On Hell and Forgiveness

[polymath257]

Which, I might add, is why metaphysics tends to be *absolutely useless* for understanding anything about the real world. In order to get anything approaching real knowledge, you need to actually do observations. Just sitting and thinking isn't going to be close to enough. So, what tends to happen is that philosophers convince themselves they are doing something deep when they are actually doing non-sense.

Math, like I said, is a *language* and has enough expressibility to help us make models of our observations.

But I reject wholeheartedly that knowledge can be gained without observation. At best, you can get arbitrary definitions, but that doesn't lead to knowledge.

In NO way is metaphysics knowledge.

That position is called Logical Positivism (and taken to the extreme you do--Scientism) and is the view that all real knowledge is empirical knowledge—that there is no rational, objective form of inquiry that is not a branch of science. At least four main problems/points:

1. Scientism is too restrictive a theory of knowledge. If science is the only path to truth, then there are no moral truths, no aesthetic truths, no philosophical truths (like human rights). Mathematics and logic are not scientific--they are presupposed as true *before* science even begins--how does is work that the only path to truth relies on other truths to get off the ground!?!?

And I would agree with this. There are moral *opinions* and aesthetic *opinions*, etc, but there is nothing inherent in the universe that dictates these. They are a matter of how we 8want* to interact with the universe.

2. Further regarding philosophy of science, scientific inquiry itself rests on a number of philosophical assumptions: that there is an objective world external to the minds of scientists; that this world is governed by causal regularities; that the human intellect can uncover and accurately describe these regularities; and so forth. Since science presupposes these things, it cannot attempt to justify them without arguing in a circle.

Well, maybe the original positivists made these assumptions. I do not. I base science on observed regularities and correlations *NOT causality*. I can test to see if these correlations are maintained and formulate (in the best cases) mathematical models for such correlations. I don't ask whether the regularities are 'correctly described' because they are regularities in observations. I use the scientific method to modify or reject proposed models, thereby allowing science to be done. I gain confidence in the models through repeated testing, always acknowledging that any new observation may require a complete re-write.

3. The claim that positivism is true is not itself a scientific claim, not something that can be established using scientific or empirical methods. That science is even a rational form of inquiry (let alone the only rational form of inquiry) is not something that can be established scientifically. So, it is self-refuting philosophy.

4. The entire philosophy was rejected by nearly everyone by the middle of the 20th century.

Yes, this is the traditional take philosophers have taken. But, taken as a *hypothesis* that this is a good way of approaching our observations, we do, in fact, find a testable hypothesis that has passed the tests with flying colors. So, instead of being self-defeating, it has shown itself quite a useful way to approach the questions of knowledge.
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And, once again, math is NOT an area of knowledge about the real world. It is a formal language that we can use to express our ideas and hypotheses about the real world.

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Explain how Russell's Paradox undermines the one-to-one correspondence concept of numbers that Frege discussed above.

Well, the issue is that the full correspondence requires proper classes to function as Frege required. And those proper classes have to be definable via arbitrary properties. And once you allow for that, Russell's paradox shows the system to be inconsistent.

There has been a partial rescue in the Von Neumann model of the ordinals (and thereby of the natural numbers) that uses a *specific* set of a certain cardinality as a model for the class Frege used. But that then allows for *any* set with that cardinality to be an equally good model, which destroys the objectivity.

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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.

Wait a minute. I did read to the bottom. The actual article was on his entire work: The Foundations of Arithmetic. It is irrelevant that some of his theories had problems. It says nowhere that his concept of numbers is wrong (the subject at hand). You left off the second half of that paragraph: "The book [Frege's Foundation of Arithmetic] can also be considered the starting point in analytic philosophy, since it revolves mainly around the analysis of language, with the goal of clarifying the concept of number. Frege's views on mathematics are also a starting point on the philosophy of mathematics, since it introduces an innovative account on the epistemology of numbers and math in general, known as logicism."

Now since this is not my area of expertise, perhaps if you explained why Frege's concept of numbers is wrong or has been supplanted...

Your point about the concept of numbers being parts of a whole seem refuted when we consider that numbers at their root are a one-to-one correspondence--not assembled by some addition.

Yes, Frege's ideas are the *starting point* of the modern views in mathematics. But the internal contradictions have to be dealt with for the subject to continue.
Instead of numbers *being* a one-to-one correspondence, which makes them 'too large' to be sets, the trick has been to pick a representative of the equivalence class of objects of that cardinality to 'stand in' for the number. But that opens up the possibility of having *different* sets that do this 'stand in' role. Which makes for the possibility that my version of 4 is not the same as yours (there is no identity because they are distinguishable as sets).