I think you’re less qualified than I am on this. “induction” is ANY inference drawn by using PATTERNS of repeated events.
Example:
Premise 1: Today is cloudy and it rained.
Premise 2: Yesterday it was cloudy and it rained also.
Premise 3: Very rarely is it cloudy without rain here.
Conclusion: It is likely that if the sky is cloudy it will rain.
Example (consensus):
Premise 1: Mr X believes that the Cosmic Radiation represents heat of an early universe.
Premise 2: Mr Y believes that the Cosmic Radiation represents heat of an early universe.
Premise 3: My Y believes that the Cosmic Radiation is light from distant galaxies.
Conclusion: The concensus (majority) of these people is that the Cosmic Radiation represents heat of an early universe.
Induction for MATH or logic (used anywhere) CAN be closed with the same strength as deduction IF IT IS COMPLETELY enumerated and is unanimously undoubted. This form of induction is NOT able to be used with observation or non-enumerated samples.
This is the form that proves something true in an initial case. Then a proof to demonstrate that any arbitrary number is true. If you are assuming this is the particular form of induction that science uses, you’d be wrong. It relates but is absolute. All other induction is no different than counting the repeated incidents whether it be ‘consensus’ (consenting majority OPINION among equals) and is NEVER ‘certain’ without absolute enumeration that math uses.
I just made up the examples quickly to make a point. But note that when someone KNOWS for certain something, they NECESSARILY “believe” what they know. So the use of the term is INCLUSIVE of ANY ‘belief’, whether rational or not. One can also ‘believe’ in the AUTHORITY of someone without actually having any inkling of wisdom to the actual direct ‘knowledge’. YOU argue just for such faith in authorities. That is a pragmatic rational choice. But it is nevertheless as irrational to ‘believe’ in someone absolutely regardless of how well that person may have demonstrated their credibility.
Knowledge implies Belief
Belief does not imply Knowledge.
Thus if you don’t believe X, you can’t even know X.
That’s where you get it wrong.
It’s faith in substantive evidence.
Why’s that?
It starts with observation, and evolves to measuring, recording, learning, then somewhere down the line something like belief does happen, but it’s always up for reassessment in light of new evidence.
As opposed to the certitude kind of belief you are discussing.
From formal logic, let B = belief and K = knowledge, and “→” for implication.
Then, one of the following must be true:
B → K, K → B, or B ⟷ K
[Belief implies Knowledge, Knowledge implied Belief, or Belief coimplies Knowledge]
Belief is not equal to knowledge and so it is not, B ⟷ K.
We do not interpret “belief” as requiring “knowledge”; But if you “know” something, I hope that such a person “believes” in that knowledge as being true. Thus, it is notB → K. This leaves K → B.
So it is K → B, “Knowlege implies belief”.
In logical conditionals, IF K is true, then B has to be true; Since B CAN be ‘true’ when K is either true or false, this conditional is true.
Now I said that if you do not believe, then you cannot know, which is
Not-B → Not-K
…which throws many off but is also true. If doubtful still, let ‘true’ = 1 and ‘false’= 0 and make a chart that show all possible truth values. I can’t make charts with only the given options and have not been able to use any html to underscore here (it assumes an escape value and opens a new page, if I recall correctly). So let’s see if this link image pasting works using P (for K)and Q (for B) instead. The second from the top and the fourth is (If not-B); Only the last line makes the statement ‘true’ (last column):
The statement is that ONE of the three options is true. It is of the same form as…
If X is a number than it is either (1) Greater than Zero, (2) Less than Zero, or (3) Equal to Zero.
If you disagree, than (4) X is not a number.
I exhausted the options. If you disagree to either (1) Belief implies Knowledge, (2) Knowledge implies Belief, or (3) both (that they are ‘equivalent’ for coimplying each other.),
…then you have to interpret Belief as NON-COMPARABLE, making your comment about ‘belief’ meaningless to whether one ‘knows’ the truth or not. That is, (4) No one can ‘believe’ what they ‘know’ nor ‘know’ what they ‘believe’. If this is the case, then what are you defining as ‘belief’ or ‘knowledge’?
Edit: trivial bolding and deleting an extra word accidentally left in. I had to just now edit “word” in the last sentence from “world”. This software should permit editing until someone else responds.
Hmmm, I’ve found this software is very liberal with its editing option. It does permit editing until someone responds, in fact I suspect we even get like 5 minutes, without being tagged with a editing tick, I see you have 2 official edits to your post.
Not only that the software is even nice enough to let us edit after a comment.
As for your post, I’m not a logic geek, so I really appreciate Lausten cutting through your Gordian Knot.
Me, I’m more down to Earth, hands on, this playing with formulas is strictly minds play in idealized dream worlds.
After all in real life, options are true, false or more usually in between - and that often true/false/inbetween changes purely on one’s point of view, or the situation of the moment.
Stuff that doesn’t fit into “logic” very convincingly.
Yes those are scare quote, since “logic” is used to create mischief, as often as it’s called upon to serve constructively.
That comment was about the fact that when we edit here, it counts EACH time even though no one has even responded yet. That is all I was asserting. And for your information, most other software recognizes that. The function of alerting ‘edits’ at all is about whether one CHANGES their content AFTER someone else posts.
As to your stance against logic, you cannot be rationally ‘scientific’ without being logical. Otherwise, you are no different than a religious believer IN science rather than one who is rationally able to deem it as ‘valid’ or ‘sound’.
And your kissing ass with lausten for no other reason than bandwagoning (oops, another logic term), is cheap.
Oh please don’t misunderstand. I appreciate the corner stone that logic is in gathering scientific knowledge, or life awareness for that matter.
What I said is a lot of mischief can also be done with logic. It’s a tool for good and for mischief.
For instance, I have a spade shovel that I use for digging holes with for planting and posts and whatnot. But if a bad person comes at me wanting to hurt me, I can also use that shovel to bash in his head before he gets to me.
In the end, it’s still a shoveling implement, but it can be multi-tasked.
Cool. The traditional “foundational” learning that begins with philosophy (general to specific) centers on both logic and rhetoric. Logic deals with validating but relies on the ‘soundness’ based upon having true inputs. You can have a valid argument with false premises but as long as the conclusion follows from the ASSUMED ‘truth’ of the premises. When the arguments are valid AND the input premises are actually true, the argument is ‘sound’.
