Explanations

D1. The explanandum is that which is to be explained in an explanation. D2. The explanans is that which does the explaining in an explanation. The difference between explanations and arguments Argument Explanation Reasons Explanans   Conclusion Explanandum (disputed) (not disputed)

Types of Explanation 1.Intentional explanations explain some fact about the world in terms of the beliefs and desires of some actor. (BDA psychology.) 2.Functional explanations explain things in terms of the ends which those things are supposed to serve. 3.Causal explanations explain things in terms of the things which cause them.

Causal explanations General principles or laws Explanans Initial conditions Phenomenon to be explained Explanandum

Example I find my pet dog dead in the yard, and testing reveals the presence of funnel-web spider venom in the dog’s blood. I then explain the dog's death by saying it was bitten by a funnel- web spider, which, in conjunction with general principles about the effects of toxins on dogs logically points to the dog’s death. Causal generalisation Any dog dies if bitten by a funnel-web Initial conditions My dog has been bitten by a funnel-web Phenomenon to be explained My dog has died

Example I find my pet dog being bitten by a funnel-web spider, and then predict the dog’s death. Causal generalisation Any dog dies if bitten by a funnel-web Initial conditions My dog has been bitten by a funnel-web Phenomenon predicted My dog will die

D3. Causal generalisations are general conditionals asserting a causal relationship between events. Example Consider the causal generalisation above: ‘Any dog dies if bitten by a funnel-web’. It is of the form: ‘For any x, if x is a dog bitten by a funnel-web, then x is a dog that will die’ or, in more English form, ‘For anything, if it is a dog bitten by a funnel-web, then it is a dog that will die’ So: – it is a general conditional (‘For any x, if x is an F then x is a G’) – that asserts a causal relationship (as opposed to, say, a mathematical or legal one) – between events (the event of a dog’s being bitten and the event of its dying).

A common use of the conditional which has causal implications is something like: If air is removed from a solid closed container, the container will weigh less than it did the cause of the weight-loss is the removal of air. By contrast If a shape is a square then it is a rectangle There is no causal connection, but rather a definitional connection.

Suppose we do have a causal generalisation: For any x, if x is an F then x is a G Then we can say that x’s having feature F is a causally sufficient condition for its having feature G and x's having feature G is a causally necessary condition for its having feature F. Example A dog's being bitten by a funnel-web is a causally sufficient condition for its dying. Its dying is a causally necessary condition of its being bitten by a funnel-web.

D4.A is said to be a sufficient condition for B just in case, if A is true then B is true as well. If A then B  sufficient condition for B Example If Phil is a wombat then he is a mammal. So, being a wombat is a sufficient condition for being mammal.

D5.A is said to be a necessary condition for B just in case B is true only if A is true. If B then A  necessary condition for B Example An argument is sound only if it is valid; if it is not valid then it is not sound; if it is sound then it is valid. So, being a valid argument is a necessary condition for being a sound argument.

Equivalent Statements StatementForm If that is a square then it is a rectangle. If A then B That is a square only if it is a rectangle. A only if B That is not a square unless it is a rectangle. Not-A unless B If that is not a rectangle then that is not a square. If not-B then not-A `

They all amount to claiming: Being a square is sufficient for being a rectangle. A is sufficient for B and Being a rectangle is necessary for being a square. B is necessary for A.

Biconditionals If A is a sufficient condition for B then it is true that: If A then B – which is to say – B, if A. If A is also necessary for B then it is true that: If B then A – which is to say – B only if A So, to say that A is both necessary and sufficient for B amounts to claiming: B if A and B only if A, or B if and only if A (Sometimes abbreviated to ‘B iff A’) Biconditionals give necessary and sufficient conditions

Example Consider the following definition using a biconditional: An object is a square if and only if (i) it is a rectangle & (ii) it has sides of equal length It states that: (a) An object is a square only if (i), it is a rectangle. Which is the same as saying If an object is a square then it is a rectangle. and An object is a square only if (ii), it has sides of equal length. Which is the same as saying If an object is a square then it has sides of equal length. So each of (i) and (ii) independently is necessary for being a square (b) If both (i), an object is a rectangle, and (ii), it has sides of equal length, then the object is a square. So (i) and (ii) jointly (though not separately) are sufficient for being a square.

The Hypothetico-Deductive Method a. Invent an hypothesis to explain a fact. b. Deduce testable consequences of the hypothesis. c. Test whether those consequences are true. d. Confirm or disconfirm the hypothesis. If the consequences that were derived from the hypothesis are observed in the test then the hypothesis is confirmed. If they are not observed then the hypothesis is disconfirmed. A. If H is true then A + A ↓ H is confirmed B. If H is true then A + not A ↓ H is disconfirmed

Fallacies in Explanatory Reasoning Confusing Confirmation and Proof Proposing an Unfalsifiable Hypothesis Example Since no state of affairs that could possibly obtain in the world is ruled out by the explanation via God’s intention, it does not tell us anything about the world as it actually is. Example Since no form of human behaviour that could possibly occur in the world is ruled out by the explanation via Freud’s psychology, it does not tell us anything about the human behaviour as it actually is.

Mill’s Methods The Sufficient-Condition Test SCT: Any candidate condition that is present when condition G is absent is eliminated as a possible sufficient condition of G. (From Mill’s Method of Agreement.) Example Table I Student 1 A B C DSick (G) Student 2~A B C~D~Sick (~G) Student 3 A~B~C~D~Sick (~G) But we might find a fourth student who ate Dumplings without getting sick. Something like this: Student 4 ? ?? D~Sick (~G)

Mill’s Methods The Necessary-Condition Test NCT: Any candidate condition that is absent when condition G is present is eliminated as a possible necessary condition of G. (From Mill’s Method of Difference.) Example Table II Student 1 A BC D~Sick (~G) Student 2~A BC DSick (G) Student 3 A~BC~DSick (G)

What the Tests Show From Table I, D is a causally sufficient condition for G; that is: Anyone who ate D got sick (G) Perhaps D is also a causally necessary condition for G: Anyone who got sick ate D So: i.These are general causal conditionals ii.Inductive arguments. iii.weak inductive arguments From Table II we might conclude that C was a causally necessary condition for G Anyone who got sick (G) ate C Again though, the conclusion is weak and we would need further data to strengthen it.

a. is a merely causally sufficient condition the cause? Example A hammer hitting a glass window is a causally sufficient (but not causally necessary) condition for the glass to break and it would be cited as the cause. b. Is a merely a causally necessary condition the cause? Example Sometimes we will cite a spark as the cause of fire (it is a causally necessary but not causally sufficient condition) but not the presence of oxygen (which is also a causally necessary but not a causally sufficient condition). Example Sometimes we will cite the presence of oxygen, but not other contributing factors. (For example, if magnesium is glowing red-hot in an oxygen-free environment and oxygen is suddenly introduced.) c. Is the necessary condition whose presence triggers the event the cause? Example The sudden presence of a spark in the presence of background necessary conditions … like the presence of oxygen.

Mill’s Methods The Method of Concomitant Variation (i) F is positively correlated with a G iff (a) increases in F are accompanied by increases in G & (b) decreases in F are accompanied by decreases in G. Example The presence of money in my pocket is positively correlated with the presence of smiles on my face. (ii) F is negatively correlated with G iff (a) increases in F are accompanied by decreases in G & (b) decreases in F are accompanied by increases in G. Example The presence of alcohol in the blood is negatively correlated with driver ability.

In the case of (i) increases in the presence of money in my pocket cause me to smile, and decreases in its presence cause decreased smiling. Similarly, in the case of (ii) increases in the presence of alcohol in the blood cause decreased driver ability, and decreases cause increased driver ability.

Fallacies in Causal Reasoning Confusing correlation and cause (which may be due to:) Coincidence Symmetry A common cause Reflexivity Insignificance

Fallacies in Causal Reasoning ‘Post hoc ergo propter hoc’ = After this therefore because of this

Evaluating Causal Reasoning Plausibility. How likely is it that the explanans will be true? Power. Can the explanans actually cause the explanandum? Relevance. Is the explanas relevant to the problem? Simplicity. ( Should ‘Occam’s Razor’ be wielded?) Generality. Do we then understand many other facts about the world? Modesty. Does it require we revise too much?