That sounds both defeatist and strangely preposterous. — Olivier5
https://en.wikipedia.org/wiki/Squaring_the_circle[The first of these two misguided visionaries filled me with a great ambition to do a feat I have never heard of as accomplished by man, namely to convince a circle squarer of his error! The value my friend selected for Pi was 3.2: the enormous error tempted me with the idea that it could be easily demonstrated to BE an error. More than a score of letters were interchanged before I became sadly convinced that I had no chance. — Carroll
I don't know why theists think "God" will guarantee the validity of science. — Gregory
Socrates went to his death asking those questions, and all should model his life in that regard. He never said, "I don't know the answer yet, so I guess I'll just stop asking the questions." That's laziness. That's a cop-out. That's what I'd call philosophical suicide. — Dharmi
And a concept is simply a what? And so on, until the whole dictionary hovers without foundation. — norm
n other words, the whole point of existence is that question. — Dharmi
Descartes, Leibniz, Giordano Bruno, Gassendi, Averroes, Avicenna...
Ari-fuckin-stotle. — Olivier5
the significant point is that the scientists are usually playing catch-up with the philosophers — Joshs
Looking at your conversation with Olivier, I should add that there are no fixed boundaries between what constitutes science vs philosophy. There are more and less theoretical or applied sciences , and the same goes for philosophy( analytic vs continental) . I’m less interested in whether a particular set of ideas is labeled philosophy or science that how profound and useful
those ideas are. I should add that all other areas of
culture including poetry, literature , music and art , contribute to the shaping of theoretical ideas. That’s why I’m fascinated by the way a particular scientific theory belongs to a large cultural
movement. — Joshs
It's a historical fact. — Olivier5
the sciences are, even when wholly speculative, based on a body of empirical knowledge acquired by testing that is usually too extensive or specialised for a single person to carry out. — Isaac
Anyone can do what Kant did. — Isaac
The mind is not an entity that could stand in a relationship to anything. All talk of the mind that a human being has and of its characteristics is talk of the intellectual and volitional powers that he has, and of their exercise. — Human Beings – The Mind and the Body: Wittgensteinian-Aristotelian Reflections - Peter M.S. Hacker, 2007
OK, but you said 'a number is simply a concept.' That's linking one controversial word to an even more controversial word. There's no question that we can use both words in practical life with no problem, but when we play the game of metaphysics and try to make some concept (whatever those are exactly supposed to be) absolute, [fizzle, endless confusion]. — norm
Empiricism insists that what is proposed must be able to be validated by sense data, including data acquired by instruments. — Wayfarer
There's a current Smithsonian Institute essay on what is math that is worth perusing. I'm *still* with the Platonists. The metaphysical impact of 'the reality of number' is that 'number is real but not materially existent'. Therefore, there is an important class of things, that is real but not materially existent. Therefore, materialism is false. — Wayfarer
A theory that can't explain a fundamental aspect of reality like conscious awareness is a theory that's already in trouble. — RogueAI
Until you ask the grocer for six bananas, and he gives you five, protesting that 'six is only a concept'.
'Concept, schmoncept', you say, storming out, without paying. — Wayfarer
At the same time I do not have an intuition of 2,343,546,343,454,654,765. I can't see it in my mind. I am confident that it can be handled with calculations, that we can make objective statements about such integers — norm
The problem or comedy is that philosophical realizations (breakthroughs, revolutions) don't necessarily provide wonder-working technical power. — norm
But here your confusing conception and imagination. A concept is different to what you can imagine. Descartes gave the example of a chilliagon, a thousand-sided polygon. You can’t reliably imagine such a thing, but if I tell you what it is, you can understand the concept and even reproduce it, albeit painstakingly. — Wayfarer
‘Platonic heaven’ is also a misconception. There is a ‘domain of natural numbers’, right? Where is it? Obviously no place. It’s not some ‘ethereal ghostly domain’. It’s not ‘out there somewhere’. Nevertheless it’s real, because 2 is ‘in’ it, while the square root of 2 is not. — Wayfarer
Platonic realism regarding numbers does not mean that imaginary number systems are real. They’re imaginary, by definition. Given the ability to grasp number, then we have the ability to invent such things. But that doesn’t undermine platonic realism. — Wayfarer
The philosophical realisation that underlies our world began with Descartes’ algebraic geometry combined with Newton’s and Galileo’s science. That philosophical revolution certainly provided wonder-working technical power. You’re looking at it. — Wayfarer
I agree that there are shades of meaning between the words, but what is it to 'understand' a concept? Call it 'grasping' (a metaphor) or whatever. The point is that some kind of 'having' of some private experience is invoked. I 'understand' what is meant in the usual way. My objection is pushing these ambiguous havings into something impossible sharp. We can't mind meld. We are stuck debating English usage, and yet the temptation is to think it's a kind of science of immaterial realms. — norm
Sets are abstract objects, lacking any spatio-temporal location. Their existence is not contingent on our existence. They lack causal efficacy. Our question, then, given that we lack sense experience of sets, is how we can justify our beliefs about sets and set theory.
There are a variety of distinct answers to our question. Some philosophers, called rationalists, claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.
I'm saying that classical metaphysical arguments don't have obvious winners in the real world. And if I give reasons for their futility, I'm also just wasting my time in practical terms, because in general people don't take such things seriously to begin with, and those who like metaphysics are often religiously-politically motivated or just still captured by the notion that they are doing some kind of higher Science. It's a harmless vice, as is critiquing it. — norm
Hence my accusation of historicism. That science did develop from philosophy tells us nothing at all about the necessary relationship between the two.
That a sequence of events happened to take place is not evidence that they are causally connected even, let alone necessarily so. — Isaac
There is a difference between historicism (the idea that history follows determinist laws à la Marx) and recognizing established historical facts. — Olivier5
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