We know by logic the laws and axioms which are visible to thought itself - Frege's 'laws of thought' - and so requiring no empirical validation, on account of their being logically necessary; they're not 'out there' but are known true a priori. — Wayfarer
Bertrand Russell said that 'physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.' — Wayfarer
These are designated the 'primary attributes' of objects, and distinguished, by both Galileo and Locke, from their 'secondary attributes', which are held to be in the mind of the observer.
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And through the quantitative method of science, the ability to reduce an objective to its mathematical correlates, the certainty provided by logical prediction can be applied to phenomena of all kinds with mathematical certainty (which is, I think, the point of Kant's 'synthetic a priori). It's the universal applicability of these logical and mathematical procedures to practically any subject which opens access to domains of possibility which would be forever out of reach to a mind incapable of counting. — Wayfarer
Hence the necessity of Platonic realism to the natural sciences. — Wayfarer
Then debating Plato Berkeley said: "an abstract object does not exist in space or time and which is therefore entirely non-physical and non-metal" — javi2541997
There are varieties of mathematical realism other than Platonism. The fact that certain relations among phenomena hold regardless of what anyone thinks about them does not entail that the corresponding mathematical objects metaphysically exist in a realm of concrete forms. As Charles Peirce maintained, echoing his father Benjamin, mathematics is the science of drawing necessary conclusions about hypothetical states of things. Abductive/retroductive explanations (theories/models) are fallible idealizations that require deductive explication (predictions) and inductive evaluation (experiments/observations) to ascertain whether and how well they match up with reality.Hence the necessity of Platonic realism to the natural sciences. — Wayfarer
Correct me if I'm wrong, but I don't think Berkeley actually resolved consciousness requiring space and time to exist, or maybe he did... . — 3017amen
But this also challenges the naturalist dichotomy of mathematics being 'in the mind' and the world being 'out there', which is how we are inclined to instinctively construe it. — Wayfarer
Hence the necessity of Platonic realism to the natural sciences. — Wayfarer
Hence the necessity of Platonic realism to the natural sciences. — Wayfarer
I am somehow disagree in Frege’s laws of thought explaining those axioms were supposedly we don’t need empirical validation because somehow is innate upon us.
Despite the concepts are clear to understand the perfect science and how physics works quoting John Locke’s primary and secondary attributes there is another philosopher which I guess is important here to disagree in these statements: George Berkeley. — javi2541997
Frege believed that number is real in the sense that it is quite independent of thought: 'thought content exists independently of thinking "in the same way", he says "that a pencil exists independently of grasping it. Thought contents are true and bear their relations to one another (and presumably to what they are about) independently of anyone's thinking these thought contents - "just as a planet, even before anyone saw it, was in interaction with other planets." '
Furthermore in The Basic Laws of Arithmetic he says that 'the laws of truth are authoritative because of their timelessness: "[the laws of truth] are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this, that they authority for our thought if it would attain to truth." — Tyler Burge, Frege on Knowing the Third Realm
The fact that certain relations among phenomena hold regardless of what anyone thinks about them does not entail that the corresponding mathematical objects metaphysically exist in a realm of concrete forms. — aletheist
scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.
Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects which aren’t part of the causal and spatiotemporal order studied by the physical sciences.[1] Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate. 1
I just realized that, although right now my mind draws a blank, there possibly are non-mathematical questions we can ask about the world or reality. — TheMadFool
'[Maths being] always out there, somewhere' [1:29] is a misleading analogy, because numbers are not 'in' time and space, so, not 'out there' anywhere. They're not located. The problem is, we instinctively seek explanations in terms of what is 'out there' - it's the habitual extroversion of Western culture. Otherwise known as 'naturalism'.
I have many times advocated on the forum, that ultimately, all of our epistemic efforts rest on preconceptions, persuasions, whatever we want to call them. That we don't access any self-evident facts, but only have attitudes that establish sustainable epistemic allostasis, guided towards epistemic homeostasis — simeonz
I believe that we have to concede that if philosophy was always conservative, we wouldn't make the progress to our present day epistemic understanding. — simeonz
if you can represent something mathematically, that you can use mathematical logic to make predictions about it. The greater the amenability of an object to mathematical description, the more accurate the prediction can be — Wayfarer
You are right, my bad--but that is precisely why I maintain that mathematical objects cannot exist in the strict sense of reacting with other like things in the environment. In accordance with that metaphysical definition, anything that exists is concrete.No, they're abstracts, by definition. — Wayfarer
I agree, and I maintain that reality is being such as it is regardless of what anyone thinks about it. In accordance with that metaphysical definition, the mistake that Platonism has in common with nominalism is treating reality as synonymous with existence. On the contrary, although whatever exists is real, there are realities that do not exist--including numbers and other mathematical objects.It is the nature of the reality of number that is the point at issue. — Wayfarer
the mistake that Platonism has in common with nominalism is treating reality as synonymous with existence. On the contrary, although whatever exists is real, there are realities that do not exist--including numbers and other mathematical objects. — aletheist
I'm not sure how the technical definition of a fractal applies here. Explain what you mean, please. — jgill
That was indeed the medieval debate, but its modern manifestation is affirming the reality of generals in addition to the existence of individuals. Peirce described himself as an extreme scholastic realist in this sense, maintaining that reality includes some possibilities and some conditional necessities, rather than consisting only of actualities.Wasn't the whole issue of scholastic realism versus nominalism is that the former accepted the reality of universals (in Aristotelian form, as mediated by Aquinas), while the nominalists did not? — Wayfarer
Of course, no disputing that — Wayfarer
The Unreasonable Effectiveness of Mathematics in the Natural Sciences' — Wayfarer
The onset of turbulence can be predicted by the dimensionless Reynolds number, the ratio of kinetic energy to viscous damping in a fluid flow. However, turbulence has long resisted detailed physical analysis, and the interactions within turbulence create a very complex phenomenon. Richard Feynman has described turbulence as the most important unsolved problem in classical physics. — Wikipedia
Math, not as effective as Eugene Wigner thought, eh? — TheMadFool
That was indeed the medieval debate, but its modern manifestation is affirming the reality of generals in addition to the existence of individuals. — aletheist
...[C]ritics of Ockham have tended to present traditional [i.e. scholastic] realism, with its forms or natures, as the solution to the modern problem of knowledge. It seems to me that it does not quite get to the heart of the matter. A genuine realist should see “forms” not merely as a solution to a distinctly modern problem of knowledge, but as part of an alternative conception of knowledge, a conception that is not so much desired and awaiting defense, as forgotten and so no longer desired. Characterized by forms, reality had an intrinsic intelligibility, not just in each of its parts but as a whole. With forms as causes, there are interconnections between different parts of an intelligible world, indeed there are overlapping matrices of intelligibility in the world, making possible an ascent from the more particular, posterior, and mundane to the more universal, primary, and noble.
In short, the appeal to forms or natures does not just help account for the possibility of trustworthy access to facts, it makes possible a notion of wisdom, traditionally conceived as an ordering grasp of reality. — Joshua Hochschild, What's Wrong with Ockham
@WayfarerFurthermore in The Basic Laws of Arithmetic he says that 'the laws of truth are authoritative because of their timelessness: "[the laws of truth] are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this, that they authority for our thought if it would attain to truth — Tyler Burge, Frege on Knowing the Third Realm
Isn't this 'biological reductionism'? That being the effort to 'explain' reasoning and mathematical capacity in terms of purported underlying regulative biological systems? — Wayfarer
The conceptual difficulty here is that science itself relies on the cogency of rational argument to establish any kind of explanatory framework. You can't examine the nature of rational thought from some point outside of it, treating it as an external or objective phenomenon, because any such explanation is already an exercise in rational thought. This point is discussed in some detail in Thomas Nagel's Evolutionary Naturalism & the Fear of Religion. — Wayfarer
I don't think present day philosophy of mind has much going for it, really. It places severe a priori limits on the nature of knowledge. Sure we have much better science and technology but are we superior in wisdom to the ancients? — Wayfarer
The device you're communicating with depends on the unreasonable effectiveness of maths. Interesting article, but the sense in which I'm arguing for Wigner's view, is certainly not that maths or the mathematical sciences are in any sense omniscient in principle or practice. Very well aware of that. — Wayfarer
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