**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 ˇK except, of course, in those
rare instances when it hasnˇ¦t. So although we canˇ¦t be certain that inductive
logic will work ** every time**, it seems to work

**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
ˇ§tails" are equal.

The result of
tossing a coin does not depend in any way on the previous results ˇV 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 monkeysˇ¨ 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 ˇK etc, etc.

**Folk Logic:**

Or plain old "common senseˇ¨: 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?