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Logic is Metaphysics (2011) [pdf]

philpapers.org

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Re: Logic is Metaphysics (2011) [pdf]

#51

Post by madmax96 »

trhway wrote: post #40
jc763 wrote: post #2

>Does the number seven exist? Does the red color exist? What evidence do we have to answer these questions? What are the truth conditions for ∃x P(x) when P(x) stands for a number or a property? To respond to these questions is to set an ontology, and setting an ontology is to do metaphysics. This is exactly what Quine does when he states some reasons to include numbers and to exclude properties from the domain of ou…

>Does the number seven exist? Does the red color exist? those ones seem to be easy. There is no number seven. I mean there seven trees, seven stones, yet there is no number seven. It is only our mental construct (note: the construct itself, ie. neuron circuits and firing sequences do exist. It is like a map of non-existent land - the map exists while the land doesn't). The same is red color. There are EM waves of dif…

>those ones seem to be easy. There is no number seven.

That's a very definitive answer for a complex question. It is not immediately clear at all that there is no number 7.

There are a few accounts for how numbers could exist. Let's break down each account:

* formalism - Mathematics is a formalized activity undertaken by humans, but is ultimately a language game. This approach is problematic because no formal system is capable of enumerating all truths about Mathematics. Hence, Mathematics is not a formal activity undertaken by humans, because otherwise the methods of its formalism would allow us to enumerate each true statement.

* intuitionism - Mathematics is a psychological artifact of minds, but is not a "natural" phenomenon. This approach has problems because it fails to account for (1) the remarkable consistency and success of Mathematics, and (2) leads us to Godel's disjunction. Godel's disjunction states that either there is no algorithm capable of enumerating all true statements that a human mind enumerates, or there are some Mathematical truths that can not be decided. If there is no algorithm capable of enumerating all true statements that a mind enumerates, then the mind is not a computational system -- meaning it can not be reduced to a mathematical model of neurons communicating -- and so the meaning of a psychological artifact needs reappraised. Specifically, numbers being a psychological artifact does not imply that they do not exist naturally. However, if a human mind is a computational entity, then intutionism doesn't work for the same reasons why formalism doesn't work.

* Realism - Mathematical objects exist. Given the problems of formalism and intuitionism, this actually is among the most probable of hypotheses.

Many Mathematicians fall into the Realist category, and there are good reasons why.

Re: Logic is Metaphysics (2011) [pdf]

#54

Post by ethn »

mcbits wrote: post #39
ethn wrote: post #35

Earlier quoted context omitted.

Bold, passive, and mistaken accusation: https://en.wikipedia.org/wiki/Proper_noun But I do see how it could be confused with platonic love, albeit I'm comfortable using it without clarification in the appropriate contexts. You're right, in German all nouns are capitalized.

A more appropriate Wikipedia article: https://en.wikipedia.org/wiki/Theory_of_forms If you simply meant to say that the idea of Santa Claus obviously "exists" in some sense, thus it's valid to compare our experiences with that idea, then I agree with the comment saying a lot of people would agree with you, but "platonic" is ambiguous at best. If you really did mean to imply that an ideal Santa Claus literally exists…

>If you really did mean to imply that an ideal Santa Claus literally exists in a literal universe of perfect ideal forms

In philosophy, this is "Platonic Realism" quite different from "platonic", the lower case helps convey information. You make a mistake by assuming "platonic" explicitly conveys "Platonic Realism", given there are many "Platonic *" theories, such as "Platonic Idealism". Because of the ambiguity, as you correctly acknowledge, you are expected to understand it as the wikipedia article on "Platonic" suggests (as some sort of abstract object): https://en.wikipedia.org/wiki/Platonic

"Plato's influence on Western culture was so profound that several different concepts are linked by being called "Platonic" or Platonist, for accepting some assumptions of Platonism, but which do not imply acceptance of that philosophy as a whole."

Re: Logic is Metaphysics (2011) [pdf]

#55

Post by teilo »

hiker wrote: post #4

The key to understanding logic constructively goes through type theory, not philosophy. I'll just leave this here https://78.media.tumblr.com/bfc158b432199a3e4f5de2ddc1bd7381...

Anyone who prefers type theory to (non-naive) set theory does so for philosophical reasons. Therefore your argument is self-defeating.

Re: Logic is Metaphysics (2011) [pdf]

#56

Post by teilo »

hiker wrote: post #46
mbid wrote: post #28

Earlier quoted context omitted.

So you think the key for understanding constructive logic is to understand some peculiar syntax for a fragment of it. Ridiculous, but sadly quite typical among type theory cultists.

> So you think the key for understanding constructive logic is to understand some peculiar syntax. It's not only a syntax, it's a functional programming language which turns out to be a computational model for logic.

No one is saying type theory is useless, particularly when it comes to computation. It works within its own boundaries, but it does indeed have boundaries. There is a reason the ZFC has triumphed in mathematics.

Re: Logic is Metaphysics (2011) [pdf]

#57

Post by danbruc »

ethn wrote: post #54
mcbits wrote: post #39

Earlier quoted context omitted.

A more appropriate Wikipedia article: https://en.wikipedia.org/wiki/Theory_of_forms If you simply meant to say that the idea of Santa Claus obviously "exists" in some sense, thus it's valid to compare our experiences with that idea, then I agree with the comment saying a lot of people would agree with you, but "platonic" is ambiguous at best. If you really did mean to imply that an ideal Santa Claus literally exists…

>If you really did mean to imply that an ideal Santa Claus literally exists in a literal universe of perfect ideal forms In philosophy, this is "Platonic Realism" quite different from "platonic", the lower case helps convey information. You make a mistake by assuming "platonic" explicitly conveys "Platonic Realism", given there are many "Platonic *" theories, such as "Platonic Idealism". Because of the ambiguity, as…

I still tend to argue that the use of »platonic» or »Platonic« most of the time implies a relation to the philosophy of Plato, the usage with the generalized meaning of something along the line of »abstract« seems to be at least quite rare. The quote from Wikipedia also seems to support this.

And that is of course why I interpreted the combination of »platonic« and »Santa Claus« as hinting at Platonic Realism, because of the implied relation to the ideas of Plato and the example of »Santa Claus« as an abstract idea. Are there any other parts to his work were »Santa Claus« could be a relevant example but that is not related to his theory of ideal forms?

Also »Platonic Realism« and »Platonic Idealism« are, as far as I can tell, the same thing. »Platonic Realism« seems to be the common term, »Platonic Idealism« seems to be a less frequently used term with its origin in the fact that Plato called his abstract objects ideal forms.

Re: Logic is Metaphysics (2011) [pdf]

#58

Post by ethn »

danbruc wrote: post #57
ethn wrote: post #54

Earlier quoted context omitted.

>If you really did mean to imply that an ideal Santa Claus literally exists in a literal universe of perfect ideal forms In philosophy, this is "Platonic Realism" quite different from "platonic", the lower case helps convey information. You make a mistake by assuming "platonic" explicitly conveys "Platonic Realism", given there are many "Platonic *" theories, such as "Platonic Idealism". Because of the ambiguity, as…

I still tend to argue that the use of »platonic» or »Platonic« most of the time implies a relation to the philosophy of Plato, the usage with the generalized meaning of something along the line of »abstract« seems to be at least quite rare. The quote from Wikipedia also seems to support this. And that is of course why I interpreted the combination of »platonic« and »Santa Claus« as hinting at Platonic Realism, becaus…

"Plato's influence on Western culture was so profound that several different concepts are linked by being called "Platonic" or Platonist, for accepting some assumptions of Platonism, but which do not imply acceptance of that philosophy as a whole."

Does not support that the "Platonic" is Platonic Realism, which is what your chief claim is and what it would implicate if the term conveyed acceptance of the entire philosophy. It merely means the acceptance of an ontology of abstractions—which is implicit when there is discussion of it, otherwise how would it be discussed?

Even if you believe Platonic Idealism and Realism are the same (which is usually meant to designate the classification between 'soft' and 'hard' Platonism), there are even different Platonic periods.

Nonetheless, it's clear that I didn't communicate this well if I'm in this conversation. Which I don't think is irrational since my discussions are usually restricted to academic contexts where this usage is ostensibly vernacular.

Re: Logic is Metaphysics (2011) [pdf]

#59

Post by coolgeek »

trhway wrote: post #40
jc763 wrote: post #2

>Does the number seven exist? Does the red color exist? What evidence do we have to answer these questions? What are the truth conditions for ∃x P(x) when P(x) stands for a number or a property? To respond to these questions is to set an ontology, and setting an ontology is to do metaphysics. This is exactly what Quine does when he states some reasons to include numbers and to exclude properties from the domain of ou…

>Does the number seven exist? Does the red color exist? those ones seem to be easy. There is no number seven. I mean there seven trees, seven stones, yet there is no number seven. It is only our mental construct (note: the construct itself, ie. neuron circuits and firing sequences do exist. It is like a map of non-existent land - the map exists while the land doesn't). The same is red color. There are EM waves of dif…

> there is no number seven

There is cardinality. There is ordinality. The "number seven" is a label for specific points in the cardinality and ordinality spaces.

> Color is mental construct triggered by perception of EM frequencies in specific range

You're conflating stimulus and sensation here

Re: Logic is Metaphysics (2011) [pdf]

#60

Post by woodandsteel »

jc763 wrote: post #2

>Does the number seven exist? Does the red color exist? What evidence do we have to answer these questions? What are the truth conditions for ∃x P(x) when P(x) stands for a number or a property? To respond to these questions is to set an ontology, and setting an ontology is to do metaphysics. This is exactly what Quine does when he states some reasons to include numbers and to exclude properties from the domain of ou…

Whether or not you should say they exist depends on the particular meaning of the term "exist" you are using. And that in turn depends on what are your motives and purposes for asking the question.

Of course, if you are a Platonist then you will believe that there is a single, perfect meaning for the term that everyone should use.

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