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RE: On Hell and Forgiveness
September 14, 2018 at 10:32 am
(September 14, 2018 at 9:36 am)RoadRunner79 Wrote: (September 14, 2018 at 9:27 am)polymath257 Wrote: Ahh...but my examples are NOT just different languages. They are different fundamentally and are *all* definitions of the *number* 4 in different contexts.
I am hung up on language because mathematics *is* a language. And the number 4 is word in that language. It doesn't have an independent existence: it is a language construct. And, in math, different aspects of the language have wildly different *definitions* of the *number* 4.
Using a language construct doesn't mean that what you are describing is subjective in it's nature. We use language to convey things. Perhaps sometimes that language is not a precise as we would like, or a word can have multiple meanings which we have to discern. I'm not talking about the language (and I don't think the others are either).
Again, what we are describing is what is objective. But we are describing the trees, not the number 4. In fact, at no point did you actually describe the number 4. And there is a good reason for that. The reason is that 4 is a language construct, not something external (and objective).
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RE: On Hell and Forgiveness
September 14, 2018 at 10:40 am
(September 14, 2018 at 6:15 am)RoadRunner79 Wrote: (September 14, 2018 at 5:27 am)Abaddon_ire Wrote: Does it? why does the "4" in 408 equal 32?
Different way of explaining or referencing the same thing.
It might be helpful to use the phrase "the concept of 4 objects". People are getting all hung up on language and mathematical set descriptions and the actual symbol--none of which we are talking about.
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RE: On Hell and Forgiveness
September 14, 2018 at 10:42 am
(This post was last modified: September 14, 2018 at 10:45 am by The Grand Nudger.)
You can't help but talk about it if you're trying to determine the status of the concept "4". If you're not talking about the concept "4"...but whatever we refer to with it..then you are not describing any way that -numbers- or -concepts- are objective, you're not even even making an attempt.
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RE: On Hell and Forgiveness
September 14, 2018 at 10:46 am
(This post was last modified: September 14, 2018 at 10:46 am by Angrboda.)
(September 14, 2018 at 10:40 am)SteveII Wrote: (September 14, 2018 at 6:15 am)RoadRunner79 Wrote: Different way of explaining or referencing the same thing.
It might be helpful to use the phrase "the concept of 4 objects". People are getting all hung up on language and mathematical set descriptions and the actual symbol--none of which we are talking about.
How does back pedaling from "the number 4" to "the concept of 4 objects" get you any closer to something objective?
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RE: On Hell and Forgiveness
September 14, 2018 at 10:50 am
(September 14, 2018 at 8:52 am)Jörmungandr Wrote: Now, I don't really expect to convince you that parts and wholes do not exist.
And therein lies the rub...you do not differentiate between accidental and essential properties except when you want to justify some secular morality based on the recognition of a common humanity, i.e. an essential human nature. Sorry, Jor, you cannot have it both ways.
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RE: On Hell and Forgiveness
September 14, 2018 at 11:27 am
(September 14, 2018 at 10:50 am)Neo-Scholastic Wrote: (September 14, 2018 at 8:52 am)Jörmungandr Wrote: Now, I don't really expect to convince you that parts and wholes do not exist.
And therein lies the rub...you do not differentiate between accidental and essential properties except when you want to justify some secular morality based on the recognition of a common humanity, i.e. an essential human nature. Sorry, Jor, you cannot have it both ways.
Wait, what? Can you provide an example of an "essential property" that isn't a pre-suppositional bag of nonsense?
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RE: On Hell and Forgiveness
September 14, 2018 at 11:50 am
(September 14, 2018 at 10:50 am)Neo-Scholastic Wrote: (September 14, 2018 at 8:52 am)Jörmungandr Wrote: Now, I don't really expect to convince you that parts and wholes do not exist.
And therein lies the rub...you do not differentiate between accidental and essential properties except when you want to justify some secular morality based on the recognition of a common humanity, i.e. an essential human nature. Sorry, Jor, you cannot have it both ways.
I don't see how that in any way follows from what I said and seems like nothing more than an off-topic snipe. You're simply talking out of your ass again.
And you still don't understand what I have said on the subject and so are attacking a straw man of your own making.
Feel free to answer any of the questions Roadie hasn't answered. Or crawl back in your hole as you're wont to do.
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RE: On Hell and Forgiveness
September 14, 2018 at 12:17 pm
(This post was last modified: September 14, 2018 at 12:25 pm by SteveII.)
(September 14, 2018 at 8:52 am)Jörmungandr Wrote: Ultimately, as I said to Neo in the thread on delusion and religion, number, and the concepts it is dependent on, are a mystery. I can suggest that number, being an example of reasoning using parts and wholes, only exists in so far as we make arbitrary identity judgements, about what is a part of what, and what is a whole. But our intuitions tend to marshall against us, at the very least, and it's not entirely clear that number is subjective in its entirety, that it doesn't have an independent, objective substance of some sort. Yet when we go the other direction, and assert that number, and part/whole distinctions are objective, we run into problems in that direction as well, problems which seem equally intractable. So we're left with a mystery, I think, and to declare that number, or parts & wholes, is definitely objective, is, to my mind, to embrace an opinion that is not in any sense fully justified. At minimum, if you can't prove that number is objective, that leaves the door open, no matter how slightly, that number is subjective, as it must be one or the other, it can't be both. So, QED, as it were, I think I've shown that number and parts & wholes being a product of mind is not a view that is as far fetched as Neo and Steve made it sound. If you disagree, please explain why.
(To rephrase in terms of your example, what makes two hydrogen atoms and an oxygen atom, close together, strongly interacting, a molecule of water, and the same group of atoms, separated by several light years of empty space, not a molecule of water?)
After a little research...
We don't reason from parts to a whole with numbers. Frege did a lot of work still respected today in the field of philosophy of mathematics and write an important work (in that field anyway) called The Foundation of Arithmetic. All references from: https://en.wikipedia.org/wiki/The_Founda...Arithmetic
Psychologistic accounts of mathematics[edit]
Frege objects to any account of mathematics based on psychologism, that is the view that math and numbers are relative to the subjective thoughts of the people who think of them. According to Frege, psychological accounts appeal to what is subjective, while mathematics is purely objective: mathematics are completely independent from human thought. Mathematical entities, according to Frege, have objective properties regardless of humans thinking of them: it is not possible to think of mathematical statements as something that evolved naturally through human history and evolution. He sees a fundamental distinction between logic (and its extension, according to Frege, math) and psychology. Logic explains necessary facts, whereas psychology studies certain thought processes in individual minds.[2]
Jorm, specific to your point above, I think this is an interesting point:
Frege roundly criticizes the empiricism of John Stuart Mill.[6][7] He claims that Mill's idea that numbers correspond to the various ways of splitting collections of objects into subcollections is inconsistent with confidence in calculations involving large numbers.[8][9] He also denies that Mill's philosophy deals adequately with the concept of zero.[10] He goes on to argue that the operation of addition cannot be understood as referring to physical quantities, and that Mill's confusion on this point is a symptom of a larger problem of confounding the applications of arithmetic for arithmetic itself.
...further down...
Frege's definition of a number[edit]
Frege argues that numbers are objects and assert something about a concept. Frege defines numbers as extensions of concepts. 'The number of F's' is defined as the extension of the concept G is a concept that is equinumerous to F. The concept in question leads to an equivalence class of all concepts that have the number of F (including F). Frege defines 0 as the extension of the concept being non self-identical. So, the number of this concept is the extension of the concept of all concepts that have no objects falling under them. The number 1 is the extension of being identical with 0.
You also might be interested in the paragraph labeled KANT, there this is discussed: He criticizes him mainly on the grounds that numerical statements are not synthetic-a-priori-, but rather analytic-a priori.
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RE: On Hell and Forgiveness
September 14, 2018 at 12:50 pm
(This post was last modified: September 14, 2018 at 12:54 pm by polymath257.)
(September 14, 2018 at 10:40 am)SteveII Wrote: (September 14, 2018 at 6:15 am)RoadRunner79 Wrote: Different way of explaining or referencing the same thing.
It might be helpful to use the phrase "the concept of 4 objects". People are getting all hung up on language and mathematical set descriptions and the actual symbol--none of which we are talking about.
I agree that the specific symbol is not what we are talking about. But the mathematical set descriptions are NOT simply different symbols for the same concept. They are actually different mathematically..different properties, etc. They are NOT the same thing.
A 'concept of 4 objects' is NOT an objective object. It is a shared language construct. And that is my point. It *only* exists in our psychology, not in the external world. It is, fundamentally, a subjective state and not an objective object.
(September 14, 2018 at 12:17 pm)SteveII Wrote: (September 14, 2018 at 8:52 am)Jörmungandr Wrote: Ultimately, as I said to Neo in the thread on delusion and religion, number, and the concepts it is dependent on, are a mystery. I can suggest that number, being an example of reasoning using parts and wholes, only exists in so far as we make arbitrary identity judgements, about what is a part of what, and what is a whole. But our intuitions tend to marshall against us, at the very least, and it's not entirely clear that number is subjective in its entirety, that it doesn't have an independent, objective substance of some sort. Yet when we go the other direction, and assert that number, and part/whole distinctions are objective, we run into problems in that direction as well, problems which seem equally intractable. So we're left with a mystery, I think, and to declare that number, or parts & wholes, is definitely objective, is, to my mind, to embrace an opinion that is not in any sense fully justified. At minimum, if you can't prove that number is objective, that leaves the door open, no matter how slightly, that number is subjective, as it must be one or the other, it can't be both. So, QED, as it were, I think I've shown that number and parts & wholes being a product of mind is not a view that is as far fetched as Neo and Steve made it sound. If you disagree, please explain why.
(To rephrase in terms of your example, what makes two hydrogen atoms and an oxygen atom, close together, strongly interacting, a molecule of water, and the same group of atoms, separated by several light years of empty space, not a molecule of water?)
After a little research...
We don't reason from parts to a whole with numbers. Frege did a lot of work still respected today in the field of philosophy of mathematics and write an important work (in that field anyway) called The Foundation of Arithmetic. All references from: https://en.wikipedia.org/wiki/The_Founda...Arithmetic
Psychologistic accounts of mathematics[edit]
Frege objects to any account of mathematics based on psychologism, that is the view that math and numbers are relative to the subjective thoughts of the people who think of them. According to Frege, psychological accounts appeal to what is subjective, while mathematics is purely objective: mathematics are completely independent from human thought. Mathematical entities, according to Frege, have objective properties regardless of humans thinking of them: it is not possible to think of mathematical statements as something that evolved naturally through human history and evolution. He sees a fundamental distinction between logic (and its extension, according to Frege, math) and psychology. Logic explains necessary facts, whereas psychology studies certain thought processes in individual minds.[2]
Jorm, specific to your point above, I think this is an interesting point:
Frege roundly criticizes the empiricism of John Stuart Mill.[6][7] He claims that Mill's idea that numbers correspond to the various ways of splitting collections of objects into subcollections is inconsistent with confidence in calculations involving large numbers.[8][9] He also denies that Mill's philosophy deals adequately with the concept of zero.[10] He goes on to argue that the operation of addition cannot be understood as referring to physical quantities, and that Mill's confusion on this point is a symptom of a larger problem of confounding the applications of arithmetic for arithmetic itself.
...further down...
Frege's definition of a number[edit]
Frege argues that numbers are objects and assert something about a concept. Frege defines numbers as extensions of concepts. 'The number of F's' is defined as the extension of the concept G is a concept that is equinumerous to F. The concept in question leads to an equivalence class of all concepts that have the number of F (including F). Frege defines 0 as the extension of the concept being non self-identical. So, the number of this concept is the extension of the concept of all concepts that have no objects falling under them. The number 1 is the extension of being identical with 0.
You also might be interested in the paragraph labeled KANT, there this is discussed: He criticizes him mainly on the grounds that numerical statements are not synthetic-a-priori-, but rather analytic-a priori.
Very good. Now go ahead a bit and see how he reacted to Russell's paradox, which showed his whole system was self-contradictory.
The *concepts* are not objective.
And yes, mathematics is analytic a priori: to the extent it has knowledge, it is all contained in the basic assumptions. It says NOTHING about the real world until we actually observe the real world.
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RE: On Hell and Forgiveness
September 14, 2018 at 1:10 pm
(This post was last modified: September 14, 2018 at 1:26 pm by Angrboda.)
Yeah, I don't see how resurrecting Frege's failed project adds any light to the discussion.
Of particular note, Steve, you apparently didn't read far enough, the Wikipedia article you quote states, "Although Bertrand Russell later found a major flaw in Frege's work (this flaw is known as Russell's paradox, which is resolved by axiomatic set theory), the book was influential in subsequent developments, such as Principia Mathematica." So the problems with Frege's concepts was resolved by appeal to set theory. Even ignoring that for the moment, unless you can argue Frege's point independently of Frege, all you're doing is making an appeal to authority which, for various reasons, is unsuccessful. But if you want to argue Frege on his own terms, knowing that he was ultimately unsuccessful, I'm more than happy to listen.
I stand by my prior arguments.
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