On Hell and Forgiveness

[SteveII]

Wow. Do you realize that reality would not even hold together without what we call 'causality.' You cannot even conceive of a world without the causal principle if you tried. Stating that science does not need a notion of causality is...just...wow. Do you understand that in order to interpret reality, you need a metaphysical system in which to process the inputs. Perhaps this will help:

Metaphysics is the branch of philosophy that studies the essence of a thing. This includes questions of being, becoming, existence, and reality.[1] The word "metaphysics" comes from the Greek words that literally mean "beyond nature". "Nature" in this sense refers to the nature of a thing, such as its cause and purpose. Metaphysics then studies questions of a thing beyond or above questions of its nature, in particular its essence or its qualities of being. Metaphysics seeks to answer, in a "suitably abstract and fully general manner", the questions:[2]

1. What is there?
   
   
2. And what is it like?
   

Topics of metaphysical investigation include existence, objects and their properties, space and time, cause and effect, and possibility.

Epistemological foundation[edit]

Like mathematics, metaphysics is a non-empirical study which is conducted using analytical thought alone. Like foundational mathematics (which is sometimes considered a special case of metaphysics applied to the existence of number), it tries to give a coherent account of the structure of the world, capable of explaining our everyday and scientific perception of the world, and being free from contradictions. In mathematics, there are many different ways to define numbers; similarly in metaphysics there are many different ways to define objects, properties, concepts, and other entities which are claimed to make up the world. While metaphysics may, as a special case, study the entities postulated by fundamental science such as atoms and superstrings, its core topic is the set of categories such as object, property and causality which those scientific theories assume. For example: claiming that "electrons have charge" is a scientific theory; while exploring what it means for electrons to be (or at least, to be perceived as) "objects", charge to be a "property", and for both to exist in a topological entity called "space" is the task of metaphysics.

https://en.wikipedia.org/wiki/Metaphysics

While everything I pasted is very important, note the underlined section and the example that follows it. You not only blur the lines between science and metaphysics, you seem to just deny the function of metaphysics. 

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!?!?

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.

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.

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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.

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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.

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