But Which Logic?

A coin is tossed in the air five times and each time it lands "heads" - what will happen when it is tossed the sixth time? The answer is logical isn't it? But which kind of logic? Here are some possible "logical" approaches, but they all give different answers!

Inductive Logic:

This is based on recognising patterns and then assuming that the pattern is going to continue. In this case the pattern is obvious, the coin when tossed comes down "heads"' so therefore it will probably come down "heads,'

the next time.

Inductive logic is the type of reasoning that, in spite of what Popper said, most of our scientific progress is based upon. Not only this, we tend to rely on it throughout our daily lives - when our foot hits the brake pedal we expect the car to stop, not because we understand about the levers, hydraulics and friction involved, but because it has always caused the car to stop in the past … except, of course, in those rare instances when it hasn’t. So although we can’t be certain that inductive logic will work every time, it seems to work most of the time so the coin will obviously come down "heads".

Deductive Logic:

Now deductive logic is the one that gives us certain answers based on forms of argument like the syllogism:

When an evenly weighted coin is randomly spun in the air the probability of it landing "heads" and "tails" are equal.

This coin is evenly weighted and is being randomly spun in the air.

Therefore the chances of it landing "heads" and “tails" are equal.

The result of tossing a coin does not depend in any way on the previous results – an unlikely occurrence is just made up of a chance encounter of such events, so that settles that - or does it?

A correctly reasoned syllogism only guarantees a valid answer - whether it is true or not is a very different matter. It depends on the truth of the premises. If we started with "All things with hair are monkeys” then what does that make you and me? This raises the question of how these premises are arrived at? Usually they are assumptions or they result from inductive logic, which, as we know, is never certain, so ... The strength of the deductive conclusion can be undermined by questioning some of the assumptions we have made about this case - how do we know that the coin really is evenly weighted, how certain are we that past events don't affect probabilities … etc, etc.

Folk Logic:

Or plain old "common sense”: the gut reaction of the average, Joe in the street. How do you find out what the answer is in this case? Well you just go and ask a sample of such specimens and they will no doubt tell you that by "the law of averages" it's about time it came down "tails", so there is a greater probability of this.

Gut reaction is the same as intuition, which we have acquired as a result of generations of evolution and natural selection. As such there are a number of reasons for relying on these gut reactions. After all, how many times have our instincts proved to be right in the past (oops - inductivism again!) and what would be the use of having such instincts if we can't rely on them?

The more mathematically minded might also point out that the chances of five successive "heads" are 1 in 32 and this would increase to 1 in 64 if it landed "heads" the sixth time, therefore 31 times out of 32 it will come down "tails" on the sixth toss! There seems little doubt it will land "tails".

So what is the right answer? Logic can't help at all unless we can decide which logic to use and it is fairly certain that each and every one of us has applied all of these types of logic to some situation in the past. Maybe the only sensible way to decide between them is to toss a coin?