Anti-Inductive Logic
As part of my continuing interest in logic, here’s a rather curious result.
Some of you are probably familiar with so-called “inductive logic”, which is usually framed more or less as something like:
If something is true for the first n instances, then it is true for the n+1 th instance.
Now, such a rule cannot be part of a formal deductive system of logic, because there are clearly counterexamples; just because something is true for the first few instances, doesn’t mean that it must be true for all of them.
Nevertheless, inductive logic does serve as a useful “logical heuristic” of sorts; for example,
For the past 4 billion years in the existence of earth, the sun has risen and set every day without fail. Therefore, it will rise and set tomorrow.
While not exactly sound deductive reasoning, it works relatively well.
However, since we’re abandoning formality, we might as well try a new, different inductive rule, which I refer to as “Anti-Inductive Logic”:
If something is true for the first n instances, then it is false for the n+1 th instance.
While this may seem odd (and blatantly incorrect), it’s not entirely unworkable; in one sense, it’s loosely related to the Gambler’s Fallacy:
The result of 1000 flips of an unbiased coin is 1000 heads. Therefore, the next flip will result in a tails.
A rather curious fact about Anti-Inductive Logic is that, to a certain extent, it is self consistent. (Again, technically, if we were working in a formal system of logic, it is not consistent, but we’re not considering formal systems right now)
Consider walking up to a practitioner of Anti-Inductive Logic, who claims the following:
For the past 4 billion years in the existence of earth, the sun has risen and set every day without fail. Therefore, it will not rise and set tomorrow.
In an effort to convince the poor soul that his Anti-Inductive Logic has led him astray, we might argue:
For the past 4 billion years, since the sun first rose and set on earth, Anti-Inductive Logic has predicted that the sun will not rise and set the next day. Therefore, for every day in the past 4 billion years, Anti-Inductive Logic has been incorrect.
Unfortunately, without regular inductive logic, the poor soul is forced to conclude:
For the past 4 billion years, Anti-Inductive Logic has not worked once in predicting whether the sun will rise or set the following day. Therefore, Anti-Inductive Logic will correctly predict whether the sun will rise and set tomorrow.
And we are forced into an endless loop, until someone actually manages to introduce formal deductive logic into the discussion. Or perhaps encourage the poor soul to run for political office.
Note: I’m not entirely sure if this was a completely original idea, or whether I read something similar somewhere – if you know this result from elsewhere, please comment below! Thanks.
Ants
Some of you might know of my continuing defense against ant invaders.
Now, at least the ants around here are relatively friendly, but for their sake, it’s better if they stay outside in the sunny Southern California weather. Nevertheless, they rather enjoy the indoor life: the shade, the water, and the sleeping late in bed.
Sure enough, they love my bed, particularly the pillow. They sometimes go after water I leave nearby (if they’re thirsty) but for the most part they just hang out on the bed. They’re nice enough to get in while I’m away during the day, but then they don’t like to be deported later.
Where they come from is a bit of a mystery, since I can’t seem to find any elsewhere in the room. They’re crawling in somewhere, for sure, but the lack of evidence is currently stalling the investigation.
So needless to say I wasn’t pleased to discover that apparently, moving in to my bed was just part of the greater international conspiracy:
BBC News: Ant mega-colony takes over world
In Europe, one vast colony of Argentine ants is thought to stretch for 6,000km (3,700 miles) along the Mediterranean coast, while another in the US, known as the ‘Californian large’, extends over 900km (560 miles) along the coast of California. A third huge colony exists on the west coast of Japan.
So really, I just ought to be happy they only asked to borrow the bed.