Right, I'll use a simplified example and hopefully I can get the point across:
H: Theism is false.Evidence to be explained
(E) : There are instances of pointless suffering in the world.
Background information
(B): Is whatever we know before testing begins, in this case we could use the background information that the theistic God is: Omnipotent, omniscient etc...
( This is all based on bayes' rule which treats evidence as relative, so it may be hard to grasp at first)
Right, so we now have our hypothesis, background information and evidence to be explained.
If we were to use a C-Inductive argument in favour of theism being false, it may go something like this.
1. If Theism is true, pointless suffering would be unexpected.
2. There are pointless cases of suffering.
C. This is evidence for the falsity of Theism.
Therefore,
P(H | E & B) > P(H | B)The above may look complicated but all it is really saying is that:
The probability of Theism being false is now more likely given the fact that there are pointless cases of suffering in the world. A P-Inductive argument probably wouldn't work with my previous example, so I will have to think of a new one:
Example: Tossing a coin.H: We will get a head on the first toss.
B: Assuming that that the coin is fair, p(H)=p(T)
E: We now learn that a magician will be throwing the coin and he is known for always getting a heads on his first toss. so p(H) in our possible world is now > 1/2.
Voila, we now have our P inductive argument where
P(H | E & B) > 1/2.This is because the new evidence has now made the hypothesis more likely than before. By virtue of induction, P(H) is virtually 1 as opposed to 1/2 F-Inductive argument:I'm not going to use any probabilistic formulations for this explanation as it will just become confusing.
Let's think of two hypotheses:
Example: I am in my bedroom and I hear a loud crash in the kitchen.B: I am at home and everyone except my cat and dog are outside.
[I don't have any pets irl
]
H1: My dog is the culprit ,he caused the noise.
H2: My cat is the culprit, she caused the noise.
E: However, I go downstairs and see some animal footprints on the floor. They are much smaller than my dogs feet.
How can I explain this?
I decide to formulate a F-inductive argument:
1. The small footprints aren't well explained given the assumption that my dog is the culprit.
2. The smalll footprints are better explained given the assumption that my cat is the culprit.
C. All else being equal, my dog probably isn't the culprit.A formal qualification of the argument:
1. E is known to be true, i.e., Pr(E) is close to 1.
2. H1 is not intrinsically much more probable than H2, i.e., Pr(H1 | B) is not much more probable than Pr(H2 | B).
3. Pr(E | H2) > Pr(E | H1).
4. Other evidence held equal, H1 is probably false, i.e., Pr(H1 | B & E) < 0.5.1. I am in my bedroom but I hear a crash in my kitchen, my cognitive faculties are fine.
2. At this stage, I can only assume that the culprit is either my cat or my dog.
3. However, I go downstairs and notice that the footprints are similar to those of my cat. The probability of my cat being the culprit given this new evidence is now greater than the probability that my dog is the culprit given this new evidence.
4. Other evidence held equal, my dog being the culprit is probably false as this hypothesis is not well explained on the new evidence.This is because hypothesis H1 is now less likely given the new evidence that I have found.Hope I did justice to the concept of inductive arguments as these explanations were simple for the purpose of avoiding confusion.
Topic: F-Inductive Arguments: A New Type of Inductive Argument