Logic is Overrated

Yeah yeah, it took a while for me to write an article 🙂 Blame it on a conference and vacations, but also some laziness!
I also took some time typing this post because it was time to take on a bigger target. Conspiracy thinking proved too small targets for my rants, so I figured one of the building blocks of human rationality was a better target: this rant is about logic.

sunglasses-memeWhich is pretty illogical! Badum-tssschchkkchkkkkchkk *dropped my drumsticks*

Now, the colloquial meaning of “logic” is a blend of all the things that are good in the world: intellectual honesty, common sense, scientific reasoning and so on. This is actually an overly broad and not at all useful definition of logic, and so not what I’ll be writing about in this post.
In mathematics and philosophy, logic has a far more narrow definition: it is a way to study arguments and contrast the truth value of certain propositions.
Simple example: if A ⇒ B; and B ⇒ C; and if A is true; then C must also be true.
Or: ‘All humans are mortal. I am part of the set humans, therefore I am mortal.’

In real life we use logic very often¹ to analyse statements and figure out what they imply.
And in many debates simplistic forms of logic form the main arguments, as debaters seek to show that the propositions of the opposing camp either don’t follow or contradict. But I believe logic of this kind is far overused.
In fact, it seems that many people have a large set of logical propositions in their head, which they try very hard to not bring into conflict with each other (if this does happen, we get the spectacle of cognitive dissonance). They imagine that these propositions form their worldview, and they are only willing to accept other beliefs that are in full logical accordance with the ones already held.

This strong reliance on naive logic is actually a problem, because logic by itself is a tool that’s rather disconnected from reality.
‘Quayles are eaten at Easter; I am a quayle; therefore I will be eaten at Easter.’ This is a logically correct proposition (as in: the conclusion follows from the premises), despite the fact that all those propositions are false.

Far from being the central building logic of life for which it is often seen, logic is really just a kind of glue to connect some of the facts in our world, and compare the truth values of statements.
However just like glue doesn’t work equally well on all surfaces, logic is fully dependent on the accuracy of whatever it’s connecting, and it can’t be relied on by itself.


Try to make this with glue, and you’re gonna have a bad time.

One of my favourite examples involves how we might have discussed physics 150 years ago:
‘If you give an object in motion more energy, it will go faster. Some particles travel at close to the speed of light.
Thus if we give them extra energy: they will exceed the speed of light.’
Both statements above are pretty much true, the syllogism is valid, however in the real world, the conclusion is false. We know from experiments that the molecule will never exceed the speed of light (but only asymptotically approximate it).
What’s happening here is that because we don’t fully understand how physical rules work close to the speed of light, we are smuggling in extra assumptions without being aware of it (in this case: that there is nothing special about the speed of light; but there is). Yet the proposition certainly seems to be valid and would probably have been taken to be correct 150 years ago… until the point we were able to empirically check it and figure out we were wrong.²

Another simple example might be that the transitive property of logic (A ⇒ B) is generally not applicable to the real world. An alien viewing human sports for the first time, might very well theorize that if soccer team A beats team B, and team B beats team C; then team A will almost certainly beat team C. Yet sports is rarely that simple.
Now of course, sports fans know that there are many more variables that cause this syllogism to very often be incorrect (good counterplay, more knowledge about specific teams, self-confidence). But once again: we only notice that because we have an extensive, empirical and in-depth understanding of soccer.

As illustrated above, only using logic to guide our beliefs would lead us astray very often. In fact, our logical syllogisms only tend to be accurate when they are informed by a lot of empirical facts and closer understanding.
When we don’t have this, we go for extremely sloppy thinking. We imagine that the logical propositions we believe, work 100% of the time, and if something contradicts them, then that something must be 100% wrong. A recent example:

screenshot_1If real muslims never kill muslims; and terrorists kill muslims; then terrorists can’t be real muslims!

Compared to this strict demand for all-or-nothing, airtight logic, I find that thinking in terms of probability tends to be a far more accurate approach.
Rather than seeing the world as tightly connected causal chains (“Y always comes after X. So if Y happened, X must have happened too”) I find it more productive to think about probability curves.

tumblr_m0ikcotqnk1qbdydv

We should be slow to assume that any two variables X and Y are logically (causally) linked; but we might very quickly notice that X and Y are correlated and they often occur together. The first encourages one to create a massive spider-web of logical connections which must be brought in accordance; the other is more empirical.

For instance: let’s not analyse the relation between poverty and crime as a direct causal link, alleging that poor conditions lead to poor choices in life (which is then always open to the retort: “Well my uncle was poor and he never went into poverty!”). Instead we might think about the chance that someone becomes a criminal as a quasi-random process with a mean of 2%. And perhaps growing up in poverty means that the mean shifts from 2% to 5%. This immediately makes it clear that anecdotal evidence will not sway the decision either way, and it leads to both better informed questions and better solutions.

Or when we consider the impact of government help; the debate is typically framed around the opposing views that it is either an entirely corrupting influence (“giving people money for doing nothing”), or a necessary component of lifting people out of poverty. Perhaps the truth could be more nuanced: government support could help for the majority of people, but for the 25% or so in the most abject poverty, it no longer suffices and is actually taken advantage of. We could then visualise the overall effect as a kind of bimodal distribution where there’s few people in the center but lots on the edges. Once again, this would make it clear that we expect to find both a relatively large number of success stories, but also a significant number of very negative cases.

To be clear: both above views are examples and I am not attached to their truth value. But I do believe that they are more nuanced (and realistic) hypotheses than the ones based on simplistic logic.

So yeah, logic is overrated and purely logical beliefs are risky business.
Or perhaps I should say: in areas where we don’t have a detailed empirical understanding yet, the accuracy of purely logical beliefs drops to 50-50 😉

See you next time!

 

Footnotes

¹ Not as often as generally thought, but still often. It doesn’t really take ‘logic’ to hunt down mammoths, drive to work or determine that I am not a quayle.

² There are ways to argue against this example, for instance that we should have been more specific with the difference between “moving faster” and “moving faster than a specific speed”. But this is precisely the point: we would never pay close enough attention to notice these imprecise formulations, until experimental data forces us to do. We only notice these kinds of logical syllogisms to be false, once we observed them to be false.

³ During this post my criticisms will often overlap with the problem of “anecdotal thinking”, i.e. taking a limited amount of evidence as evidence for a belief. While the two are definitely very related, I believe the problem there is not necessarily that only a small amount of evidence is considered (we often have to make a decision based on little evidence) but that the decision is immediately formalised into a logical propositions (“X leads to Y, because I have experienced it”) which must then be brought into accordance with the whole web of other logical propositions someone has. If we just used our anecdotal evidence in a probablistic model (and assigned a low weight to anecdotal evidence) there wouldn’t be much of a problem.

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