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

That's true. And that applies to induction too. It applies to any kind of algorithm. 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. That's what "back-propagation" does to neural networks. Hardly ground-breaking.

The problem is that the manner in which we describe inductive reasoning is not exhaustive. We leave out many premises from our description. They thus become hidden premises.

Here's an example:

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.

This is a gross over-simplification of the process of inductive reasoning but it is nonetheless less of a simplification than the usual description.

Is that enough to prove my point?

I recall reading how children observer occurrences, develop hypotheses and then test them, apparently on a inherently statistical basis which the paper described as Bayesian (A Gopnik et al).

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

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.

See?

I don't object to Bayesian inference.

But that's not induction.

SO folk think that by dismissing induction I am dismissing science. Noting could be further from the truth. — Banno

SO how strongly do you doubt an inductive conclusion? Do you doubt it absolutely? Or is that unreasonable?

It’s a funny thing. Folk can really hate Cartesian doubt being applied too liberally. They bang on about not denying what you believe in your heart, not doubting the knowledge you are prepared to act upon.

Yet they talk as if there are no grounds to believe inductive methods of reasoning. And this red herring of deductive validity is all that is offered as an excuse. Whereas the beliefs we are prepared to act on are all derived from inductive generalisations.

I don't object to Bayesian inference.

But that's not induction. — Banno

Wiki says:

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

Do you think scientific method must be algorithmic?

I suspect that is a bit of this underpinning the defence of inductivism.

An algorithmic science would be dreadfully impoverished.

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

Again, logical conclusions, whether they are deductive or inductive, are empirically uncertain which means they can turn out to be wrong regardless of the premises they are derived from.

For example:

1. All men have blonde hair.
2. Barack Obama is a man.
3. Therefore, Barack Obama has a blonde hair.

Although logically certain, it is not empirically certain that Barack Obama has a blonde hair. In fact, he does not. So the premises can be accepted as true and the conclusion can turn out to be empirically false.

Things have reached a pretty pass when Apo relies on Wiki.

Sure; but this is not the same as being invalid in the first place.

Induction is just invalid.

It must be.

Sorry - are you saying induction must be valid?

Cool.

Why?

Do you think science would fail without induction? I think not.

Again, my point is a small one - by calling what happens when we move from a sequence of observations to a prediction, inductive logic or some such, we obscure what is actually going on.

And what is actually going on is far more human, humane and downright interesting than following a mere algorithm.

Sorry - are you saying induction must be valid? — Banno

No, I am saying that induction must be invalid . . . because you say so.

And what is actually going on is far more human, humane and downright interesting than following a mere algorithm. — Banno

Now you sound like a mystic.

. . . 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.

Cheers.

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

What you did is called backpedalling.

You were wrong in this post of yours:

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

You never addressed that.

What? Where is my error?

The fact that you ignore unspoken premises.

My response was this:

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

And yours?

Here's the first paragraph form the Shorter Rutledge Encyclopedia of Philosophy, inductive inference.

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.

Now, does anyone here think that this is wrong? Surely at least we have agreement on this.

It is so apparent that inductive syllogisms are invalid. — Banno

Inductive reasoning, per se, is neither valid nor invalid; your mistake consists in applying a principle to it that is relevant to deductive reasoning only. You haven't given any argument to support your claim that inductive reasoning has no place in science. Also, as I have shown inductive reasoning can be re-framed in valid deductive terms. You claimed my re-framing is not valid; but you are yet to support that claim.

Inductive reasoning, per se, is neither valid nor invalid; — Janus

I can live with that, if you prefer. Just so long as we drop the pretence of its being valid.

Also, as I have shown inductive reasoning can be re-framed in valid deductive terms. You claimed my re-framing is not valid; — Janus

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.

That's what I suggested happens in statistical inference. But even there some folk are asserting that stats is based on induction.

Do I have to point out that the second premise is false?

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

Yes, that's another example of an inductive argument being framed validly in deductive terms. Of course the argument is unsound because the second premise is false. Also it is not a good inductive argument because we had no reason to believe, prior to comprehensive exploration of the Earth, that swans if they occurred in unknown lands, would be white.

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

The thing is though, that the reasoning behind the assumptions that form the premises in the deductive re-framing is not itself deductive, but inductive or abductive. As with all premises of all deductive arguments (which, in terms of soundness, but not in terms of validity, are only as good as their premises); they are not themselves supported by the argument, but instead support it.

↪Magnus Anderson Do I have to point out that the second premise is false? — Banno

The point is that in the following argument it is impossible for the premises to be true and the conclusion to be false:

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.

If both premises are true then every swan in the future must be white.

This is where I came in...

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

If you like, my objection is that inventing induction as a reason for being confident that the sun will rise tomorrow is already a step too far.

Maybe it would help to think of it thus: which is more likely, that the sun will not come up tomorrow, or that there is something amiss with inductive reasoning?

I hope you will agree that we can be more confident about the sun coming up than about the theory surrounding induction.

A weaker theory cannot support a stronger. So the theory of induction does not help us reach the conclusion that the sun will come up tomorrow.

SO you have re-framed induction as a deduction with a false premise.

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"

I wouldn't put it that way. I would say instead that " an inductive inference is sometimes an inference from a premise of the form "all observed A are B" to a conclusion of the form "All A are likely to be B" or "All A are possibly B".

As you know, though, false premises do not entail that deductive arguments are invalid, just that are unsound.

But any reasoning that says that the Sun is likely to rise tomorrow is, by definition, inductive reasoning.

↪Magnus Anderson SO you have re-framed induction as a deduction with a false premise. — Banno

What I did is I made induction more explicit.