here's no such thing as what pixels "really" look like, if this is supposed to mean how they look when nobody is looking (which is why naive realism is false). — Michael
"For what we thereby show is that there is a way of grasping a rule which is not an interpretation, but which, from case to case of application, is exhibited in what we call “following the rule” and “going against it” — Banno
I guess Meta is a math skeptic.
— frank
I like to apply a healthy dose of skepticism to any so-called knowledge. Nothing escapes the skeptic's doubt. — Metaphysician Undercover
These issues are actually specifically addressed by Wittgenstein. — Hanover
but I'll consistently reject scientific alternatives because they it's a category error to argue how a scientific theory of reality can replace a grammar theory. — Hanover
So when you say "my headache" and you mean the actual pounding you're feeling right now, how am I to know what you're talking about other than how you use the term consistently with others who I have seen use the term, which must be related to behaviors and the use of other terms I am already familiar with. — Hanover
Regardless of what you assert, to say that the value represented is an object called "a number" is platonism. — Metaphysician Undercover
This issue is more complicated though. The Neo-Platonists took Plato's name and claimed to continue Plato's school, but their ontology is consistent with what you call platonist. Aristotle's school claimed to be the true Platonists but the Neo-Platonists took the name. So you have to take on the Neo-Platonists, and tell them that they should call themselves Neo-platonists, as not true Platonists. But this problem has been around for millennia, and they do not like being accused of misrepresenting Plato, they like to claim the true continuation of Plato's teaching. — Metaphysician Undercover
I agree. but my spell check doesn't like little p platonism. And, I count the distinction as unimportant because there really would be no such thing as big P Platonism if we maintained that distinction. Plato pitted ideas against each other so there's no real ontological position which could qualify as big P Platonism. So they end up being the same meaning anyway. — Metaphysician Undercover
1. Two views about mathematics: nominalism and platonism
In ontological discussions about mathematics, two views are prominent. According to platonism, mathematical objects (as well as mathematical relations and structures) exist and are abstract; that is, they are not located in space and time and have no causal connection with us. Although this characterization of abstract objects is purely negative—indicating what such objects are not—in the context of mathematics it captures the crucial features the objects in questions are supposed to have. According to nominalism, mathematical objects (including, henceforth, mathematical relations and structures) do not exist, or at least they need not be taken to exist for us to make sense of mathematics. So, it is the nominalist's burden to show how to interpret mathematics without the commitment to the existence of mathematical objects. This is, in fact, a key feature of nominalism: those who defend the view need to show that it is possible to yield at least as much explanatory work as the platonist obtains, but invoking a meager ontology. To achieve that, nominalists in the philosophy of mathematics forge interconnections with metaphysics (whether mathematical objects do exist), epistemology (what kind of knowledge of these entities we have), and philosophy of science (how to make sense of the successful application of mathematics in science without being committed to the existence of mathematical entities). These interconnections are one of the sources of the variety of nominalist views. — SEP
Oh oh, the set {1,2,3} has 3 numbers. :gasp: — jgill
Again, "integer" is a faulty concept, because it assumes that "a number" is a countable object. — Metaphysician Undercover
Yes, I'm aware of that - and of the startling results that followed when his view was set aside and infinity was treated as real, thus enabling the invention/discover/development of the calculus. — Ludwig V
When you said a picture of Cagney is a representation of Cagney, that's true, but it's a different sort of representationalism than what we're talking about. That's just a picture. — Hanover
Therefore, the representation (assuming indirect realism) would be of the object Cagney versus the phenomenal Cagney or it could be of the picture of Cagney versus the phenomenal state of the picture. As you've described it, you have the real Cagney versus a picture of Cagney. That is not the sort of representationalism we're interested in here. — Hanover
So you're acknowledging rampant equivocation, where we call objects and representations the exact word in all cases outside philosophical circles. The noumenal Cagney and the phenomenonal Cagney are always called "Cagney."
Under what scenario do you distinguish the noumenal from the phenomenonal, and can you tell me the specific difference between the two? If you use the term interchangeably, and you don't even know how the two are different from one another, what exactly are you protecting? — Hanover
I think that it is not necessary for the infinite number of numbers to exist in my mind. All I need to have in my mind is S(n) = n+1. — Ludwig V
If they're different, why do you call them both "Trump"? — Hanover
If that, why not for simplicity sake just consider the noumena the same as the phenomena since you can't tell me how the specific distinction between what is and what is perceived except to say there is general consensus as to what the ship is. That sounds like a form of direct realism. — Hanover
I reject the assumption of any "mathematical objects" finite or infinite, as Platonism, and unacceptable. — Metaphysician Undercover
You want I should be awe struck into agreement? Nuh. — Banno
Your jump from "neural processes are necessary for perception" all the way to "the world is generated by the brain" is illegitimate. — Banno
Or is it that you hung your flag on the "indirect realist" mast, then found that you basically agreed with what I had to say? — Banno
An hallucination is defined precisely by there being no object of which one is aware, only a belief-like state produced in a derivative way. — Banno
Got ya. :up: — Tom Storm
I'm not sure I know what that might mean; but I do hear my wife's voice, through the telephone. — Banno
The causal chain remains the same, but our attention(the blanket) can be placed in differing locations. So in one throw we can refer to your wife’s voice, in another to the electronically constructed reproduction, and so on. — Banno
See the weasel word? Did you hear your wife's voice? what dis she say? Were have you thrown the Markov Blanket? Were else might you throw it? — Banno
Rather, having an experience is having that flood of electrical data. What you experience, if we must talk in that way, is the cat. — Banno
You see the cat, not your neural activity. Your neural activity is seeing the cat. — Banno
