Definitely! :) Yes I would seek to find some sort of compromise. — Perplexed
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.
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
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
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
The problem is that you do not understand what logical consequence is. — Magnus Anderson
the logical consequence of "Some Ps are Qs" is "All Ps are Qs" — Magnus Anderson
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
This is simply mistaken; the only logical consequence of "Some P's are Q's" is that some P's are Q's.
That's exactly what logical consequence is in the broad sense of the wrong. — Magnus Anderson
And here you're defining the concept of logical consequence narrowly. — Magnus Anderson
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
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
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
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
This is valid:
1. Some Ps are Qs
2. All Ps are Qs — Magnus Anderson
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
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
Constraint is, as I understand it, simply a limit to what is possible. The opposite of it is freedom. — Magnus Anderson
The world we live in, in other words, is stable enough to make induction good at making predictions. This makes perfect sense. — Magnus Anderson
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
This is not so unreasonable: all the evidence that we have of such invariances is in the past. — SophistiCat
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