused E: C is causally sufficient on its own ∴ While C causes E, had C not occurred, E would still have occurred (otherwise caused by D) EXAMPLE 2 (Redundant Causation): David Beckham and Ryan Giggs taking a free kick together (Aston Villa v. Man Utd in Aug 2001) EXAMPLE 3 (Schaffer, 2000): According to the law of magic, the 1st spell on a given day will match the enchantment that midnight At 12 noon, Merlin casts a spell S1 (the 1st of its kind that day) to turn the prince into a frog At 6 pm on the same day, Morgana casts a spell S2 (the only other spell of its kind that day) to turn the prince into a frog At 12 midnight, the prince becomes a frog (F) Merlin's spell S1 is the trumping cause Morgana's spell S2 is the trumped backup cause The effect is F (i.e. the prince becoming a frog at 12 midnight) Merlin's spell S1 causes F at 12 midnight However, there is no counterfactual dependence of F on S1 Morgana's spell S2, cast at 6 pm, is the dependency-breaking backup cause Trumping pre-emption is a special case of redundant causation ∴ The counterfactual theory of causation cannot handle cases of pre-emption
	Had F not occurred, C would not have occurred Had C not occurred, E would not have occurred either Had F not occurred, E would not have occurred However, there is no causal relation between E and F In the actual world @, C temporally precedes F ∼F ☐⟶ ∼C — Had F not occurred, C would not have occurred Lewis calls '∼F ☐⟶ ∼C' a backtracking counterfactual: this backtracking counterfactual is problematic ∴ We need to patch up our counterfactual semantics to more systematically exclude backtracking counterfactuals
	The 4 STEPS in Lewis' counterfactual theory of causation: STEP 1: Analysis of the truth conditions of counterfactuals in terms of possible and actual worlds (@, w1, w2, etc) STEP 2: Analysis of counterfactual dependence in terms of counterfactuals STEP 3: Analysis of causal dependence in terms of counterfactual dependence STEP 4: Analysis of causation in terms of causal dependence This theory aims to deliver causal relationships in terms of counterfactual dependence However, there are cases of counterfactual dependence that are not cases of causal dependence ∴ It appears that the relevant cases of counterfactual dependence must still be defined in terms of causal relationships This would result in a circularity of analysis In EXAMPLE 1: EVENT 1: I draw a figure with five sides. EVENT 2: I draw a pentagon. EVENT 2 depends counterfactually on EVENT 1: Had I not drawn a figure with five sides, then I would not have drawn a pentagon However, EVENT 1 does not cause EVENT 2 Instead, EVENT 1 constitutes EVENT 2 In EXAMPLE 2: EVENT 1: One commits an act of murder. EVENT 2: One breaks the law. EVENT 2 depends counterfactually on EVENT 1: Had one not committed the act of murder, then one would not have broken the law However, EVENT 1 does not cause EVENT 2 Instead, EVENT 1 constitutes EVENT 2
PROBLEM 5: No guidelines for establishing degree of causal influence	Any event that has a small influence on the timing or manner of the effect can be said to be a cause However, there is no discussion in the counterfactual theory of causation of the degree to which a cause influences an effect

Probabilistic Theory of Causation

1. Even with complete knowledge of the world and all the relevant information, the cause does not always produce the effect without fail
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4. According to the probabilistic theory of causation (Reichenbach, 1956, Good, 1961, Suppes, 1970, Eells, 1991):
1. C is a positive cause of E if C raises the probability of E occurring
2. X causes prima facie Y iff P(Y|X) > P(Y)
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4. C is a negative cause of E if C lowers the probability of E occurring
5. X causally inhibits prima facie Y iff P(Y|X) < P(Y)
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7. Otherwise, C is causally neutral w.r.t. E
8. X is not a prima facie cause (positive or negative) of Y iff P(Y|X) = P(Y)

1. METHOD 1: Information-based theories
2. A cause provides some information about the effect that cannot be gained in other ways
3. METHOD 1 (or one of its appropriate variants) is used to infer causal relationships from observational data
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6. METHOD 2: Manipulation theories
7. A cause is a means of bringing about an effect
8. The probability or value of the effect alters when its cause is manipulated
9. METHOD 2 relies on the manipulation of causes
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12. Neither METHOD 1 nor METHOD 2 subsume each other
13. In addition, there are counterexamples to both METHOD 1 and METHOD 2

PROBLEMS with the probabilistic theory of causation
Problem	Description
	EXAMPLE: Smoking (S) is the common cause of yellow-stained fingers (Y) and lung cancer (L) ∴ Possessing yellow-stained fingers (Y) raises the probability of lung cancer (L) However, there is no causal relationship between Y and L When we hold fixed the common cause S (viz. smoking), we screen off Y and L from each other (Reichenbach, 1956)
	EXAMPLE (Hesslow, 1976, Cartwright, 1989): The birth control pill (BCP) raises the probability of a blood-clotting chemical (BC) forming BC raises the probability of thrombosis (T) At the same time, the birth control pill (BCP) lowers the probability of pregnancy (P) As P raises the probability of T, BCP also lowers the probability of T Thrombosis (T) raises the probability of chest pain (CP) ∴ Multiple paths between pairs of nodes BCP and T can cause path cancellation ∴ We could have causality without probability-altering
	In deterministic cases, an effect E occurs with P(E|C) = 1 as a result of a cause C In more complex cases, there may be multiple causes C1, C2, …, etc, each of which leads to the effect with a probability P(E|(C1 ∨ C2 ∨ …)) = 1 ∴ Even if C1 had not occurred, E would still have occurred with a probability of 1