Causal Reasoning. Note. Being g is necessary for being f iff being f is sufficient for being g

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1 145 Often need to identify the cause of a phenomenon we ve observed. Perhaps phenomenon is something we d like to reverse (why did car stop?). Perhaps phenomenon is one we d like to reproduce (how did I get extra money in my bank?). Causal claims often rest on special kind of generalization (a causal generalization) C (event 1) caused E (event 2) e.g. firing a gun caused someone to have a bullet wound e.g. running out of fuel will cause any car to stop running (this is a generalization) Causal generalizations have predictive force : when you combine a causal generalization with facts in a particular case, you generate a prediction about what will happen in that case Causal generalization can be represented using a conditional : a general condition of form of all x, if x if F, then x is G A shorthand way of talking about these conditionals in terms/necessary (or sufficient) conditions Necessary Conditions X s being G is a necessary condition for x s being F iff for all x, if x if F, then x is G [for all x: (F x ) Gx )] Sufficient Conditions X s being F is a sufficient condition for x s being G iff for all x, if x is F, then x is G [for all x: (Fx ) Gx)] Note Being g is necessary for being f iff being f is sufficient for being g G F e.g. being a square is sufficient for being a rectangle

2 145 e.g. being a rectangle is necessary for being a square True/ false? 1. Being a car is sufficient condition for being a vehicle (T) 2. Being a car is necessary 2 and condition 3 are for pretty being much a vehicle same (F) 3. Being a vehicle is a sufficient condition question for being a car (F) 4. Being a vehicle is necessary condition for being a car (T) 5. Being an integer is a sufficient condition for being an even number (F) 6. Being an integer is a necessary condition for being an even number (T) Important: not all relationships of necessity/sufficiency are causal (e.g. relationship b/w being a square and rectangle). Cause PRECEDES the effect this does not apply to a square as it does not precede to be a rectangle it happens at the same time. But plausibly all causal generalizations encode sufficient conditions (the cause is sufficient for effect) The sufficient condition test By looking at specific cases we can gather evidence about whether something is (or not) a sufficient condition for something else The sufficient condition test (SCT) If feature F is present when feature G is not, then F is eliminated as a possible sufficient condition for G Look at where target condition is NOT present Why? If F were sufficient for G, then any time F were present, G would need to be present too, so if G = absent, then F must be absent too Note : eliminating a condition as possibly sufficient for G by the SCT is deductively valid method of arguing Target Case 1: A B C D G Case 2: A B C D G Case 3: A B C D G Case 1 : irrelevant, no possible violation of SCT target feature(g) is present in this case therefore, does not matter Case 2: SCT eliminates B and C as possibly sufficient for G Case 3: SCT eliminates A as possibly sufficient for G Does it follow that D is sufficient for G? (not necessarily) o Case 4 exists: A B C D G

3 145 There are too many cases to check for sufficiency, but must simply notice that it is not possible to come up with counter examples Case 4: SCT eliminates D as possibly sufficient for G But: the SCT can inductively support the inference that something is sufficient for G. If The Necessary Condition Test (NCT) By looking at specific cases, we can gather evidence about whether something is (or not) a necessary condition for something else If feature F is absent when feature G is present, then F is eliminated as possible necessary condition for G e.g. Look at where the target condition IS present Case 1: A B C D G : irrelevant, no possible violation of NCT Case 2: A B C D G : NCT eliminates A as possibly necessary for G Case 3: A B C D G: NCT eliminates B and D as possibly necessary for G Does it follow that C is necessary for G? not necessarily Case 4: A B C D G o NCT eliminates C as possibly necessary for G BUT: the NCT can inductively support the inference that something is necessary for G. if we never are able to eliminate a condition via NCT, there are inductive grounds for thinking it is necessary for G *as long as no counter example, have good proof that generalization is true * Note: if C is necessary for G, Using SCT to reach positive conclusion To infer that C is sufficient for G [for all x : (C x) Gx)]. We must give conclusion plenty of chance to be falsified SCT to generalization 1. Test cases where C is present 2. Test Cases where G is absent 3. Fail to find any case where C is present and G is absent 4. Test enough cases of various kinds that would be likeliest to include a case where C is present and G is absent *condition 4 relies heavily on background knowledge : look for counter examples of where they would be the most likely to arise*

4 145 Using NCT to reach positive conclusion To infer that C is necessary for G [for all x: (Gx)Cx)], we must give conclusion plenty of chance to be falsified SCT to Generalize 1. Test cases where C is absent 2. Test cases where G is present 3. Fail to find any case where C is absent and G is present 4. Test enough cases of various kinds that would be likeliest to include a case where C is absent and G is present *condition 4 relies heavily on background knowledge: look for counter examples of where they would be the most likely to arise* Combining SCT and NCT Ideally, applying SCT and NCT, will gather inductive evidence that identifies the cause behind given event Inferring Causation 1. Observation of phenomenon P requiring causal explanation 2. Use SCT and NCT to isolate some Q necessary and sufficient for P 3. Conclusion : infer that Q was causally responsible for P Such reasoning can be presented as either justificatory or explanatory Inference is defeasible at 2 steps: inferring that something is necessary/sufficient (since new cases could always arise) as well as inferring from this that it was a cause (since many conditions that are necessary/sufficient are not themselves causal) Combining results of SCT and NCT is important because: Being sufficient for something isn t nearly enough to have caused it o Causal Preemption: imagine 2 guns firing, one right after another, at same deer. Both shots are sufficient to cause death but only one does (cannot infer which bullet killed deer) Being necessary for something isn t nearly enough to have caused it

5 145 o Causal Underdetermination: being in hotel where Legionnaire s Disease originated was necessary for contracting it then. But this isn t what caused ppl to contract Legionnaire s disease (need both necessity AND SUFFICIENCY) Complication: Assuming Normality Very natural to think that striking a match causes it to light, b/c it is both necessary and sufficient for getting the match to light. But there are exceptions Not physically necessarily to strike match to light it : a match can light if surrounding environment gets hot enough Nor is it physically sufficient : match can fail to light when struck (e.g. if struck underwater) It might seem impossible to write all these exceptions into useable causal claim: match lit b/c it was struck in an environment that was (i) relatively cool, (ii) not underwater Generally, we get around this by simply assuming that conditions were normal : striking match in normal conditions is necessary and sufficient to light match Assuming normalcy introduces another point of defeasibility into our causal reasoning : conditions that are normal (and that license thinking of something as a cause) can become abnormal when further Co variation Suppose want to know whether CO2 emissions from burning of fossil fuels are causing melting of polar ice caps. Can we use NCT and SCT to guide us? NO Causal feature seems to be introduction of CO2 into atmosphere from terrestrial sources ( C ), while target feature seems to partial melting of polar ice caps (M) Testing whether C is necessary for M (NCT) requires looking at cases where C. but never observe such cases there is always introduction of CO2 into atmosphere from terrestrial sources. Testing whether C is sufficient for M (with SCT) requires looking at cases where M is absent. But can never observe such cases every summer, polar ice caps melt significantly NCT and SCT are not well suited to cases like this. Instead we need tests that track whether w/ abundance of causal feature co varies (is correlated) w/ target feature Method of Co Variation Q1 : does change (+/ ) in the causal feature C imply change (+/ ) in target feature G?

6 145 Q2: does change (+/ ) in target feature G imply change (+/ ) in causal feature C? Yes answers to both questions will often inductively support concluding that a change (+/ ) in C is cause of change (+/ ) in G Co variation and Causation Important to note that changes in C can be very highly correlated w/ changes in G without there being any causal relationship b/w them. Co variation does not imply causation For one, co variation is symmetric: A co varies w/ B iff B co varies w/ A. but causation is non symmetric : if A is cause of B, then B cannot be cause of A o Correlation is symmetric For two, co variation between A and B if often explained by fact that both A and B have common cause, while A and B have no causal relationship to one another Last, co variation is sometimes accidental (for e.g. causes of autism Background Knowledge Need extensive background knowledge to disentangle co variation from causation: method of co variation is good way to discover potential causal connections, but further investigation is generally needed to identify a causal mechanism.

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