Introduction

In this course we have seen how arguments may be considered, very roughly speaking, as a series of statements that are intended to justify some disputed statement. It is said that there are other uses for arguments – as excuses or refutations or confirmations or what have you – but all those other uses of arguments are probably best looked at as derivative from this primary usage, and most of them don’t need to be looked at any further than that. There is, however, another attitude that we can take towards the conclusion of an argument which gives rise to a form of argument (in some people’s view) which is really quite distinct. What I have in mind is the class of explanatory arguments – or explanations.

I have mentioned several times in the course of these lectures that explanations are closely related to arguments: they often have the same structure and employ many of the same techniques. But explanations, when they are called for, are requested to explain why some state of affairs is the case, not to convince that some situation is the case; and, consequently, in explanatory arguments it is a description of the state of affairs that occupies the place of the target proposition.

For example, if one asks why some computer is not working, in the context it is assumed that the computer does not work and we are seeking some account or explanation of this fact which, in the context, is uncontested or accepted. We are, therefore, not seeking to justify the phenomenon in question (e.g. the malfunctioning of the computer), we are seeking reasons for it that will shed light on it. One way in which reasons might be offered and light shed is by way of argument. We offer reasons to explain an accepted state of affairs by constructing an argument which has a description of the state of affairs as its conclusion, and the reasons as premises of the argument. Thus we might say that the computer is malfunctioning because it is not plugged in and without power such machinery will not work. This use of the connective ‘because’ indicates the presence of an argument, but in the context it cannot be considered a justificatory argument since, in the context, the conclusion is not in dispute. We are dealing with an explanatory use of the term 'because'.

As explanatory arguments – arguments used to provide explanations, to explain why some accepted fact or event has occurred – seem quite distinct from other forms of arguments, it is normal to use a special vocabulary when talking about them. And I’m going to start by saying that from now on I’m going to go back to talking consistently about justificatory arguments as just plain arguments and about explanatory arguments as just plain 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 can be diagrammatically represented thus:

                                Argument                                                              Explanation

                                Reasons                                                                 Explanans

                            ß                                                             ß

                                Conclusion                                                            Explanandum

                                (disputed)                                                              (not disputed)

Causal Explanations

There are several 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 are by far the most important. Just what justifies us in calling something a/the ‘cause’ of something else is an ongoing philosophical problem that we can’t dwell too much on here. Let’s just take it for granted that we can say that event A is the cause of event B in the real world if in any possible world where everything is the same as it is in the real world except that A does not occur, then B does not occur in that world.

Such arguments are often said to proceed from the explanans consisting of general principles or laws and initial conditions to the phenomenon to be explained, the explanandum. That is, they are often seen as instantiating the following form:

                General principles or laws                                                   }Explanans

                Initial conditions                                                                  }                                             

                -----------------------------------                                 -----------------

                Phenomenon to be explained                                             Explanandum

Given this form of explanation it’s clear that an important part of the search for an explanation of an event is going to be the search for general principles which, in conjunction with other facts, would show why it happened — these principles are causal generalisations. Later on we’ll have to look more closely at this part of the process of forming or discovering an explanation, but let’s first get an idea of the sort of thing that we’re talking about.

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.

In this example we have:

                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

It is important to note that we use the same general principles – causal generalisations – in conjunction with other facts to predict what will or may happen in relevant situations. This ability to predict is one of the criteria that we use to distinguish good explanations from not-so-good explanations. We’ll talk more about these criteria later too, but let’s see an example of it now.

Example

I find my pet dog being bitten by a funnel-web spider, and then predict the dog’s

death.

In fact the prediction of the death proceeds from the fact of the dog’s being bitten in conjunction with the causal generalisation that all dogs die when bitten by funnel-web spiders.

In this example we have:

                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

Causal Generalisations

So what are these causal generalisations? Though contested, we shall treat them in the following way.

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).

I believe I have remarked a few times that conditionals often assert causal connections. I made this point, for example, when we briefly had a look at propositional logical translations of English language sentences. The so-called material conditional, which we took to translate ‘if A then B’ was said to be true whenever A was false or B was true. But this led to peculiar results like saying that ‘if 2 + 2 = 5 then giraffes are fish’ is a true statement. The problem was that that interpretation of the conditional ignored much of the meaning that the conditional has in real language. The possibility of causal implications, for example is ignored. A more common use of the conditional which has such causal implications is something like:

If air is removed from a solid closed container, the container will weigh less than it did

In which case it is implied that the cause of the weight-loss is the removal of air.

Let me emphasise, however, that there are not always such implications. For example:

If a shape is a square then it is a rectangle

There is no causal connection being alluded to, but rather a definitional connection.

But suppose we do have a causal generalisation, for example:

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.

These are actually fairly important concepts to get straight on if we’re going to understand explanations, so let’s have a bit of a digression here.

Necessary and Sufficient Conditions

Sufficient Conditions

Necessary and sufficient conditions can be defined more generally as follows.

D4.          A is said to be a sufficient condition for B just in case, if A is true then B is true as well.

Which you may recognise as being the same as saying that it is true that if A then B. So to assert the conditional ‘If A then B’ is to claim that A is sufficient for B. So: 

  If A then B

  Ý

     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.

Necessary Conditions

D5.          A is said to be a necessary condition for B just in case B is true only if A is true.

Which, again you may recognise as being the same as saying that

B is not true if A is not true, or

If B is true then A is true, or

If B then A.

So to assert the conditional ‘If B then A’ is to claim that A is necessary for B. So

If B then A

             Ý    

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

I guess the upshot of all this is that we can identify what is being claimed as a sufficient or necessary condition for something if we can identify the conditional being asserted.

To assist in this identification, note that the following are equivalent:

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’)

Statements of this last kind — i.e. ‘... if and only if ...’ – are known as biconditionals. Biconditionals give necessary and sufficient conditions and so are often used to state the exact conditions under which something is caused or the exact definition of a concept. (Note that ‘B iff A’ means exactly the same thing as ‘A iff B’.)

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.

Summarising then, we can say that conditions (i) and (ii) are independently necessary for being a square, and are jointly sufficient for being a square.

The Hypothetico-Deductive Method

So much for the necessary and sufficient background, now let’s get back to explanations. You will recall that I said that discovering causal generalisations was an important part of the process by which we discover explanations. Well it’s now time to have a look at what sort of process I’m talking about there. Unfortunately, it’s no mechanical process like doing long division, or filling in a truth table to find out whether an argument is valid or not. There is no algorithm for discovering explanations, no infallible procedure that we can apply mindlessly. Explanations have to be invented by the ingenuity of the explainer. That is why science is an adventure with many mistakes. Nor is there an infallible procedure for deciding which explanations are good ones – as I say more on that later. Nevertheless there is a well-known general method for coming up with reasonable explanations that seems to be as good as any other, and it seems to look like what scientists or others actually do when they follow reasonable procedures to get to reasonable explanations.

This is the Hypothetico-Deductive Method. And it goes like this:

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.

Note the results of the testing have the structure (H is the hypothesis):

A.                            If H is true then A                +              A

                                                ---------------------------------------------------   

                                                                                ↓    

                                                                H is confirmed

B.                            If H is true then A                +              not A

--------------------------------------------------------

                                                                                ↓    

                                                                H is disconfirmed

In A, when H is confirmed we seem to have an example of the fallacy of affirming the consequent. But this would only be a fallacy if we were claiming that A. proves H. We are not saying that. We are only saying that H has survived a test that was intended to disprove it. The intuition is that the more of these sorts of tests that H survives the more likely it is to be true (or nearly true – whatever that means.)

In B, when H is disconfirmed we seem to have a perfectly good example of modus tollens. However, we do not generally immediately conclude that H is false, because it may be that there are plausible explanations for why the test failed in that particular case. (Perhaps we have drawn the wrong conclusions, made incorrect assumptions, gotten the hypothesis just slightly wrong, etc.) In fact there are always excuses that can be made: it is a matter of judgement whether we are to take these excuses as legitimate or not. That is why we call it a disconfirmation rather than a disproof.

Notwithstanding the cautions just mentioned, it is much more useful to seek disconfirmations than confirmations. We can never come close to proving H true but if we get enough disconfirmations we may come to be very confident that H is false.

Fallacies in Explanatory Reasoning

There are two important fallacies of explanatory reasoning whose fallaciousness this model makes clear.

Confusing Confirmation and Proof

See the discussion just above.

Proposing an Unfalsifiable Hypothesis

If H is able to explain every possible event in the world then it is not possible to come up with any testable consequences and so we can never disconfirm the hypothesis. This is not to say that only false hypotheses are good ones – the hypothesis that the Earth is round, for example, is falsifiable by trying to sail around it and falling off the edge. The hypothesis that our actions are fated to be what they are is not falsifiable at all – and therefore it can’t really be said to explain anything.

Example

This is the standard objection to explanations that invoke the agency of God. Since God (the one we usually invoke anyway) is omnipotent and omniscient and omni all other desirable things, He can be used to explain anything at all. Why is the sky blue? Because God said so. Why is there a diversity of species upon the Earth? Because God said so.  Why do chickens have four feet and a pink curly tail? Because God said so.

The last example makes it clear that 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

A more plausible example is Freudian psychology. This was once very popular but has now largely fallen out of favour. Science has its fads too. The characteristic feature of Freudian psychology was that there was no conceivable human behaviour that could not be explained by it. Do you love your mother? It is an unresolved Oedipal Complex. Do you hate your mother? It is a repressed Oedipal Complex with a touch of resentment for alienated affections. Do you neither hate nor love your mother? You are in denial. Etc.

Once again, 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.

Testing Causal Generalisations - Mill's Methods

And so we come to the problem of actually finding the causal generalisations, which, as you now see, is only a part of the whole explanation generating process – though it is an important one. How do we decide what is a reasonable hypothesis to begin the hypothetico-deductive method? Well, of course, there’s no infallible rule, but there is a set of methods invented by John Stuart Mill in his System of Logic (building on work done by the great Francis Bacon) which have proven to be quite reasonable and which are known as Mill’s Methods. We’ll have a look at some simple varieties of Mill’s methods now. Those who are keen to in look at this in more detail are referred to Mill – or to Copi.[1]

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

Suppose that some of a group of students in college have become ill after a meal and we want to test for conditions that might be causally sufficient for their apparent food poisoning so that we might thereby explain the poisoning. Three students are interviewed.

The first got sick after eating Avocadoes (A), Broccoli (B), Carrots (C) and Dumplings (D). The second didn't get sick and ate Broccoli (B), Carrots (C), no Avocadoes (~A) and no Dumplings (~D). The third didn't get sick and ate Avocadoes (A), no Broccoli (~B), no Carrots (~C) and no Dumplings (~D). See Table I below.

Applying SCT, we can eliminate – on the basis of student 2 – Broccoli and Carrots as possible sufficient conditions for the food poisoning. On the basis of student 3's testimony we can also eliminate Avocadoes.

                The only remaining possible sufficient condition is the Dumpling.

However, there may be some as yet unnoticed candidate which is another possible sufficient condition for getting sick which further cases would bring to light.. Or we might hope to find a fourth student who ate Dumplings without getting sick. Something like this:

If however no such student is found and we have reason to think that A-D are all the possible candidates for the outbreak of food poisoning then we can reasonably conclude that eating Dumplings is causally sufficient for getting food poisoning, if anything is.

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

Using another scenario like that above let us try to establish a necessary condition for getting sick. The details of the food eaten on this occasion are given below in Table II.

                Student 2 shows eating Avocadoes cannot be necessary.

                Student 3 shows eating Broccoli or Dumplings cannot be necessary.

                Now the only remaining possible necessary condition for getting sick is the eating of Carrots.

Again, so long as we have reason for thinking one of the four food-types was necessary for the illness, then we can reasonably conclude that it was probably the eating of Carrots that was causally necessary, if anything was.

What the Tests Show

From Table I we might conclude that D is a causally sufficient condition for G; that is:

Anyone who ate D got sick (G)

Notice that we might further conclude that D is also a causally necessary condition for G:

 
Anyone who got sick ate D

(However, we might subsequently find a student who did not eat the Dumplings, they only picked the Raisins out and ate them, yet they too got sick. What this would show – on the basis of the information available – is that, whilst eating the Dumplings was still a causally sufficient condition, it was not a causally necessary condition. The Necessary Condition Test would rule out dumplings as causally necessary since a sick student did not eat them. It might then be concluded that the eating of raisins, contained within the dumplings, was both a causally necessary and sufficient condition.)

So what have we got so far?

i.                     These are general causal conditionals inferred from the data presented.

ii.                    Of course these conditionals do not follow with certainty from the information and they can be undermined by subsequent information – thus, the argument for D as a causally necessary condition and the argument for D as a causally sufficient condition for G are inductive arguments.

iii.                  Notice also that they are rather weak inductive arguments – further testing of the conditions thought causally necessary and sufficient would be needed before one could be confident in the conclusions.

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.

What about causal claims we might want to make on the basis of such tests? If, after extensive testing, some event F can be reasonably said to be a causally sufficient and/or causally necessary condition for an event E would we say that it is the cause of E? There is no clear answer here, but F can reasonably be said to be causally related to E – that much is clear.

Causes are commonly considered to temporally precede (i.e. come before) their effects. So given a causally sufficient or causally necessary condition for some event, we would call it the cause of the event only if it came before the event. Also, it is typically that event or change which stands out against background conditions that we identify as the cause of an event. You can read more about this sort of thing in your text.[2]

a.                    Sometimes we call a condition that is merely a 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.                    Sometimes we call a condition that is 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.                    Usually it is that necessary condition whose presence triggers the event in question (as opposed to those necessary conditions that are more or less constant in the background) that we call the cause.

Example

The sudden presence of a spark in the presence of background necessary conditions … like the presence of oxygen.

The Method of Concomitant Variation

The previous tests enable us to eliminate certain conditions as causally necessary and others as causally sufficient. With additional premises we might then, with varying degrees of strength, argue inductively in favour of some remaining condition as causally necessary or causally sufficient. In this way we might argue inductively for particular causal claims.

Sometimes however, such tests fail us. They rely on cases where a target feature – G, say – is present or absent and other features (possible causes) are present or absent. An alternative method is required for situations in which features are always present or absent to some degree.

Such a method is The Method of Concomitant Variation.

(i)            Some feature F is positively correlated with a target feature 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)           Some feature F is negatively correlated with a target feature 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.

Suppose we observe after many trials that some feature F is positively correlated with some feature G or F is negatively correlated with a feature G. What might we conclude from such correlations?

In the case of (i) it seems a reasonable hypothesis that increases in F cause increases in G and decreases in F cause decreases in G (all other things being equal). So, in the particular example:

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), it seems reasonable to suppose that increases in F cause decreases in G and decreases in F cause increases in G (all other things being equal). So, in the particular example:

increases in the presence of alcohol in the blood cause decreased driver ability, and decreases cause increased driver ability.

These hypotheses are arrived at inductively. They are strongly suggested but not certain. They could be undermined by further evidence not yet considered.

Testing Causal Generalisations - Mill's Methods

And so we come to the problem of actually finding the causal generalisations, which, as you now see, is only a part of the whole explanation generating process – though it is an important one. How do we decide what is a reasonable hypothesis to begin the hypothetico-deductive method? Well, of course, there’s no infallible rule, but there is a set of methods invented by John Stuart Mill in his System of Logic (building on work done by the great Francis Bacon) which have proven to be quite reasonable and which are known as Mill’s Methods. We’ll have a look at some simple varieties of Mill’s methods now. Those who are keen to in look at this in more detail are referred to Mill – or to Copi.[1]

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

Suppose that some of a group of students in college have become ill after a meal and we want to test for conditions that might be causally sufficient for their apparent food poisoning so that we might thereby explain the poisoning. Three students are interviewed.

The first got sick after eating Avocadoes (A), Broccoli (B), Carrots (C) and Dumplings (D). The second didn't get sick and ate Broccoli (B), Carrots (C), no Avocadoes (~A) and no Dumplings (~D). The third didn't get sick and ate Avocadoes (A), no Broccoli (~B), no Carrots (~C) and no Dumplings (~D). See Table I below.

Applying SCT, we can eliminate – on the basis of student 2 – Broccoli and Carrots as possible sufficient conditions for the food poisoning. On the basis of student 3's testimony we can also eliminate Avocadoes.

                The only remaining possible sufficient condition is the Dumpling.

However, there may be some as yet unnoticed candidate which is another possible sufficient condition for getting sick which further cases would bring to light.. Or we might hope to find a fourth student who ate Dumplings without getting sick. Something like this:

If however no such student is found and we have reason to think that A-D are all the possible candidates for the outbreak of food poisoning then we can reasonably conclude that eating Dumplings is causally sufficient for getting food poisoning, if anything is.

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

Using another scenario like that above let us try to establish a necessary condition for getting sick. The details of the food eaten on this occasion are given below in Table II.

                Student 2 shows eating Avocadoes cannot be necessary.

                Student 3 shows eating Broccoli or Dumplings cannot be necessary.

                Now the only remaining possible necessary condition for getting sick is the eating of Carrots.

Again, so long as we have reason for thinking one of the four food-types was necessary for the illness, then we can reasonably conclude that it was probably the eating of Carrots that was causally necessary, if anything was.

What the Tests Show

From Table I we might conclude that D is a causally sufficient condition for G; that is:

Anyone who ate D got sick (G)

Notice that we might further conclude that D is also a causally necessary condition for G:

 
Anyone who got sick ate D

(However, we might subsequently find a student who did not eat the Dumplings, they only picked the Raisins out and ate them, yet they too got sick. What this would show – on the basis of the information available – is that, whilst eating the Dumplings was still a causally sufficient condition, it was not a causally necessary condition. The Necessary Condition Test would rule out dumplings as causally necessary since a sick student did not eat them. It might then be concluded that the eating of raisins, contained within the dumplings, was both a causally necessary and sufficient condition.)

So what have we got so far?

i.                     These are general causal conditionals inferred from the data presented.

ii.                    Of course these conditionals do not follow with certainty from the information and they can be undermined by subsequent information – thus, the argument for D as a causally necessary condition and the argument for D as a causally sufficient condition for G are inductive arguments.

iii.                  Notice also that they are rather weak inductive arguments – further testing of the conditions thought causally necessary and sufficient would be needed before one could be confident in the conclusions.

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.

What about causal claims we might want to make on the basis of such tests? If, after extensive testing, some event F can be reasonably said to be a causally sufficient and/or causally necessary condition for an event E would we say that it is the cause of E? There is no clear answer here, but F can reasonably be said to be causally related to E – that much is clear.

Causes are commonly considered to temporally precede (i.e. come before) their effects. So given a causally sufficient or causally necessary condition for some event, we would call it the cause of the event only if it came before the event. Also, it is typically that event or change which stands out against background conditions that we identify as the cause of an event. You can read more about this sort of thing in your text.[2]

a.                    Sometimes we call a condition that is merely a 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.                    Sometimes we call a condition that is 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.                    Usually it is that necessary condition whose presence triggers the event in question (as opposed to those necessary conditions that are more or less constant in the background) that we call the cause.

Example

The sudden presence of a spark in the presence of background necessary conditions … like the presence of oxygen.

The Method of Concomitant Variation

The previous tests enable us to eliminate certain conditions as causally necessary and others as causally sufficient. With additional premises we might then, with varying degrees of strength, argue inductively in favour of some remaining condition as causally necessary or causally sufficient. In this way we might argue inductively for particular causal claims.

Sometimes however, such tests fail us. They rely on cases where a target feature – G, say – is present or absent and other features (possible causes) are present or absent. An alternative method is required for situations in which features are always present or absent to some degree.

Such a method is The Method of Concomitant Variation.

(i)            Some feature F is positively correlated with a target feature 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)           Some feature F is negatively correlated with a target feature 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.

Suppose we observe after many trials that some feature F is positively correlated with some feature G or F is negatively correlated with a feature G. What might we conclude from such correlations?

In the case of (i) it seems a reasonable hypothesis that increases in F cause increases in G and decreases in F cause decreases in G (all other things being equal). So, in the particular example:

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), it seems reasonable to suppose that increases in F cause decreases in G and decreases in F cause increases in G (all other things being equal). So, in the particular example:

increases in the presence of alcohol in the blood cause decreased driver ability, and decreases cause increased driver ability.

These hypotheses are arrived at inductively. They are strongly suggested but not certain. They could be undermined by further evidence not yet considered.

Fallacies in Causal Reasoning

There are some common mistakes that are made in proposing causal explanations. Here are a few of the best ones:

Confusing Correlation and Cause

Take the case of the method of concomitant variations that we’ve just been looking at. The method involves going from observation of correlations to suppositions of causal relationships; but it is a fallacy to suppose too hastily or without sufficient care that if property F is observed to be correlated with property G then F is the cause of G. [cf also Currie, Intro to Phil. Course p. xiv - reasons for believing identity theory. Also recent suggestion that the negative correlation between low literacy levels and high unemployment suggests that the former causes the latter.]

Even if the correlation is strongly supported by the data, thus establishing a strong inductive argument from the data to the correlation, the move from correlation to cause can be problematic. There are many ways in which this deduction can be fallacious.

a.                    Coincidence

The correlation may be purely coincidental!

Example  

An inference from the strong positive correlation between Holland 's birthrate and the number of stork's nesting in chimneys would be fallacious.

In fact, though correlated, there is no causal connection at all it seems. The correlation appears purely accidental.

Example  

Is an inference from the strong positive correlation between an individual's level of literacy and their participation in volunteer work to a causal connection from the former to the latter fallacious or not? (In the inaugural lecture of the Keith Murdoch Oration, hosted by the State Library of Victoria, October 11, 2001, Rupert Murdoch claimed such a causal connection as part of an argument for the importance of higher education and corresponding need for increased funding. The enthymematic implication of the claimed causal connection was that higher literacy, achieved through education, causes a social good which, in conjunction with the suppressed premise that we should pursue social goods, implies that we should endeavour to increase literacy and thus ensure proper funding for education.)

b.                    Symmetry

Correlation is symmetrical – F is correlated with G if and only if G is correlated with F so the same correlation would justify the conclusion that G causes F.

Example

                Consider the positive correlation between time spent in hospital and risk of death.                                                               Does the risk cause one to spend more time in hospital or does spending more time in                                                             hospital cause an increased risk of death (due to non-treatable infections found in hospitals)?

c.                    Common cause

It may be that neither is the cause of the other, but that both are the effects of some other property H.

Example

                Does the El Nino effect cause drought in Australia or might both El Nino and drought in Australia be caused

                by some third factor? Their positive correlation does not answer this question.

                Cf interactionist dualism vs pre-established harmony parallelists on mind-body correlation.

Example

An inference from the strong positive correlation between shoe-size and quality of handwriting to some causal connection between them would be fallacious (and there is no accepted theory which would suggest such a connection). In fact they are correlated by virtue of their having a third common cause — maturity.

d.                    Reflexivity

There may be a complex causal interrelationship of F and G such that F is to some extent the cause of G and G is also the cause of F. 

Example

Is a chicken the cause of an egg, or is an egg the cause of a chicken.

There are any number of positive feedback loops in the ecology. Any one of these could probably serve as an example here.

e.                    Insignificance

The causal relation may be real but insignificant, in which case P may contribute to Q but it could not be claimed to be the cause of Q.

A similar fallacy can also arise in connection with uses of the Sufficient Condition Test and the Necessary Condition Test.

Example

Suppose (as was claimed in the Australian yesterday) that homosexual males are discovered to have a certain brain property X. Having brain-property X is a necessary and sufficient condition for being a gay male. (In this case it was found that women and homosexual men registered a reaction in the anterior hypothalamus when tested with 4, 16-androstadien-3-one, but women and heterosexual men did not.)

The mere correlation of being a homosexual male with the presence of brain-property X doesn't necessarily show that this brain property causes sexual orientation (nor has it been suggested this time). Only a correlation has been established and this might well be explained by means of something other than a causal connection between sexuality and the brain-property. It might turn out that both homosexuality and the brain-property X have a common cause in biological and environmental factors.

Post Hoc Ergo Propter Hoc

Also known as simple Post hoc. The Latin tag just means ‘After this therefore because of this.’ A fallacy of supposing that because event G follows event F in time that therefore event F causes event G. Of course, there is no such necessary connection. Although, as I said earlier, we do expect that if F is the cause of G then F will precede G temporally. Which is to say that if G precedes F we think that it is absurd to suppose that F is the cause of G. (Naturally none of this applies in advanced Physics.)

Evaluation

Bearing in mind the very different function that an explanation has from an argument, it is not surprising that the criteria which are of interest to us in evaluating the two are quite different. What makes a good explanation depends upon the particular use that the explanation is intended for, but there are two principal factors to be considered:

1.                    Plausibility. How likely is it that the explanans will be true.

2.                    Power. Can the explanans actually cause the explanandum.

These are pretty obvious criteria and don’t need too much explanation by me, but there are many other factors that should be considered in deciding whether we have a ‘good’ explanation or not. There are any number of different lists of desirable criteria, and it’s an area of ongoing dispute amongst philosophers of science, but here is a list that is taken from a well-known introductory text.[1]

3.                    Relevance. Is the explanation overly complex? We should prefer the simplest possible explanations. (Look up ‘Occam’s Razor’)

4.                    Simplicity. Is the explanation overly complex? We should prefer the simplest possible explanations. (Look up ‘Occam’s Razor’)

5.                    Generality. Can the same explanation help us to understand a wide variety of other facts about the world? The more it explains the better – but if it tries to explain everything it may end up explaining nothing. (This is the problem of ‘unfalsifiability’ we’ll talk about later.)

6.                    Modesty. Does the explanation require us to change too much of what we think we already know about the world? The less we change the better – intellectual laziness can be a virtue. Great changes require great justifications, but they are possible; for example, it has been suggested that to understand some quantum physical facts we need to change our beliefs about logic.