Explanation

• Explanation: Answers to ‘why’ questions

• Beliefs are often justified because they help explain our experience.

• What kinds of explanation are there?

• saying how something is the consequence of more general facts (deductive)

• stating the causes of an event (causal)

• stating the purpose of an event (teleological)

Causal explanation• Generally, we're interested in stating the necessary (not

sufficient) conditions of an event

• Note:

• necessary conditions must obtain (but don't guarantee the result)

• sufficient conditions together guarantee a result (although they might not have to obtain).

• E.g.,

• The vase broke because I knocked off the table

• The vase broke because I hit it with a hammer (it’s glass, I hit it hard, …)

Evaluating causal explanations

• Usually, causal explanation is about constructing an 'abductive' argument (aka Inference to the Best Explanation, IBE)

• These are of the form (non-deductive/invalid):

• One observes O

• E is part of the best explanation for O

• Therefore, E.

• E.g.: I see a broken vase and small, muddy feline like foot prints nearby. My cat breaking the vase is part of the best explanation for it being broken. Therefore, my cat broke the vase.

Observation

• What counts as an observation is relative to context.

• The context is generally determined by what we permit ourselves to take for granted (which can easily vary).

• So, we must agree on what the observations are before trying to compare explanations of the phenomena.

Finding the best explanation

• Determining which explanation is the best can be quite difficult.

• Generally we should prefer:

• explanations that rely on already widely established theories

• explanations that specific (hence more evaluable)

• Often the best explanation will come from/be part of the best established theory (we will return to this later).

Induction• Also very common in science

• Of the form:

• All observed A are B

• Therefore all A are B.

• E.g.,

• All observed crows are black

• Therefore all crows are black

U of Waterloo

Example: Inductive failure• All observed philosophy professors are at UW

• Therefore all philosophy professors are at UW

Induction (cont.)

• How do we know the argument form isn't deductively valid?

• Determining when it is justified can be done by considering it as we have considered cases of abduction.

• Suppose we identify the implicit premise:

• E is part of the best explanation for the first premise [where E=All A are B]

• What do we have?

• abduction (i.e., IBE!)

Induction (cont.)

• The main determinant of the goodness of E will be how the statistics are collected (a later topic)

• In particular, E should reflect a good sampling of the relevant target population (e.g., ‘florks are white’ vs. ‘florks have livers’)

• Given this characterization of induction, we know that we can evaluate such arguments in the same way we evaluate abductions (IBE).

• Much of the latter part of the course is about how to evaluate IBE, because it is about how to evaluate theories.

Three kinds of argument• Deduction

• All balls from this bag are red• These balls are from this bag. • Therefore, these balls are red.

• Abduction• All balls from this bag are red• These balls are red. • Therefore, these balls are from this bag.

• Induction• These balls are from this bag. (& these balls, …)• These balls are red• Therefore, all balls from this bag are red.

Analogy

• Example: Electrons are to their nuclei as planets are to their sun.

• Uses: discovery (Eureka!), explanation, argument

Source(analog)

Target(principle subj. matter)

orbit (S1, S2) orbit (T1, T2)

S1: planets T1: electrons

S2: sun T2: nucleus

 

Analogy (cont.)

• Example (Vitruvius): Voice is a flowing breath of air, perceptible to the hearing by contact. It moves in an endless number of circular rounds, like the innumerably increasing circular waves which appear when a stone is thrown into smooth water, and which keep spreading indefinitely from the center unless interrupted by narrow limits, or by some obstruction which prevents such waves from reaching their end in due formation. When they are interrupted by obstructions, the first waves, flowing back, break up the formation of those that follow. In the same manner the voice executes its movements in concentric circles; but while in the case of water the circles move horizontally on a plane surface, the voice not only proceeds horizontally but also ascends vertically by regular stages. (Holyoak and Thagard, 1995)

Analogy as argument

• Formal: Construct an analogy with the same formal structure in source and target to show the strength/weakness of the target.

• Example:

• (Target) If I spend my money then I will have nothing in my bank account. I didn't spend any money so I still have something in my bank account.

• (Source) If I get drunk then I will fall over. But I didn't get drunk so I won't fall over.

Analogy as argument

• Informal: Rhetorical motivation for hypothesis/formal argument.

• Example: The way I look at it, the liver is like a muscle. Just as you keep a muscle in shape by exercising it, you need to exercise your liver by drinking an ample quantity of alcoholic beverages.

• Logical Form (modus ponens):

• (P1) A->B (general principle: e.g. if you want healthy organs, use them)

• (P2) A (target: e.g. you want a healthy liver)

• (C) B (conclusion: e.g. use your liver by drinking)

Analogy as argument• Sometimes the analogy can obscure the deduction.

• [S]uppose I had found a watch upon the ground, and it should be inquired how the watch happened to be in that place (...) There must have existed, at some time, and at some place or other, an artificer or artificers, who formed [the watch] for the purpose which we find it actually to answer; who comprehended its construction, and designed its use. (...) Every indication of contrivance, every manifestation of design, which existed in the watch, exists in the works of nature (…) The marks of design are too strong to be gotten over. Design must have had a designer. That designer must have been a person. That person is God."

• William Paley, Natural Theology (1802)

• The analogy only supports the weaker conclusion that there is some designer or other.

Analogy as argument • Form:

• (1) Like A, most things with P1-Pn and have G (connecting principle).

• (2) B is like A (in having P1-Pn).

• (C) B has G.

• Sometimes the general/connecting principle (1) is not easy to state and becomes:

• (1) A has G.

• In such cases, (2) often becomes more of the form:

• (2) B is like A in ways that are relevant to having G.

Analogy as argument • Example (Franklin): Electrical fluid agrees with lightning in

these particulars: 1. Giving light. 2. Colour of the light. 3. Crooked direction. 4. Swift motion. 5. Being conducted by metals. 6. Crack or noise in exploding. 7. Subsisting in water or ice. 8. Rending bodies it passes through. 9. Destroying animals. 10. Melting metals. 11. Firing inflammable substances. 12. Sulfureous smell. -the electric fluid is attracted by points. -we do not know whether this property is in lightning. -but since they agreed in all the particulars wherein we can already compare them, is it not probable they agree likewise in this? Let the experiment be made.

• Note that there are no claims regarding ‘relevant similarity’. We have to judge relevance for ourselves.

Evaluating analogies

• Irrelevant analogies are bad analogies

• Example: Electricity and lightning produce light, are attracted by points, etc. Lightning is only produced when there are clouds so electricity is only produced when there are clouds.

Criticizing analogies

• Formulate the connection principle and evaluate the logical form of the argument.

• Otherwise,

• Determine what (and how many) properties are being mapped and whether these are likely to be relevant to the conclusion that is drawn.

• Otherwise,

• Construct a disanalogy

Criticizing analogies

• Example: [Kao-Tzu suggests making morality out of human nature is like making cups and bowls out of the willow] "Can you," said Mencius, "make cups and bowls by following the nature of the willow? Or must you mutilate the willow before you can make it into cups and bowls? If you have to mutilate the willow to make it into cups and bowls, must you, then, also mutilate a man to make him moral? Surely it will be these words of yours men in the world will follow in bringing disaster upon morality."

Causal reasoning• We can characterize causal arguments as 'double'

abduction (IBE).

• These arguments are of the form:

• P1: Observed A and B are correlated

• P2: C1 is part of the best explanation for P1

• C1: Therefore, A and B are generally correlated

• P3: C2 is part of the best explanation for C1

• C2: Therefore, events of kind A cause events of kind B

• P1, P2, and C1 form the first abduction and C1, P3, and C2 form the second abduction.

Causal conclusions (cont.)• P1: In most cases when I turn my key (A) my car starts (B).

• P2: Turning my key being generally correlated with my car starting is part of the best explanation for those observations

• C1: Therefore, turning my key is generally correlated with my car starting

• P3: That turning my key causes my car to start is the best explanation for that correlation

• C2: Therefore turning my key causes my car to start

Causal explanation (cont.)• However, Correlation ≠ Causation:

• P1: In most cases when I have lunch (A) the peace tower bells ring (B).

• P2: My having lunch being generally correlated with the ringing bells is part of the BE

• C1: Therefore, my having lunch is generally correlated with ringing bells

• P3: That my having lunch causes ringing bells is the BE

• C2: Therefore my having lunch causes ringing bells

Causal conclusions (cont.)

• Why use correlation? Because:

• Claiming that A is a cause is not the claim that A is sufficient for B, but rather that it is a necessary part of the sufficient conditions for B.

• The other conditions that make the sufficient set may vary from case to case (and we may not know what they are), we must rely on imperfect correlations to suggest when events are causally related.

Causal conclusions (cont.)• E.g., Helicobacter pylori hypothesis (Nobel Prize)

• Bacterium causes ulcers (but not in everyone all the time)

• Supported by an imperfect correlation (i.e. not everyone exposed to helicobacter gets an ulcer)

• The reason is that the remaining ‘background’ or ‘structuring’ conditions must be met as well

• They are only met in some individuals, so exposure to the bacterium only works in those cases.

• However, even in those individuals who do meet these conditions, ulcers won't appear unless they are exposed to the bacterium.

Causal conclusions (cont.)

• How can you help rule out other causes?

• “in the lab”, i.e., perform controlled experiments (we will talk about these in detail two classes from now).

• Criticizing such causal arguments is much like criticizing abduction (or IBE). Except we can apply the criteria twice.

• To criticize the first premise, in particular, it is useful to understand the pitfalls of statistical data... which is a later topic

Question

• Question: