I suppose one would need to get to the bottom of the source of their feeling in order to understand the connection it has to the direction they have chosen in their life. This is a very personal kind of truth though which could lead to relativism. Is the truth different for everyone?

I suppose one would need to get to the bottom of the source of their feeling in order to understand the connection it has to the direction they have chosen in their life. This is a very personal kind of truth though which could lead to relativism. Is the truth different for everyone? — Perplexed

In a way yes. As Shakespeare put it "This above all, to thine ownself be true".

We are just Navigators in Life. There is not just one path. We are learning as we go along, and should we encounter turbulence, maybe it is a good time to steer in a different direction. This choice in particular is what we have, the skills we learn along the way is what we seek.

Could this method not lead to avoidance of difficult situations? If one changes their course each time there is turbulence are they not just victims of circumstance?

Could this method not lead to avoidance of difficult situations? If one changes their course each time there is turbulence are they not just victims of circumstance? — Perplexed

It's all about developing skills. Think of yourself as a sailor. What would you do if you got turbulence? How skilled are you? Is there anyone who can give you advice? How does it compare to other times? There are no right and wrongs. Everyone is different and everyone will learn as they will.

Yes, the methods we use to gain knowledge of the world, whether for its own sake or for practical purposes, are not arbitrarily chosen but are developed over time based on what seems to work. Can you imagine an alternative approach?

the very fact that science gets along quite well with little or no metaphysics - and in particular, without ever needing to resolve the question of metaphysical determinism - is suggestive. — SophistiCat

In actual fact, current science is plagued by an enormous metaphysical dispute, specifically, whether string theory actually is scientific, or not. Current physics now is only thought to account for 4% of the known mass and energy of the universe. And the ‘standard model’ of particle physics is also regarded as metaphysically unsatisfactory. So the fact that modern technology and science produces what we consider to be good technology doesn’t actually entail that science is any closer to understanding metaphysical truths.

Why should science be expected to "understand metaphysical truths"?

It was in response to the remark that science ‘gets along quite well without metaphysical truths’ How are we to judge in what sense it is ‘getting along very well’? The anomalies that I have mentioned are all basically metaphysical in nature but have been thrown up by science itself. So I’m questioning whether such a sanguine view is justified.

I think it is an exaggeration to say that "current science is plagued by an enormous metaphysical dispute, specifically, whether string theory actually is scientific, or not". First I think the question is a methodological, not a metaphysical, one. It is a question of whether string theory is testable, and whether if it is not testable, it should be counted as a scientific theory at all. That question can only be resolved over time within the practice of physics itself.

Also, physics is just one area of science. Science as a whole does not seem to be in any kind of life-threatening crisis, so I think it is fair to say that it is getting along "quite well" if not that it is getting along "very well". (Note that the "quite well" is Sophisticat's and the "very well" is yours).

But here is how this justification can be undermined.

A plausible account of our inductive instincts is our evolutionary history as creatures that emerged in a relatively orderly, stable environment.... — SophistiCat

Note that this explanation that you are taking to undermine induction is itself inductively derived. It relies on that which it purports to undermine.

I think it is an exaggeration to say — Janus

Well, it's not. It's a very big argument, and it is exactly a metaphysical dispute, as it's about the nature of reality, the nature of science itself, what is knowable, and many other metaphysical questions of that nature. And that's only one of the issues. But because nobody takes metaphysics seriously, then they don't see that it's that kind of problem.

But I do agree with your above remark concerning the weakness of appealing to evolution in support of induction. That is exactly the territory of Plantinga's 'evolutionary argument against naturalism'.

My point was that, regardless of whether the question is "very big" or not, science is not "plagued by" it. Some philosophers might be.

In regard to my "remark"; ironically I wasn't targeting the weakness of appealing to evolution in support of induction, but the opposite; appealing to evolution to undermine confidence in induction.

Popper, Logic of Scientific Discovery:

A theory of induction is superfluous. It has no function in a logic of science.

The best we can say of a hypothesis is that up to now it has been able to show its worth, and that it has been more successful than other hypotheses although, in principle, it can never be justified, verified, or even shown to be probable. This appraisal of the hypothesis relies solely upon deductive consequences (predictions) which may be drawn from the hypothesis: There is no need even to mention “induction”.

He was a staunch opponent of induction. The purpose of thinking is to generalize. A theory (what he calls a hypothesis) can fit the data very well but be pretty bad at going beyond it. The question is: how do we generalize? "Conjectures and refutations" does not answer that. We do not assume the unknows randomly.

Yes, he was. My target in that post was those who might be tempted to think he was not.

Just trolling along. Isn't Bayesian inference based on induction?

That's what I thought. I merely wanted to confirm it. Yes, Popper hated induction.

A lot of people think there's a problem with induction. They think that the fact that inductive conclusions can turn out to be wrong is an argument against it. As if deductive conclusions aren't equally uncertain. As if thinking that "Because all swans are white and this is a swan, this swan is also white" means that the conclusion that this swan is white cannot turn out to be wrong. Yet we all know that it can. The problem is caused by equivocation. It appears strange to say that deductive arguments, and also inductive arguments, can be both certain and uncertain. That's because we're confusing logical certainty (or properly speaking validity) with empirical certainty. Deductive arguments can be logically certain/valid but they can never be empirically certain; they are always empirically uncertain. The same applies to inductive arguments. They can be logically certain/valid but they can never be empirically certain. Nietzsche said that "absolute certainty is a contradictio in adjecto" and he's right. Assumptions cannot be empirically certain because they are by definition empirically uncertain. Reasoning is the process of forming assumptions regarding events that we haven't observed. Because we didn't observe them, this means that what we think they are can always turn out to be wrong.

Popper's solution to the imaginary problem of induction was his theory of reasoning where we reason by making conjectures (i.e. by making shit up) and then by seeking refutations. He thought that relying on induction is dogmatic i.e. it makes us unwilling to adapt our models of reality in the face of new evidence. What he was blind to is the fact that adaptability is not enough. Models of reality must adapt in a specific manner. In statistics, there is something called "overfitting". It's the situation in which our models fit the data perfectly but do not go beyond it in the way that we expect it. According to Popper, this would be fine. So you have a sequence of observations such as 1 2 3 and you want to model it. Popper says you do so by coming up with any kind of model that fits the data. Okay, so I come up with a model. Now Popper says you use deduction to make predictions i.e. what kind of observations you assume will come next in the sequence. I use deduction and I get something like 1 2 3 0 0 0 0 0. I then set out to test my theory by testing my predictions against reality. I then realize that the next observation in the sequence, quite suprisingly, is number 4. I ask Popper what to do now and he says "adapt!" And I do so by changing my model so that it now makes the following predictions: 1 2 3 4 0 0 0 0. Pretty neat, huh? Well, not so if we ask our intuition. Our intuition wants to build a different model, a model that makes the following predictions: 1 2 3 4 5 6 7 8. Of course, Popper was aware that his theory is stupid, so in order to save it, he added additional rules such as Occam's rule of razor otherwise known as the principle of economy. But he never bothered to define these rules. Is it because he was afraid of doing so? what if he realized that thinking is in fact a rule-bound, deterministic, process? that thinking is fundamentally inductive?

...inductive arguments... can be logically certain/valid but they can never be empirically certain. — Magnus Anderson

Well, no, thy can't be valid. Validity happens only with deductive arguments. Ascribing validity to inductive arguments is at best metaphorical, and more often than not a philosophical feint.

Isn't Bayesian inference based on induction? — Cavacava

How so?

An argument is logically valid if it does not violate the rules of reasoning. Both deduction and induction must follow some rules of reasoning.

This is logically valid:

1. All swans in the past were white.
2. Every swan in the future will be white.

This is logically invalid:

1. All swans in the past were white.
2. Every swan in the future will be black.

This is not merely a metaphor and certainly not a deception.

1. All swans in the past were white.
2. Every swan in the future will be white. — Magnus Anderson

No, it is not valid.

Sure, it is not valid. Because you say so. We'll leave it at that.

It's not valid because it contains two unrelated relations - "...in the past..." and "...in the future..."; and so the conclusion doe snot follow from the premise.

If it is valid, show us its form.

And if it is cogent, why are the swans around here black?

Inductive reasoning operates according to some set of rules. This is obvious from the fact that some conclusions are permitted (e.g. that every swan in the future will be white given that all swans in the past were white) and that some conclusions are not permitted (e.g. that every swan in the future will be black given that all swans in the past were white.) When there are no rules, every premises-conclusion combination is fine.

Things exist whether we are aware of them or not. This means that rules exist whether we are aware of them or not. If we are not aware of the underlying rules of reasoning that does not mean that there are no such rules. Does that make sense? When we reason inductively we follow a set of step-by-step instructions on how to do so. But when we describe how we reason inductively we usually leave out a lot of detail. Our descriptions are not exhaustive and detailed but simplistic and shallow. We do not list EVERY SINGLE PREMISE that leads to our conclusions. So if you do not see how premises are bound to a given conclusion, that does not mean that they aren't bound.

If it is valid, show us it's form. — Banno

Do I have to show you its form, i.e. describe the process in detail, in order for you to accept that inductive reasoning is a rule-bound process? Is that necessary? Shouldn't that be obvious from the fact that some premises-conclusion combinations are legal and others aren't?

And if it is valid, why are the swans around here black? — Banno

If an argument is valid that does not mean that its conclusion is empirically true.

Here's a valid logical argument:

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

Does that mean it is empirically true that Socrates has a blonde hair? No.

Popper, Logic of Scientific Discovery:

A theory of induction is superfluous. It has no function in a logic of science.

The best we can say of a hypothesis is that up to now it has been able to show its worth, and that it has been more successful than other hypotheses although, in principle, it can never be justified, verified, or even shown to be probable. This appraisal of the hypothesis relies solely upon deductive consequences (predictions) which may be drawn from the hypothesis: There is no need even to mention “induction”. — Banno

Questions:

Is "a theory of induction" equivalent to the practice of inductive reasoning?

Are predicted consequences deductive? If they were they would be logically entailed by a theory being correct. I don't think this is the way it works. Think about the prediction that gravitational lensing would be observed if Einstein's theory that mass warps spacetime were correct. Gravitational lensing is not logically entailed by curvature of spacetime, but analogically suggested by knowing how a curved lens refracts light. The prediction is thus inductive and abductive not deductive, because it is based on the expectation that curved spacetime will act like curved glass or polycarbonate is observed to.

Inductive reasoning is indispensable to science, to any non-arbitrary conjecture at all. It is as much an example of inductive reasoning to think that natural processes, and the behavior of materials, were the same in the past as it is to think that they will be the same in the future. Cosmological theories and the theory of evolution would be incoherent without the assumption that the laws of nature have not changed. Without stable laws of nature we would not be able to reliably test, to verify or falsify, any theory at all.

This would seem to an example of Popper being either obtuse or disingenuous; unless he was referring to "a theory of induction" rather than to the practice of inductive reasoning, per se.

BTW, you still haven't told me why you think my deductive framing of the belief that the Sun will rise in the future is invalid.

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.

Are you seriously suggesting that Popper supported induction?

No, I am saying he was inconsistent and mistaken if he did not support it.

One of the things that has been troubling me is the passionate adherence to induction being displayed here. I couldn't fathom it. It is so apparent that inductive syllogisms are invalid. How could the reasonably intelligent folk hereabouts not see this? But then:

Inductive reasoning is indispensable to science, — Janus

Ah.

Overly simplistic descriptions of scientific method do say things like that. SO folk think that by dismissing induction I am dismissing science. Noting could be further from the truth.

Cool. I think Popper's account of scientific method wrong, too.

But Popper being wrong does not make induction right.