Would you agree that we have little doubt in local or everyday contexts? I do of course see a connection to religion and culture here. I personally think it is clear that concepts exist. The first question might be: "In what way do concepts exist?" But the second question is fascinating, too: "What sort of conclusive answer to the first question can we really hope for?" Is there a shared criterion in place that allows us to agree on a correct answer-- assuming one "exists"? — R-13
[Rationalists] claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. These claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.
Pure theory can be viewed as the quest to construct indestructible tools that never become obsolete — R-13
The point I make is fairly simple but has profound consequences: that if numbers are indeed real, but not material, then this contradicts materialism and empiricism, as mathematical objects are precisely not object of experience, or really objects at all in the material sense. — Wayfarer
However I would rather believe the rationalists. — Wayfarer
Sometime before that I had been struck by an epiphany of sorts, which was that natural numbers are different to phenomenal objects in two principle ways: they are not composed of parts, and they don't begin and end in time. (Later I realised that strictly speaking, this describes prime numbers.) I wondered if this was something that was understood in philosophy, and found that it was characteristic of the Pythagorean-Platonic attitude. I learned that the Platonism generally had the understanding that this enabled the mathematician to grasp a higher order of truth. — Wayfarer
Nominalism can be falsified: simply show evidence for a real universal. — Terrapin Station
Nominalism can be falsified: simply show evidence for a real universal.
Of course that's not so simple as there are no real universals, but if there were, one would just have to show evidence of one, and that would falsify nominalism. — Terrapin Station
How do you circumvent "the problem of abduction" - i.e. that it's just another name for induction, which never happens in reality, because it can't. — tom
I roughly believe that the human being is "essentially" an engineer and that thinking is usefully conceived of in terms of engineering. — R-13
I would probably not go quite that far. However, I do think that Peirce's characterization of inquiry as the struggle prompted by doubt, which has the fixation of belief as its goal, is analogous to ingenuity as the struggle prompted by uncertainty, which has the fixation of decision as its goal. — aletheist
Abduction is not another name for induction, and induction can and does happen in reality. The scientific method employs both of them routinely. It seems like you may not be familiar at all with what Peirce meant by these terms. — aletheist
Both abduction and induction are ... certainly not part of the scientific method as expounded by Popper. — tom
The histories of quantum mechanics and relativity for example bear no traces of tales of abduction or induction ... — tom
Right - Peirce once described pragmatism as "scarce more than a corollary" of Alexander Bain's definition of a belief as "that upon which a man is prepared to act." — aletheist
This is the point of view I was coming from as a critic of "terminological" disputes or "differences that make no difference." — R-13
The Popper who wrote Conjectures and Refutations? Conjectures result from what Peirce called abduction (or retroduction), and refutations (or corroborations) result from what Peirce called induction. — aletheist
Do you really want to claim that quantum mechanics and relativity did not begin as plausible conjectures to explain surprising phenomena (abduction), which had predictable experiential consequences (deduction) that were subsequently evaluated through rigorous experimental testing (induction)? — aletheist
What does happen according to the scientific method is a problem is encountered and a solution is conjectured, and there is no method for this part of problem-solving. — tom
We live in a world where there are numbers, people, ideas, chairs, germs, atoms, etc. — R-13
, we agree more or less on what's going on in a practical sense, so it's seems largely of matter of taste as to how we frame this all up metaphysically. — R-13
I’m very comfortable with the universals of rudimentary geometric figures, but I don’t take these to be numbers. Numbers, on the other hand, to me are cognitive models, or representations, of quantity. Geometric points then seem to naturally be the core root of all mathematical universals: via multiplicity of geometric points one attains quantity (numbers) and geometric forms, dimensions, etc. Yet geometric points as well are a human model, or construct. This leads me to believe that they too represent some universal that is independent of human models—such as, for example, can be stated of quantity and its relations being independent of human models. — javra
If you were doing one of those tests where they asked you to identify the anomolous members of a set, then 'numbers' and 'ideas' would certainly jump out, possibly followed by 'germs' and 'atoms'. — Wayfarer
This is very well said, and I agree very much. I associate philosophy with (among other things) becoming more conscious of these judgments that function as lenses. We are free to question and possibly replace such a judgment only after we become aware that we've been taking it for granted all along as a sort of necessity. This is the value, as I see it, in questioning the question. Let's say that we assume that either nominalism or realism is correct. Would we not still need a criterion to establish the correctness of one or the other? And yet philosophy seems largely to be the endless construction, criticism, and refutation of such criteria. The dream or goal seems to be something like a self-founding or self-justifying criterion or authority.Our perceptions and conceptions are inextricably bound up with rational judgement; we see 'through' those judgements, without realising that we're doing it. That is the sense in which the elements of rational judgement inform and underlie our 'meaning-world'. — Wayfarer
Let's say that we assume that either nominalism or realism is correct. Would we not still need a criterion to establish the correctness of one or the other? And yet philosophy seems largely to be the endless construction, criticism, and refutation of such criteria. The dream or goal seems to be something like a self-founding or self-justifying criterion or authority. — R-13
But the dream, or goal, is what it always was: the vision of truth. — Wayfarer
So if we ask, do geometric forms, scientific laws, and so on, exist, the answer is not obvious; they don't exist as phenomena, although geometric forms can clearly be represented phenomenally. And, even if number is 'the representation of quantity', it is still something that can only be grasped by an intelligence capable of counting. So what intrigues me, is that these are in some sense 'independent of any mind' i.e. they exist independently of anyone thinking about them, but they're still only perceptible to a mind. I think that is very near the meaning of 'objective idealism'. — Wayfarer
I agree. We seek the truth. And this seems to include the truth about truth-seeking. We find ourselves debating about how truth is or should be established. It seems that one aspect of philosophy is particularly concerned with the truth about truth, rather than the truth about life, for instance. It aspires to be meta-knowledge. Religious traditions might have it easier. What assumptions motivate us to defend the truths we are sure of? Philosophy seems to assume that truth is the result of or at least subject to debate. — R-13
Some would say that universals hold constraints upon particulars; else stated, that there is a top-down causation imposed upon particulars by universals. — javra
That was indeed Popper's view, but not Peirce's. The latter suggested - long before Popper wrote anything - that the logical form of abduction looks something like this:
The surprising fact, C, is observed.
[*}But if A were true, then C would be a matter of course.
Hence there is reason to suspect that A is true.
Indeed, this is deductively invalid - reasoning from consequent to antecedent, which is why Peirce also called it retroduction and acknowledged that its outcome is merely plausible at best. However, it furnishes the components of a perfectly valid deductive syllogism in which the conclusion is the surprising fact (C), the minor premiss is the credible conjecture (A), and the major premiss is the reason why C follows necessarily from A. In other words, A explains C in light of other known information, so a well-prepared mind is absolutely essential to the generation of viable hypotheses. — aletheist
Nevertheless, the logical form of induction is such that if the hypothesis is false, this will eventually come to light - it is by no means infallible, but it is self-correcting over the long run. — aletheist
What would you count as evidence for a real universal? — aletheist
On the other hand, is realism is falsifiable? — aletheist
The innate notion of good--i.e., of what is beneficial--is, I argue, a universal. By this shouldn’t be interpreted concrete examples of what is good—be these either presumed relative to context or independent of context. Nor do I intend issues regarding good for whom. Instead, I merely intend that the innate awareness of what is beneficial is universal and stands apart from any sentience in and of itself: good is a property that can be divorced from the properties of an individual sentient being. Yes, what is good to you is not always likewise good to me (sometimes), yet despite this there is yet the universal awareness of there being something which we cognize and label “good”. For one extreme example, ameba won’t cognize the concept of good but will yet be endowed with awareness of what is good, i.e. beneficial. — javra
Sure, and no matter how many times I ask for an example of abduction or induction, I never get one. — tom
So, here are a few surprising facts (C) that have been encountered. — tom
There is no "logical form of induction" it is a fallacy. — tom
We'd need to be able to somehow "point" ... at a property that particulars can instantiate, where it's clear that what we're pointing at isn't simply us thinking about the property/formulating a mental concept of the property. — Terrapin Station
The more we look for the above and don't find it, the stronger the falsification is. — Terrapin Station
What would you count as an example of each? Abduction happens every time someone devises a new theory. Induction happens every time someone experimentally tests a proposed theory. — aletheist
To take one of your examples: No one "observed" the Higgs boson until they went looking for it (induction) because it was a necessary consequence (deduction) of an explanatory hypothesis (retroduction). — aletheist
Your view of logic seems too narrow. Again, no one is claiming that retroduction or induction is deductively valid. — aletheist
But you can't give a single example of either. — tom
Just to point out, you previously claimed testing of a theory was a deductive process. — tom
But you are claiming that they happen, they are useful, and that you can appeal to them for justification. — tom
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