At the risk of belaboring the point, it is an all-too-common nominalist mistake to insist that if abstract objects are real, then they must also exist. These are two very different concepts--whatever is real is such as it is regardless of what anyone thinks about it, while whatever exists reacts with other like things in the environment. Again, there are varieties of mathematical realism other than Platonism.But if they’re real, then what kind of existence do they have? What does it mean to say abstract objects exist? — Wayfarer
These are two very different concepts--whatever is real is such as it is regardless of what anyone thinks about it, while whatever exists reacts with other like things in the environment — aletheist
What more could be said about the ontological status of abstracts other than that they are real abstracts? — Janus
That is the point at issue! If numbers are real, but not corporeal, then it's a defeater for philosophical materialism - there are reals that are not material. — Wayfarer
They (numbers) don't exist in the same way that flowers or pens or chairs exist but are real nonetheless. — Wayfarer
No, it does not. Hamlet, the fictional character in Shakespeare's play, is the object of the sign that is the first word of this sentence. — aletheist
At the risk of belaboring the point, it is an all-too-common nominalist mistake to insist that if abstract objects are real, then they must also exist. These are two very different concepts--whatever is real is such as it is regardless of what anyone thinks about it, while whatever exists reacts with other like things in the environment. Again, there are varieties of mathematical realism other than Platonism. — aletheist
it is an all-too-common nominalist mistake to insist that if abstract objects are real, then they must also exist. — aletheist
Trying to establish a separation between "real" and "existent" just muddies the water by creating ambiguity, and is counterproductive toward understanding. — Metaphysician Undercover
ruining the good old word "exist". — Quine, On What There Is
Again, in semeiotic a subject is a term within a proposition that denotes one of its objects. "Hamlet" is a sign, a subject of a proposition such as "Hamlet killed Claudius." The fictional character in Shakespeare's play is its object. Other subjects of that proposition are "killing" and "Claudius," which denote a relation and another fictional character in Shakespeare's play as their objects. The predicate is signified by the syntax, conveying that something called "Hamlet" stood in the relation of "killing" to something called "Claudius" within the universe of discourse, which in this case is Shakespeare's fictional play--not the real universe.Fictional characters are known as subjects, not objects. — Metaphysician Undercover
It is firmly supported by what is known as speculative (theoretical) grammar within semeiotic, the science of all signs.Your claim that "Hamlet" refers to an object is unsupported by any conventional grammar. — Metaphysician Undercover
No one is claiming that fictional, imaginary things are real. In fact, being fictional is precisely the opposite of being real. That which is fictional is such as it is only because someone thinks about it that way; Hamlet was the prince of Denmark only because Shakespeare created a story in which that was the case. By contrast, that which is real is such as it is regardless of what anyone thinks about it; Platonism is one form of mathematical realism in this sense, but not the only one.Even if I grant you that fictional, imaginary things may be called objects, my point was that some form of Platonism, as an ontology is required to support the claimed reality of such objects. — Metaphysician Undercover
On the contrary, I have found that carefully drawing the proper distinction between reality (whatever is such as it is regardless of what anyone thinks about it) and existence (whatever reacts with other like things in the environment) is extremely clarifying and helpful. Treating them as synonymous is what muddies the water by imposing nominalism, effectively begging the question against realism.Trying to establish a separation between "real" and "existent" just muddies the water by creating ambiguity, and is counterproductive toward understanding. — Metaphysician Undercover
The first sentence is false, but the second is true. The kind of effects that ideas, concepts, and abstractions have on the physical world is obviously very different from the kind of effects that physical things have on the physical world. The former are not like things in the (physical) environment, so they do not exist in that sense. Nevertheless, some of them are real--they are such as they are regardless of what anyone thinks about them--but this does not require them to be "located" in a Platonic realm.As well as being "real", ideas, concepts and abstractions are obviously "existent". They have a significant effect on the physical world as clearly demonstrated by engineering. — Metaphysician Undercover
At the risk of belaboring the point, it is an all-too-common nominalist mistake to insist that if abstract objects are real, then they must also exist. These are two very different concepts--whatever is real is such as it is regardless of what anyone thinks about it, while whatever exists reacts with other like things in the environment. Again, there are varieties of mathematical realism other than Platonism. — aletheist
Surely you can see how this poses a problem for naturalism? If you can’t see it, then sure, there’s nothing to discuss. — Wayfarer
Frege's 'laws of thought' — Wayfarer
Add to that, that concepts are not things so much as a way of behaving; that is, concepts are best not considered as things in people's minds, but as ways of talking and acting. — Banno
Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all?
Massimo Pigliucci, a philosopher at the City University of New York, was initially attracted to Platonism—but has since come to see it as problematic. If something doesn’t have a physical existence, he asks, then what kind of existence could it possibly have? “If one ‘goes Platonic’ with math,” writes Pigliucci, empiricism “goes out the window.” (If the proof of the Pythagorean theorem exists outside of space and time, why not the “golden rule,” or even the divinity of Jesus Christ?)
Standard readings of mathematical claims entail the existence of mathematical objects. But, our best epistemic theories seem to debar any knowledge of mathematical objects. Thus, the philosopher of mathematics faces a dilemma: either abandon standard readings of mathematical claims or give up our best epistemic theories.
Mathematical objects are not the kinds of things that we can see or touch, or smell, taste or hear. If we can not learn about mathematical objects by using our senses, a serious worry arises about how we can justify our mathematical beliefs.
... 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.
concepts are not things so much as a way of behaving; that is, concepts are best not considered as things in people's minds, but as ways of talking and acting.
— Banno
Tosh. — Wayfarer
I think the issue around Platonic realism is simply that it torpedoes one of the beloved dogmas of empiricism, ‘no innate ideas’. — Wayfarer
1. Despite the title, Wigner is merely expressing a sentiment . — Banno
I offered by way of example good reasons to suppose that numbers do not refer to anything — Banno
The use of "real" in Platonic realism needs justification. It is not at all clear what it is that Platonic Realism claims is real... — Banno
Bare assertion with no supporting argument. — Wayfarer
You simply referred to behaviourism, which has been obsolete since the 1940's. — Wayfarer
It's not clear to you. — Wayfarer
What more could be said about the ontological status of abstracts other than that they are real abstracts? Analogously what more could be said about real physicals other than that they are real physicals? — Janus
I left out Frege. What is self-evident to one person may be rejected by another. In particular Frege's desire to develop a logical basis for arithmetic and hence for maths as a whole has been show impossible. Maths cannot be derived in its entirety from self-evident truths. — Banno
Gödel was a mathematical realist, a Platonist. He believed that what makes mathematics true is that it's descriptive—not of empirical reality, of course, but of an abstract reality. Mathematical intuition is something analogous to a kind of sense perception. In his essay "What Is Cantor's Continuum Hypothesis?", Gödel wrote that we're not seeing things that just happen to be true, we're seeing things that must be true. The world of abstract entities is a necessary world—that's why we can deduce our descriptions of it through pure reason. 1 — Rebecca Goldstein
Where can I find a real platonic circle? — Banno
Then show me were Wigner does more than I say... — Banno
Isaac Newton noticed that the path of a falling body (perhaps a thrown rock) on the Earth and the path of the moon in the sky are two particular cases of the more general notion of an ellipse. From this observation, he postulated the universal law of gravitation, which states that the gravitation between two objects is proportional to their masses. While Newton, given the restrictions of his day, could only verify the results with an accuracy of 4%, the law was later proved to be accurate to within less than a ten thousandth of one percent. This law, therefore, is a fantastic example of a mathematical formalism that has proved accurate beyond any reasonable expectations.
Quantum mechanics gives an even more astounding example. Matrix algebra had been studied independently of any applications by pure mathematicians for some time when Max Born realized that Werner Heisenberg’s rules of computation were formally identical with the rules of computation of matrices. Born, Pascual Jordan, and Heisenberg then replaced the position and momentum variables of Heisenberg’s equations of classical mechanics by these matrices and applied that result to an idealized problem. The new formulation worked, but would it work in a realistic setting, not just a toy problem? Within months, Wolfgang Pauli applied the new formulation to a realistic problem (a hydrogen atom) and the results matched up. Since Heisenberg’s original calculations were abstracted from problems that included the old theory of hydrogen atoms to begin with, this result was not too surprising. However, the “miracle” occurred next, when the matrix mechanics were applied to problems for which the Heisenberg rules no longer applied. — equations of motion of atoms with greater numbers of atoms. These observations were shown to agree with experimental data to within one part in ten million! Once again, mathematics developed independently of physics has been applied to physics to give spectacularly accurate results, far beyond the expectations of the original theory. 2.
Yep - as I said,...the point I was illustrating from Frege is that mathematical platonism is simply assumed by many logicians and philosophers — Wayfarer
We might consider this alternate definition of real......all this to say that Platonic Realism towards mathematical objects is not wrong, but just one way of treating those objects. It comes about by extending the notion of what is real to encompass numbers. — Banno
On this account a painting is real, but it is also a construction. Our two views may not be mutually exclusive.whatever is real is such as it is regardless of what anyone thinks about it — aletheist
Again, in semeiotic a subject is a term within a proposition that denotes one of its objects. — aletheist
No one is claiming that fictional, imaginary things are real. In fact, being fictional is precisely the opposite of being real. That which is fictional is such as it is only because someone thinks about it that way; Hamlet was the prince of Denmark only because Shakespeare created a story in which that was the case. By contrast, that which is real is such as it is regardless of what anyone thinks about it; Platonism is one form of mathematical realism in this sense, but not the only one. — aletheist
(I have to sign out for some hours, I supposed to be doing a self-training course, so have to drag myself away.) — Wayfarer
Empiricism has to insist that they're the product of the mind, otherwise there's no conceptual space for them to be — Wayfarer
Simple--in semeiotic, anything that is denoted by a sign is, by definition, its object. Since all thought is in signs, anything that we can think about--real or fictional, existent or imaginary--is an object in this sense.You assume that fictional characters are objects, but you deny that they are real, and you deny that they are existent. How do you validate your claim that they are objects? — Metaphysician Undercover
Simple--in semeiotic, anything that is denoted by a sign is, by definition, its object. Since all thought is in signs, anything that we can think about--real or fictional, existent or imaginary--is an object in this sense. — aletheist
The only signs that theoretically could signify something without denoting anything are pure icons, unembodied qualities that would only convey themselves as they are in themselves. Any sign that stands for something else denotes that other object.To adhere to the distinction you made for me in the other thread, in much usage of signs, probably the majority actually, the signs have significance without denoting anything. — Metaphysician Undercover
On the contrary, "going for" denotes a certain kind of relation as its object, and "a walk" denotes a certain kind of activity as its object. In fact, as symbols, words and phrases typically denote general concepts like these as their objects. The syntax of the sentence is what signifies the interpretant, which is the relation among the denoted objects that the corresponding proposition conveys.For instance in "I'm going for a walk", the only object denoted is "I". — Metaphysician Undercover
If this were true, then the author could not create those "images of characters" in the first place, and we could not think or talk or write about them afterwards. Again, the sign "Hamlet" denotes the fictional character in Shakespeare's play as its object.And in your example of fictional writing, there are no objects denoted. The author simply builds up images of characters without denoting any objects. — Metaphysician Undercover
It's a real abstract object - its not...? — Banno
It's a real physical object - it's not an illusion, it's not a reflection, its not a mirage...
It's a real abstract object - its not...? — Banno
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