Sloping Burdens

Over at Brainstab we’ve been having a bit of a debate on the nature of certain slippery slope arguments. The slippery slope argument is one of those ‘sometimes fallacious’ lines of reasoning. The actual structure of a slippery slope is what is called an hypothetical syllogism (or chain argument) which looks like:

P1. If A then B
P2. If B then C
Therefore,
C. If A then C

It is a perfectly valid argument form, but that doesn’t mean much at all, because the premises themselves can be implausible, such as this example shows:

Socrates is a man. Now if Socrates is a man then he is mortal, and we know that if you are mortal you are a manticore. Thus we can safely say that Socrates is a manticore.

I don’t think I need to say much more on that.

Slippery slopes are troublesome for another reason aside from premise plausibility, and that reason is that probabilistic conditional statements such as ‘If A occurs then it is likely B will occur as well’ carry. Each premise of the chain argument can have high probability even though the conclusion might not. Suppose the first premise says:

If condition 1 holds, then condition 2 holds

has 80% chance of being true. and suppose that the second premise says:

If condition 2 holds, then condition 3 holds

which also has 80% chance of being true, then if you conclude from just

If condition 1 holds, then condition 3 holds

you are committed to believing something which has only 64% chance of being true.

All of which brings me to Conspiracy Theories, in two related parts.

The first is the use of chain arguments. Chain arguments are often used to describe causal sequences (one action leading to another to another, thus resulting in the end of the American Way, et al). The issue of whether History is best described as causal sequences, lawlike situations or intentional descriptions is a matter best left to another time, but causal sequences can be, at worst, a useful kind of shortcut to show how we think the actions of individuals and groups relate to other actions or events. Thus when we say that the earthquake caused the humanitarian disaster we are saying something like ‘If a natural disaster occurs in a situation where the local government is unprepared, then a humanitarian disaster will occur.’ Conspiracy Theories use such sequences all the time. However the problem that often occurs in these situations is that the causal sequence is implausible. Take, for example, the 911 Truth Movement claim that the Twin Towers collapsed in the manner of a controlled demolition, which can be construed as:

If the towers fell in the way described, then the destruction of the towers was a controlled demolition

The statement itself has a fine logical form: If A then B, but the premise should not be taken as being immediately plausible. Sure, the towers’ fall did look like a good example of how a controlled demolition would run, but there are two things to note. Just because the towers fell in a particular way doesn’t tell you that they fell that way for one particular reason. A statement of the form ‘If A, then B’ can be separated into two smaller statements, the antecedent and the consequent. The antecedent is the event you put forward as being causal of the next event, or consequent (see how that works?). Still, just because A follows B doesn’t mean that we know all that much. Let me explain via example:

If it has been raining then the car will be wet

If we know that the antecedent is true then we know that the consequent is true, but if we know that the consequent is true… Well, we don’t know much more than that the consequent is true. The car could be wet for a whole host of reasons other than the presence of rain. It’s a bit like finding a brick in your living room and a shattered window. Sure, the brick might have come through the window, but you can’t be guaranteed of this information unless you have supporting evidence.

Secondly, the link between the two events, the towers’ fall and the reason as to why they fell that way has a long causal story to it, so even if you do think it seems likely that the tower fell by controlled demolition you need further supporting evidence, which gets me to point two, probability.

Recall the discussion of probability that I ran before; every piece of probability effects the next probabilistic statement that is made. Once you explicate the causal sequence it can turn out that no matter how logically possible the sequence is the likelihood of it working out could be low.

Food for thought.

I have another thought and it isn’t as relevant as I thought it was when I started this post. It’s on the burden of proof. Conspiracy Theories tend (depending on how you take the term ‘theory’) to go against the official (usually consensus) view and thus the burden of proof is on the conspiracy theorist. Still, if the evidence is good then you should always follow that; it’s just that when it isn’t (i.e. it doesn’t decide between hypotheses) the burden of proof gives you a reason to take one side or the other. Climate Change Skepticism is a good example here; even if, in the worse scenario, you think that the evidence doesn’t decide either way then the burden of proof dictates that in a matter of public health and safety (as, arguably, the thesis of Climate Change belongs to or affects) you act as if Climate Change is occurring because, well, it is the safest option (acting as if it is not in a situation where it might be only makes things worse whilst acting as if it is occurring where it might not be only seems to reduce the number of luxuries you have).

Yeah, it seemed more relevant earlier this afternoon.

Night night.