Let us look at abduction more closely.
To understand the similarities and
differences between deduction, abduction and induction,
let us look at the relationship between a rule, cause and effect.
Let's consider a simple rule like, if it cloudy, it rains.
So it is cloudy, is the cause.
It rains, is the effect.
If it's cloudy and it rains, it's a rule.
>> Another example of a rule, would be the rule that Bob hates Joe.
So Bob hates Joe, so whenever Joe walks in, Bob leaves.
The cause is Joe walking in.
The effect is Bob leaving.
And the rule is Bob hates Joe.
You already come across yet another instance of this particular arrangement,
when we were talking about flu and fever.
So the rule might be; if flu then fever.
Flue is the cause.
Fever is the effect.
Non-deduction, in one fundamental kind of inference.
We know the rule and the cause, and we need to deduce the effect.
So, given the rule, if it is cloudy, then it rains, and
given the cause, it is cloudy, we can deduce that it rains.
>> Similarly, in our rule that Bob hates Joe,
we can say that if Joe just walked in, we can deduce that Bob will leave.
Part of the rule is, if flu, then fever.
And we know that a shortcut's flu, then we can deduce that, a shortcut's fever.
This is simply an instance of more despondence, and
we discussed this in detail when we were talking about logic.
Now let us look at induction.
Given a relationship between a cause and an effect, we can try to induce a rule.
For example, if we observe repeatedly that when it is cloudy,
it rains, and we may induce a rule.
If it is cloudy, then it rains.
>> Same thing with Bob and Joe.
If we observe repeatedly that every time Joe arrives, Bob leaves.
we can induce a rule that Bob must hate Joe.
If every time a patient goes to a doctor with flu,
and the patient has fever, then we can induce a rule if flu then fever.
In can of abduction, given a rule and an effect, we can abduce a cause.
As an example, given the rule if it is cloudy then it rains, and
the effect that it is raining, we can ask of ourselves is it cloudy.
And once again with Bob and Joe, given our rule that Bob hates Joe, and
given that we just arrived at the party, and we see that Joe is here but
not Bob, we might be able to adduce that Bob left when Joe arrived.
>> Or given the rule, if flu then fever and
that fact Ashok that has fever, we might be able to adduce that Ashok has flu.
First of all notice that we are back to diagnosis.
Diagnosis is an instance of abduction.
But notice several of the properties.
First, deduction is truth preserving.
If the rule is true, and the cause is true,
we can always guarantee that the effect is true as well.
Induction and abduction are not truth-preserving.
If we know something of the relations between cause and effect for
some sample, that does not mean that the same relationship holds for
the entire population.
Induction does not always guarantee correctness.
Same for abduction.
We may know the rule and the effect, and we may suppose that the cause is true.
But that need not necessarily be true.
It may be the case the flu then fever.
And Ashark may have fever, but
that does not necessarily mean that a shark has flu.
Fever can be caused by many many things.
The reason that fever does not necessarily mean that Ashkk has flu is
because there can be multiple causes for the same effect.
Multiple hypothesis for the same data.
This is exactly the problem that we had encountered earlier,
when we were talking about what makes diagnosis hard.
We said that deduction, induction, and
abduction, are three of the fundamental forms of inference.
We can of course also combine these inferences, science is a good example,
you and I as scientists, observe some data about the world.
Then we induced some explanation for it.
Having induced such an explanation for it, we induce a rule.
Having induced a rule, now we can use production to predict new data elements.
We going to observe some more.
Again, we adduce, induce, deduce.
And we continue the cycle.
Might the cycle also explain a significant part of cognition?
Is this what you and I do on a daily basis?
Adduce, induce, deduce?