See the end of this post for how the class might work and details about the video. Video Yes, the lighting is terrible. I give sallow a bad name. Links: YouTube Twitter Rumble Lecture There are really only two areas of philosophy when it comes to science: that of what is, and that of how we know of what is. We need both and neglect neither, though we will concentrate on the latter; epistemology. This is a course on philosophy, mathematics and science. But geared toward understanding understanding, and not so much on making new science, which I’ll leave to you.
This reminds me of pre-calculus class, where at the close of 10th grade, the teacher said, "If I had known how dumb all of you really are, I´d have spent the whole semester telling jokes!"
Absolutely interesting lecture, William! Your unique twist has breathed new life into this age-old topic. I look forward to more of the same. There's a lot of hand ringing out there about what Jaynes is saying about probability and statistics. I love the theory but in application is see nothing but rubbish so I'm inclined to side with him. Thank you for doing this.
So about the homework. It kind of seems like this to me: It seems as though the plausibility of A is conditional on the plausibility of B. This is kind of weak since we do not know anything about the plausibility of A or B actually. It could be many things make A or B true. All we can know is that if B is true that’s one less possibility that makes A true and likewise we do not know that B being true was from A. It's just one less thing that could have cause B to be true. Oh, I get it....to B or not to B that is the question! HAHAHA.
Dubious: "The only way we know, or rather assume, that B can be true, logically, is if A is true."
How do you figure that? What prevents us from investigating things for B directly? Or for logical reasons to believe in B which aren't dependent upon A? It appears that you've misconstrued the conditionality of A→B, as if it were A<-->B.
Dubious: "So it does indeed follow logically that because A is false B is now less plausible."
Aren't you relying on an unstated premise that the set of true conditionals {A→B, B→B, C→B,...} is both finite and not very large? If the set is infinite, ruling out A leaves a set of with infinitely many elements to be investigated. This gives us no more reason to doubt B, so we need to slip in yet another premise: A matters much more than B, C, D, and so on. If the set of true conditionals is finite but large, subtracting A still won't make much difference unless it happens to be true, again, that A matters proportionally much more than B, C, D, etc.
Now denying the antecedent (as a way of reducing plausibility of the consequent) appears no less strictly fallacious than I supposed before reading this piece. Likewise, the inference "Therefore, A because more plausible" doesn't follow from the premises A→B and B. The inference that probability is a matter of logic will have to be set aside as unsubstantiated, at least by the reasons which you have given here.
This brings me to the perplexing conditionality you presented in the 7th paragraph. Suppose we have the argument...
A→A, and
A.
Therefore, A.
What counts most, affirming the antecedent or affirming the consequent? If the latter, the conclusion is subverted by our supposedly objective logic. Their equality leaves us in a similar predicament. So do we need to rule out A→A as false? This would be weird. Doesn't the truth of a proposition entail that same proposition? If we hang on to A→A as true, we could declare that affirming the antecedent is inherently most weighty for all conditionals. This would makes your conclusion about probability look more plausible.
We can use this syllogism introduced in the lesson to solve the homework:
((A -> B) & !B) -> !A
For the homework we are given this:
A -> (B is more plausible)
Using the syllogism I mentioned, we can rearrange what we are given to get the following:
!(B is more plausible) -> !A
We also have the trivial observation that:
B -> (B is plausible)
We can combine all the facts we have together:
A -> (B is more plausible)
!(B is plausible) -> !A
B -> (B is plausible)
B
---
A is less plausible
Which works because we have identified a situation where B is plausible, and therefore ruled out one of the things that would imply that A is false.
The train of logic is that:
1. We have B
2. Because we have B, we know that B is plausible
3. Because B is plausible, we know that the condition !(B is plausible) is not met, and therefore that particular proposition is unable to imply A be false.
4. We have removed a proposition which would imply A be false, so there are less things implying A be false, therefore we think A is more likely to be true.
Just a thought, but if you like to talk to people while you’re teaching, why not make it a live Zoom class? Although admittedly, the logistics of that can quickly become a nightmare.
Regarding the assigned homework for this first class, imagine this background condition of reality:
A is 10% of the sole causes of B (which satisfies "If A is true, then B is becomes more plausible.")
C is 20% of the sole causes of B
D is 30% of the sole causes of B
E is 40% of the sole causes of B
100% of the causes of B have been identified, and now we proceed ...
------------------
...
B is true.
Therefore, A because more plausible.
------------------
But when B is true, A isn't any more plausible than C, D, or E. When compared to the 3 other sole causes of B, A actually becomes "less plausible" when B becomes true. Whether A can exist without causing B appears to matter for the answer. This is true of the other 3 sole causes of B as well.
Given B, the relative proportion of causes covered by A (10% of them), along with the relative proportion of instances of A which do not actually result in B, along with those same two kinds of proportions for those other 3 sole causes of B would tell you the answer.
It could be this:
99% of instances of A do not result in B (1% do)
67% of instances of C do not result in B (33% do)
33% of instances of D do not result in B (67% do)
1% of instances of E do not result in B (99% do)
With those values, A is many times more likely to exist without having caused B than with having caused B.
This reminds me of pre-calculus class, where at the close of 10th grade, the teacher said, "If I had known how dumb all of you really are, I´d have spent the whole semester telling jokes!"
If you're using a newish Mac you can turn off auto display dimming under system settings then 'Lock Screen'. There's a control for it there.
You will know the truth and the truth will set you free! Thank you Mr W M Briggs
For everyone wanting to learn some more about the truth
https://youtu.be/dWU-2w0L-9o?si=7ktDtfC3sETkA3ND
Absolutely interesting lecture, William! Your unique twist has breathed new life into this age-old topic. I look forward to more of the same. There's a lot of hand ringing out there about what Jaynes is saying about probability and statistics. I love the theory but in application is see nothing but rubbish so I'm inclined to side with him. Thank you for doing this.
So about the homework. It kind of seems like this to me: It seems as though the plausibility of A is conditional on the plausibility of B. This is kind of weak since we do not know anything about the plausibility of A or B actually. It could be many things make A or B true. All we can know is that if B is true that’s one less possibility that makes A true and likewise we do not know that B being true was from A. It's just one less thing that could have cause B to be true. Oh, I get it....to B or not to B that is the question! HAHAHA.
Dubious: "The only way we know, or rather assume, that B can be true, logically, is if A is true."
How do you figure that? What prevents us from investigating things for B directly? Or for logical reasons to believe in B which aren't dependent upon A? It appears that you've misconstrued the conditionality of A→B, as if it were A<-->B.
Dubious: "So it does indeed follow logically that because A is false B is now less plausible."
Aren't you relying on an unstated premise that the set of true conditionals {A→B, B→B, C→B,...} is both finite and not very large? If the set is infinite, ruling out A leaves a set of with infinitely many elements to be investigated. This gives us no more reason to doubt B, so we need to slip in yet another premise: A matters much more than B, C, D, and so on. If the set of true conditionals is finite but large, subtracting A still won't make much difference unless it happens to be true, again, that A matters proportionally much more than B, C, D, etc.
Now denying the antecedent (as a way of reducing plausibility of the consequent) appears no less strictly fallacious than I supposed before reading this piece. Likewise, the inference "Therefore, A because more plausible" doesn't follow from the premises A→B and B. The inference that probability is a matter of logic will have to be set aside as unsubstantiated, at least by the reasons which you have given here.
This brings me to the perplexing conditionality you presented in the 7th paragraph. Suppose we have the argument...
A→A, and
A.
Therefore, A.
What counts most, affirming the antecedent or affirming the consequent? If the latter, the conclusion is subverted by our supposedly objective logic. Their equality leaves us in a similar predicament. So do we need to rule out A→A as false? This would be weird. Doesn't the truth of a proposition entail that same proposition? If we hang on to A→A as true, we could declare that affirming the antecedent is inherently most weighty for all conditionals. This would makes your conclusion about probability look more plausible.
We can use this syllogism introduced in the lesson to solve the homework:
((A -> B) & !B) -> !A
For the homework we are given this:
A -> (B is more plausible)
Using the syllogism I mentioned, we can rearrange what we are given to get the following:
!(B is more plausible) -> !A
We also have the trivial observation that:
B -> (B is plausible)
We can combine all the facts we have together:
A -> (B is more plausible)
!(B is plausible) -> !A
B -> (B is plausible)
B
---
A is less plausible
Which works because we have identified a situation where B is plausible, and therefore ruled out one of the things that would imply that A is false.
The train of logic is that:
1. We have B
2. Because we have B, we know that B is plausible
3. Because B is plausible, we know that the condition !(B is plausible) is not met, and therefore that particular proposition is unable to imply A be false.
4. We have removed a proposition which would imply A be false, so there are less things implying A be false, therefore we think A is more likely to be true.
Just a thought, but if you like to talk to people while you’re teaching, why not make it a live Zoom class? Although admittedly, the logistics of that can quickly become a nightmare.
Loved it. Can't get enough. :)
HW: let C be (B is more plausible)
we deduced if A -> C and C means A is more plausible. But B->C, since if B is certain it is surely more plausible. So B -> C -> (A is more plausible)
Regarding the assigned homework for this first class, imagine this background condition of reality:
A is 10% of the sole causes of B (which satisfies "If A is true, then B is becomes more plausible.")
C is 20% of the sole causes of B
D is 30% of the sole causes of B
E is 40% of the sole causes of B
100% of the causes of B have been identified, and now we proceed ...
------------------
...
B is true.
Therefore, A because more plausible.
------------------
But when B is true, A isn't any more plausible than C, D, or E. When compared to the 3 other sole causes of B, A actually becomes "less plausible" when B becomes true. Whether A can exist without causing B appears to matter for the answer. This is true of the other 3 sole causes of B as well.
Given B, the relative proportion of causes covered by A (10% of them), along with the relative proportion of instances of A which do not actually result in B, along with those same two kinds of proportions for those other 3 sole causes of B would tell you the answer.
It could be this:
99% of instances of A do not result in B (1% do)
67% of instances of C do not result in B (33% do)
33% of instances of D do not result in B (67% do)
1% of instances of E do not result in B (99% do)
With those values, A is many times more likely to exist without having caused B than with having caused B.
Good stuff! Makes my brain hurt, but it's a good pain.