Here's a funny thing. In deductive logic, if the premise is true, and the argument valid, then the conclusion will be true. That's what it is to be valid.
So, in your deductive example:
1. all men have blonde hair,
2. Socrates is a man.
3. Therefore, Socrates has a blonde hair.
If one and two are true, three must also be true. As it turns out, (1) is false, adn hence so is the conclusion.
But in your inductive example
1. All swans in the past were white.
2. Every swan in the future will be white.
(1) is true, and yet (2) is false. That is, the premise is true, the conclusion false - the very opposite of validity. — Banno
1. All swans in the past were white.
2. Every swan in the future will be the same color that every swan in the past was.
3. Therefore, every swan in the future will be white. — Magnus Anderson
SO folk think that by dismissing induction I am dismissing science. Noting could be further from the truth. — Banno
I don't object to Bayesian inference.
But that's not induction. — Banno
As a logic of induction rather than a theory of belief, Bayesian inference does not determine which beliefs are a priori rational, but rather determines how we should rationally change the beliefs we have when presented with evidence. We begin by committing to a prior probability for a hypothesis based on logic or previous experience, and when faced with evidence, we adjust the strength of our belief in that hypothesis in a precise manner using Bayesian logic.
If you want an algorithm to be able to map its inputs to its outputs in a way that it previously didn't, you must modify it. — Magnus Anderson
No.
It is not the case that because every swan seen by white fellas was white, they will never see a black swan in the future. — Banno
. . . because you say so. — Magnus Anderson
Magnus, I've shown repeatedly that in an induction the conclusion does not follow from true premises. It's not just my say so. — Banno
Here's a funny thing. In deductive logic, if the premise is true, and the argument valid, then the conclusion will be true. That's what it is to be valid.
So, in your deductive example:
1. all men have blonde hair,
2. Socrates is a man.
3. Therefore, Socrates has a blonde hair.
If one and two are true, three must also be true. As it turns out, (1) is false, adn hence so is the conclusion.
But in your inductive example
1. All swans in the past were white.
2. Every swan in the future will be white.
(1) is true, and yet (2) is false. That is, the premise is true, the conclusion false - the very opposite of validity. — Banno
1. All swans in the past were white.
2. Every swan in the future will be the same color that every swan in the past was.
3. Therefore, every swan in the future will be white. — Magnus Anderson
According to a long tradition, an inductive inference is an inference from a premise of the form "all observed A are B" to a conclusion of the form "All A are B". Such inferences are not deductively valid, that is, even if the premise is true it is possible that the conclusion is false, since unobserved A's may differ from observed ones.
It is so apparent that inductive syllogisms are invalid. — Banno
Inductive reasoning, per se, is neither valid nor invalid; — Janus
Also, as I have shown inductive reasoning can be re-framed in valid deductive terms. You claimed my re-framing is not valid; — Janus
1. All swans in the past were white.
2. Every swan in the future will be the same color that every swan in the past was.
3. Therefore, every swan in the future will be white. — Magnus Anderson
To be sure, if you can indeed reframe inductive reasoning in deductive terms, it is no longer inductive reasoning, and I would have no problem with it. — Banno
↪Magnus Anderson Do I have to point out that the second premise is false? — Banno
The right question is "What grounds do you have to think that the future will be different?"
What ground do you have for supposing that the sun will not rise tomorrow? — Banno
an inductive inference is an inference from a premise of the form "all observed A are B" to a conclusion of the form "All A are B"
↪Magnus Anderson SO you have re-framed induction as a deduction with a false premise. — Banno
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.