Perplexed by name; perplexed by nature. Seems you want to keep your deterministic cake but want to eat the free will topping too. — charleton

Definitely! :) Yes I would seek to find some sort of compromise. Are you saying you'd be happy to give up free will?

The concept of logical necessity has been mystified. In order to demystify it we must first understand that a logical argument is nothing more than a mathematical function; or more generally, a relation between two sets. You have premises, which are analogous to inputs, and a conclusion, which is analogous to outputs. It's pretty straightforward to determine whether an equation is true or false. If f(a, b) = a + b then f(2, 2) = 5 is not true. The conclusion (5) does not follow from the premises (2 and 2.) That would be analogous to a logically invalid argument. I think this is pretty clear to everyone. What's not clear is that this is exactly what it means for an argument to be logically invalid. Most people think in terms of truth-preservation. But truth-preservation and logical validity are two different things. In the example above, we're dealing with tautalogical (or unconditional) truths. 2, 2 and 5 are all logically true. It is thus impossible for the premises to be true and the conclusion to be false. And yet, the argument is not valid. Truth-preservation is just a common symptom of validity. Nothing more. To equate the two is to say that 2 + 2 = 5 is valid which is counter-intuitive. And to say that induction is invalid merely because it is not explicitly truth-preserving is deceptive since it indicates there is something wrong with it.

Truth-preservation is a very deceptive concept because it suggests that if you know the past that you can predict the future with certainty. That's not true. A much more careful definition is required in order to avoid that but that is a non-trivial task.

Every logical conclusion is empirically uncertain. This means that even if you know all of the past with perfect accuracy, your predictions can still turn out to be wrong. Thus, it makes no sense to emphasize that inductive conclusions are probable since deductive conclusions are no less probable.

Definitely! :) Yes I would seek to find some sort of compromise. — Perplexed

There is no compromise. Just one choice, one probabilistic (or random choice), no matter how small, destroys determinism. Compatibilism attempts to compromise but any reading of it yields a contortionist mess. Something like you can will want you want, but if you want what you will, you'll end up with wants but no will ... or some silliness like that.

In any case, no compromise. However, since what you think is determined (if you are still a determinist at this reading), it should be of no mind to you. When the Laws of Nature get around to allowing you to believe in something else, they'll let you know. I hope you are happy with whatever decision that had been already made for you.

What we need to remember about Popper's version of Peirce's triadic modelling relation is of course that Popper makes the leap from merely a psychology of reasoning to claims about a transcendental or objective truth. The signs are cut adrift from their interpretant..

Popper seems to take his three worlds more ontologically seriously than I had assumed. It is more than just a metaphor or a convenient figure of thought. He credits Plato with the discovery of the third world, but differs from him as to it divine origin and claims that it is too restrictive in its scope. The stoics, he recalls, took over the Platonic realm of forms and added to it, not only objects, such as numbers, but relations between them, such as expressed by theorems. Problems too were to be part of it as well.

https://www.researchgate.net/file.PostFileLoader.html?id=59ae71f3ed99e178ec7dd8b6&assetKey=AS%3A535179471343618%401504608137511

Strictly speaking, there is no such thing as the inductive logic.

Ssssh. They don’t want to know.

Not true.

Here's an inductive argument:

1. Some Ps are Qs
2. Therefore, all Ps are Qs

The conclusion necessarily follows from the premise. You cannot conclude something like "Therefore, no P is Q". It is necessary that you conclude "Therefore, all Ps are Qs". Note that we're talking about logical necessity and not objective necessity. — Magnus Anderson

1. Some men are bald

Do you seriously believe that this logically entails that all men are bald?

Wow, man, if you really believe that then I'm not sure there is any point conversing with you further.

The theory of evolution, like any theory, is based on what we already know. Induction is a way of inferring what we don't know, whether it occurs in the past or in the future. — SophistiCat

Evolution is based on the assumption that the invariances of nature have been consistently the same during the past as we find them today. I am pointing out that this assumption is as just as warranted or unwarranted as the assumption that the invariances of nature will be the same in the future as today. So, my point was that inductive inferences are essential to the theory (Evolution) that you were purporting to use to undermine the justifiability of inductive reasoning. I'm surprised you cannot see the problem with this.

No problem. I guess it was how I perceived your tone that led me to believe that you wanted to disagree but apparently I was mistaken. :)

1. Some men are bald

Do you seriously believe that this logically entails that all men are bald?

Wow, man, if you really believe that then I'm not sure there is any point conversing with you further. — Janus

Maybe you should start paying attention to what other people are saying.

I've already said that every conclusion is empirically (or semantically) uncertain. Even if you knew everything there is to know about the past, your predictions can still turn out to be wrong. The future is under no obligation to mimic the past.

The problem is that you do not understand what logical consequence is.

The problem is that you do not understand what logical consequence is. — Magnus Anderson

No, the problem is that you apparently cannot explain what you think logical consequence is. You also need to explain what you think the difference between logical and objective necessity is, and for that matter what you think objective necessity could even be.

I can say the same about you. In fact, I'd probably be more right than you are. A lot of people think they understand what they are talking about; and they do, but very superficially. If I asked you to define logical consequence, I'm pretty sure you'd struggle. Either that or you would define it the same way that I do just unnecessarily narrowly.

The logical consequence of 2 + 2 is 4. That's what you get when you follow the rules of addition. In the same way, the logical consequence of "Some Ps are Qs" is "All Ps are Qs". That's what you get when you follow the rules of induction. Very simple.

the logical consequence of "Some Ps are Qs" is "All Ps are Qs" — Magnus Anderson

It's just not so; and I doubt anyone would agree with you. Have you studied logic at all?

In predicate logic

• ∀ x: P(x) or (x) P(x) means P(x) is true for all x. ( 'x' here substitutes for 'Q' in your example)

• ∃ x: P(x) means there is at least one x such that P(x) is true.

( '∀ x' means "all x" or "for all x". '∃ x' means "there exists x").

There is a clear logical distinction between these two types of propositions, but in your understanding they are conflated, and the distinction is discarded.

You seem to think that if the logical entailment of "Some P's are Q's" is not "No P's are Q's" then it must be "All P's are Q's". this is simply mistaken; the only logical consequence of "Some P's are Q's" is that some P's are Q's.

Fair point.

Odd, that you find yourself arguing my case against Magnus.

You seem to think that if the logical entailment of "Some P's are Q's" is not "No P's are Q's" then it must be "All P's are Q's". — Janus

That's exactly what logical consequence is in the broad sense of the wrong.

This is simply mistaken; the only logical consequence of "Some P's are Q's" is that some P's are Q's.

And here you're defining the concept of logical consequence narrowly.

That's exactly what logical consequence is in the broad sense of the wrong. — Magnus Anderson

I am left wondering what that even means.

And here you're defining the concept of logical consequence narrowly. — Magnus Anderson

Logical entailment is a very precise ("narrow" if you like) concept.

I don't know...I hadn't formed the opinion that we disagree when it comes to logical entailment. :)

You are focusing too much on specifics. Sort of like Banno. This can be dangerously deceptive. Banno says that induction is invalid which suggests that there is something wrong with it. You try to counter this by saying that induction is neither valid nor invalid. But does Banno really care? Of course not. He's focusing on his extremely narrow definitions. Nothing can change his mind because what he says is true by definition. Both of you are being too formal. Both of you ignore there's much debate about what logical consequence is. Both of you restrict yourself to Wikipedia and high-school textbooks. I am certainly not the first to speak of inductive validity but is that really important?

An argument is valid in the general sense of the word if it does not violate the rules of reasoning.

This is valid:

1. Some Ps are Qs
2. All Ps are Qs

This is invalid:

1. Some Ps are Qs
2. No P is Q

This is also invalid:

1. Some Ps are Qs
2. Half of Ps are Qs, half of Ps are not Qs

It's all relative to the rules of reasoning.

This is valid:

1. Some Ps are Qs
2. All Ps are Qs

This is invalid:

1. Some Ps are Qs
2. No P is Q

This is also invalid:

1. Some Ps are Qs
2. Half of Ps are Qs, half of Ps are not Qs

It's all relative to the rules of reasoning. — Magnus Anderson

OK, I think I see where you are coming from now. It may be consistent with "some Ps are Qs" that all Ps are Qs, but not that no Ps are Qs. So, you are thinking of logical consequence, not in the sense of logical entailment, but of semantic consistency.

I don't see why

1. Some Ps are Qs
2. Half of Ps are Qs, half of Ps are not Qs

is counted by you as invalid by this criterion of consistency, though, because it seems perfectly consistent with "some Ps are Qs" that half of Ps could be, and the other half not be, Qs.

Banno says that induction is invalid which suggests that there is something wrong with it. You try to counter this by saying that induction is neither valid nor invalid.But does Banno really care? Of course not. He's focusing on his extremely narrow definitions. Nothing can change his mind because what he says is true by definition. — Magnus Anderson

Where I disagree with Banno is that it is appropriate to submit inductive reasoning to the criterion of logical validity; which belongs to only to deductive reasoning. I also may disagree with him in thinking that all inductive reasoning can be reframed in deductive form and that it then does become subject to what you would call the "narrow" notion of validity.

OK, I think I see where you are coming from now. It may be consistent with "some Ps are Qs" that all Ps are Qs, but not that no Ps are Qs. So, you are thinking of logical consequence, not in the sense of logical entailment, but of semantic consistency. — Janus

I am not sure we are on the same page. I don't think that the argument is valid because the two sentences are consistent. I don't even know what that means. I am saying that the argument is valid because it does not violate the rules of that particular type of reasoning. In induction, the rule is "if most Ps are Qs then you must conclude that all Ps are Qs." The rule is implicit in the narrow definition of induction making inductive reasoning necessarily valid (i.e. it cannot be invalid.) I covered this in one of my previous posts.

Here's a general form of probabilistic argument:

1. X out of Y Ps is Q
2. Therefore, this P is R

I intentionally define probabilistic reasoning to be of this general form in order to make it possible for it to be invalid.

Here's a valid probabilistic argument:

1. 3 out of 5 men are alcoholics
2. Therefore, this man is an alcoholic

Here's an invalid probabilistic argument:

1. 3 out of 5 men are alcoholics
2. Therefore, this man is not an alcoholic

Why is this argument invalid? Because it violates the rules of probabilistic reasoning. The main rule of probabilistic reasoning is that if most Ps are Qs then you must conclude that a particular P is also a Q. If you don't, the argument is invalid.

Where I disagree with Banno is that it is appropriate to submit inductive reasoning to the criterion of logical validity; which belongs to only to deductive reasoning. I also may disagree with him in thinking that all inductive reasoning can be reframed in deductive form and that it then does become subject to what you would call the "narrow" notion of validity. — Janus

If you define validity the way he does, as truth-preservation, then yes, he's right, induction is invalid because its conclusion can be true and its premises, defined restrictively, false. There is no arguing with this. The question is: why is that relevant? The answer is probably that it isn't relevant. The "problem" with induction is that there is no problem with induction but with deduction. The problem is our understanding of logical necessity. It's a very deceptive concept. We say that a deductive argument is valid if it is impossible for the premises to be true and for the conclusion to be false. This suggests that there is such athing as absolute certainty. And this is caused by the fact that we are confusing two different types of premises: low-level premises (such as observations) and high-level premises (such as general statements.) Put simply, we are confusing observations with assumptions. That's a problem. Induction operates on low-level premises (observations) whereas deduction operates on both low-level premises (observations) and high-level premises (generalizations.) Observations cannot contradict other observations. What observations can do is they can contradict our generalizations or assumptions. This is because generalizations are derived from observations. So if the base of observations from which a generalization is derived changes, it's very possible for the generalization to change as well. Take a look at the following argument:

1. All men are white
2. Socrates is a man
3. Therefore, Socrates is white

Insofar the second premise is a raw observation it cannot change if the conclusion turns out to be false. However, the first premise can because it is a general statement. Such a general statement is derived inductively from previous observations. It's an open system. If it is possible for the set of observations on which it is based to change, for example by making a new observation, then it is possible for the statement to change as well. If the conclusion turns out to be false then we'll have a new observation in our set of observations and this observation, telling us that there exists a man who is not white, would require that we change our conclusion. On the other hand, exceptions do not disprove the rule, they merely make it weaker. So if a thousand men are white and a single man is black then we can preserve our general statement. But if we reach a point where a thousand men are white and a ten thousand of men are black, then we'd have to change it. This is, of course, a simplification of what's going on in reality. Our conclusions need not be this simplistic in practice. We can let exceptions influence our actions. But describing in words how this process works is a chore.

Both deductive and inductive arguments are adaptive it's just that deduction adapts through contradiction whereas induction adapts through observation. The second might also be true of deduction but it's usually not the case because most people see deduction as distinctively negative (or eliminative) process. In fact, they think of it so negatively that they think that every contradiction requires a change in one of the premises. Which is sort of true but is also sort of insane. As Einstein said and Popper thought, "No amount of experimentation can ever prove me right; however a single experiment can prove me wrong." The question is, of course, how precise you want to be. Most people are fine with ignoring exceptions. Within that sort of mindset, falsification/negation is not so different from verification/affirmation. Many deductionists also think that deduction can only tell you what's wrong and never what's right. Think of Socrates, think of his dialectic, think of his famous statement "the only thing I know is that I know nothing."

This is valid:

1. Some Ps are Qs
2. All Ps are Qs — Magnus Anderson

Ah! Magnus might think that because both can be true, it is valid.
but unfortunately these can also both be true:

1. Some Ps are Qs
2. Not all Ps are Qs

Anyway, he's a newbie, and will probably realise his error eventually.

That's not what I think. Just because the premises are true, or can be true, does not mean the argument is valid. "True xor true = true" is not valid even though its premises and conclusion are all logically true and equal to true.

Evolution is based on the assumption that the invariances of nature have been consistently the same during the past as we find them today. I am pointing out that this assumption is as just as warranted or unwarranted as the assumption that the invariances of nature will be the same in the future as today. So, my point was that inductive inferences are essential to the theory (Evolution) that you were purporting to use to undermine the justifiability of inductive reasoning. I'm surprised you cannot see the problem with this. — Janus

I understand what you are saying. I am granting, for the sake of an argument, one half of your "invariances of nature," so to speak: those that lie in the past. This is not so unreasonable: all the evidence that we have of such invariances is in the past.

Will these invariances persist into the future? You gave a kind of transcendental argument (correct me if I am wrong): our shared inductive intuitions provide us with a reason to believe the affirmative. But, as I have argued, the fact that we have those intuitions is not independent from the (already assumed) fact that nature exhibited invariances in the past. So what I am saying is that shared intuitions do not provide you with a reason to believe that invariances will persist into the future, over and above the assumption of invariance in the past.

good. You are slowly working it out.

The more I observe this thread, the more I realize (empirically) how useless logic is. What is literally happening is that not-logical thinking it's being used to figure out whether the conclusions of deductions and inductions are reasonable. Very instructive.

I am going to return to something @apokrisis said in response to me on page 8.

Constraints generate regular patterns in a probabilistic fashion. So that is how science understands physical systems. And it is how we would speak of nature if we take a systems view where we grant generality a reality as a species of cause.

So again, it is simply a reflection that I am arguing from a consistent metaphysical basis. It is how reality would be understood if you believe in an Aristotelean four causes analysis of substantial being. — apokrisis

I am struggling to understand what you mean when you say "constraint". The way I understand it, and the only way I can sensibly interpret it, is that the word "constraint" means nothing other than pattern, regularity, law, order, etc. However, as it appears, that's not what you mean by the word. Instead, you mean something . . . else. What this else is I don't know. I think it has something to do with "downward causation". Which is another obscure term that is often thrown around. Perhaps I should start a new thread dedicated to this concept? Just to see if someone else can elucidate it for me. Or maybe someone here can help me with it?

Constraint is, as I understand it, simply a limit to what is possible. The opposite of it is freedom. It is that which allows us to discriminate between those possibilities that are more likely and those that are less likely. It's a very simple concept. But your exposition is generally quite obscure and complicated (as is that of Charles Sanders Peirce.) This suggests to me that we might not be on the same page.

You say that "history builds constraints on free possibility". The only sensible manner in which I can interpret this statement is in the sense that the world we live in is relatively constant. The universe is flux, i.e. it is constantly changing, but it is doing so at a rate that is sufficiently low to make induction successful in most cases. The world we live in, in other words, is stable enough to make induction good at making predictions. This makes perfect sense. But the fact that you do not express yourself in such simple terms suggests to me that your point is a different one. In fact, it suggests to me that you find this type of process philosophy, the one championed by Heraclitus and Nietzsche, deficient in certain regards.

Constraint is, as I understand it, simply a limit to what is possible. The opposite of it is freedom. — Magnus Anderson

Yep. Simple really.

The world we live in, in other words, is stable enough to make induction good at making predictions. This makes perfect sense. — Magnus Anderson

Yep. You got it again.

If you define validity the way he does, as truth-preservation, then yes, he's right, induction is invalid because its conclusion can be true and its premises, defined restrictively, false. — Magnus Anderson

"Truth-preservation" is really just consistency, which means not having premises which contradict one another or the conclusion. The validity of deductive arguments is independent of the truth of premises, maybe that's where you're becoming confused; I don't know.

This is not so unreasonable: all the evidence that we have of such invariances is in the past. — SophistiCat

Yes, but even counting written records of the human past as knowledge relies on the assumption that those written records have not themselves changed; that they are the same as when they were written. When it comes to the pre-historic past all bets are off. If the laws of nature could change in the future then why could they not have changed innumerable times in the past? How could we know? All of what we count as knowledge is based on the assumption that they have not changed, just as all our predictions of the future assume that they will not change. Even out trust in our own memories assumes that they have not changed. Once you open the Panodra's Box of radically questioning belief in natural stability and invariance the logical conclusion is chaos; the total undermining of all our supposed knowledge. Hume just didn't go far enough; he didn't see where his questioning would logically lead.

Oh sure, inferences of past events are as vulnerable to skepticism as inferences of future events, and at some point, when you come to question your cognitive abilities, you immediately undercut your own line of reasoning.

Hume was an empiricist, not a skeptic. He believed that perceptions were the ultimate source of truth. He also apparently believed that at least some understanding of the world could be firmly grounded in perceptions and thus be validated. Of course, a thoroughgoing skeptic could destroy this worldview without breaking a sweat.

So what can we do? Well, if you seek the ultimate grounding of your beliefs in rules - be they the rules of deduction or some other epistemic rules, such as the wisdom of the crowds - then you are setting yourself up for disappointment. I think that induction is normative, not unlike ethics, which similarly resists grounding in something external to itself. You believe in it not for any reason, but because you can't help it.