Argument for predictions made on the basis of majority or APBM:
If all the possible future variations concerning a particular state of affairs are known,
And if no probability can be assigned concerning the potential occurrence to those states of affairs,
And a similarity is present among the majority of the possible states of affairs,
Then it is reasonable to believe that an outcome will occur in which the similarity is present.
The soundness of this argument is illustrated in the following example.
Imagine you know the following and only the following:
There is a dice,
It has six faces,
It will land on one of its faces,
You must make a prediction regarding whether or not the dice will land on 1.
It is more reasonable to believe that it will land on a face higher than 1 than it is reasonable to believe it will land on 1. This is because the similarity of "being a number higher than one" is present among the majority of the possible outcomes.
Thus if we must make a decision, it is reasonable to predict that the dice will land on a number higher than one.
We must make a prediction.
Thus it is reasonable to predict that the dice will land on a number higher than one.
Similarly:
If we consider how many times a pattern observed in the past could continue in the future, we find that there are more possibilities in which the pattern continues at least once than there are possibilities to the contrary.
We must make a prediction regarding whether or not the pattern will continue.
It is more reasonable to believe that the pattern will continue at least once than it is reasonable to believe that the pattern will not continue at least once. This is because the similarity of "the pattern continues at least once" is present among the majority of the possible outcomes.
Thus if we must make a decision, it is reasonable to predict that the pattern will continue at least once.
We must make a prediction.
Thus it is reasonable to predict that the pattern will continue at least once.
APBM does not give us certain knowledge. It instead provides us with a justification for inductive reasoning. Once a pattern is observed it is more reasonable to make a prediction regarding whether or not the pattern will continue then it is reasonable to not make a prediction. This is because one is more likely to make a correct prediction if one makes a prediction. APBM shows that when forced to make a prediction regarding the patterns continuation it is more reasonable to predict it will continue than it is reasonable to make a prediction to the contrary. To deny this is to deny the reasonableness of the initial prediction made in the dice example. That is to say to deny the previous conclusion would be to claim that it is more reasonable to predict that the dice will land on one as opposed to a number higher than one.
S
"It is more reasonable to believe that it will land on a face higher than 1 than it is reasonable to believe it will land on 1. This is because the similarity of "being a number higher than one" is present among the majority of the possible outcomes."
ReplyDelete"Majority of possible outcomes" implies a probability, as you are claiming there are a limited known quantity of outcomes, and that you know the majority among them; 1:(>1) is still a probability.
ie. This example either works with a fair (probabilistic) dice, or not at all.
-M
by "this example" i assume you mean the first two quotes?
Deleteyes that example works with a fair dice.
it also works with an unfair dice.
Furthermore, with no limited definition of "pattern", this is actually bad for induction because it means we should believe in unintuitive things eg.
ReplyDeleteIt was raining and I got shot, next time it rains it is more reasonable to believe I will get shot than not as set one (The rain/getting shot pattern will not repeat itself) is certainly smaller than set two (The rain/getting shot pattern will repeat once, the rain/getting shot pattern will repeat twice, the rain/getting shot pattern will repeat thrice, etc.).
-M
This seems to be more of a problem about induction in general and how it works. I assume you are not denying that we reason inductively? if not, then you bring up an interesting point about how we reason and how we reconsial contradicting patterns such as "weather doesnt effect whether or not i get shot" and "i got shot in the rain". in my solution i am only looking for a justification for general induction (assuming patterns will continue). i suggest that you should either refute my justification for general induction or deny general induction (and explain our reasoning in a different way).
DeleteP.S. this is a bit of a dodge, and ill think more about it. i think my explaination of reasoning would be that we reaon in a more general way, and there would be more patterns which refute the conclusion that "rain causes you to get shot" then patterns confirming it considering all that we know about weather and how a gun works ect. someone who had never experienced rain or guns before and got shot in the rain my very well hold some conection between the two. however we find it "unintuitive" as you put it, i think this is because of our general body of knowledge founded on our inductive reasoning.