And the problem with saying that it’s ‘merely’ an invention of the human mind, is that it doesn’t allow for the unreasonable effectiveness of mathematics in the natural sciences. — Wayfarer
If this is what Platonists believe, then where do they think that these objectcs exist? If it's not inside our physical realm then in what realm do these objects exist and do they move inside of it? — Prishon
If this is what Platonists believe, then where do they think that these objectcs exist? If it's not inside our physical realm then in what realm do these objects exist and do they move inside of it? — Prishon
the problem with saying that it’s ‘merely’ an invention of the human mind, is that it doesn’t allow for the unreasonable effectiveness of mathematics in the natural sciences. Maths is predictive, through it you can discern facts about nature which you would have no way of finding otherwise. — Wayfarer
Intuitionists" believe that mathematics is just a creation of the human mind. In that sense you can argue that mathematics is invented by humans. Any mathematical object exists only in our mind and doesn't as such have an existence.
"Platonists", on the other hand, argue that any mathematical object exists and we can only "see" them through our mind. Hence in some sense Platonists would vote that mathematics was discovered. — Prishon
We can distinguish two kinds of mathematical objects: concrete and abstract. For example, there are concrete triangles (like concrete "give way" road signs) and one abstract triangle, which is a property instantiated in all concrete triangles. The Platonist objects are the abstract ones. Some people think that the abstract objects don't "really exist", that they are just words or ideas in our heads. Yet these words or ideas express an objective similarity between concrete objects, so the abstract objects can also be understood as being in a sense "dispersed" in concrete objects. — litewave
The math. forms are indeed not part of the physical world. But neither in an unaccessible metaphysical realm. — Prishon
In contrast, the Form of Triangle is one, unchanging, and eternal. It is beyond space and time and cannot be expressed in language. — Apollodorus
It sounds even religious. — Prishon
If something is beyond space and time, then where could it be? — Corvus
Yet these words or ideas express an objective similarity between concrete objects, so the abstract objects can also be understood as being in a sense "dispersed" in concrete objects.
“I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science recently retired from the University of Toronto. “Working mathematicians overwhelmingly are Platonists. They don't always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”
Other 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. — Smithsonian Magazine, What is Math?
Is God A Mathematician? — Many have asked
Mathematics is the language in which God has written the universe. — Galileo Galilei
the Form of Apple, the Form of Triangle) — Seppo
I think the idea that there is a Form for every conceivable thing under the sun is unwarranted. Different Forms would be perfectly capable to combine to form virtually any perceptible object.
Yeah but for the materialist, these mental objects are located in the brain. — Count Timothy von Icarus
There is a model for explaining how concepts like God — Count Timothy von Icarus
Not really. I'm not saying it's the case, it's just a model that explains the forms and how they could arise from material processes. — Count Timothy von Icarus
Maybe Forms for geometrical shapes or objects all reduce to more fundamental concepts like the Form of Line Segment or Angle? — Seppo
They have a physical being in the neurons of their hosts. — Count Timothy von Icarus
The problem there, is that, as Aristotle showed, and Plato acknowledged in the Parmenides, the world would be filled with various infinitely regressing forms- a whole dimension of reductio ad absurdum infinities. — Count Timothy von Icarus
...Among all the kinds of forms which can be signified by terms, according to Aquinas, there is no one uniform way in which they exist. The existence of the form “sight,” by which the eye sees, may be some positive presence in the nature of things (which biologists can describe in terms of the qualities of a healthy eye that gives it the power to see), but the existence of the form 'blindness' in the blind eye need be nothing more than the nonexistence of sight ‒ the 'form' of blindness is just the privation of the form of sight and so not really an additional form at all.
In general, distinguishing and qualifying the different ways there can “be” a form present in a thing goes a long way toward alleviating the apparent profligacy of the realist account of words signifying forms. ....
Aquinas’s famous thesis of the unicity of substantial forms is an example of another strategy: linguistically I may posit diverse forms (humanity, animality, bodiliness) to account for Socrates being a man, an animal, and a body, but according to Aquinas there is in reality just one substantial form (Socrates’ soul) which is responsible for causing Socrates to be a man, an animal, and a body. In this and other cases, ontological commitment can be reduced by identifying in reality what, on the semantic level, are treated as diverse forms. As Boethius had seen, what the mind is capable of logically distinguishing need not be actually distinct in the nature of things.
In principle, any number of strategies for reducing overall ontological commitment are available within the framework of realist semantics, so that in general, the kind of form that fulfills the required semantic function did not need to be the kind of form that has a distinct and positive metaphysical presence in the nature of things. — Joshua Hothschild, Whats Wrong with Ockham?'
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.