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PhilosophyGround >> There is no math


2/16/05 1:01 PM
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vermonter
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Edited: 16-Feb-05
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*The following is from a series of threads to stimulate some conversation. They do not mean i know anything about the topic, and do not necessarily express my opinion* Rather... statements of math are true inasmuch as "Superman is from Krypton" is true. The latter is true in the story of superman, and the former is true in the story of mathematics. Granted it has real applications, but statements of math are not real themselves, they are logical expressions. Or something like that. -doug-
2/17/05 11:57 AM
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vermonter
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Edited: 17-Feb-05
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Walt, I think that we are agreeing. I wish i knew more about logic, but a particular philisophical project is one that reduces math to logic (something that can be expresses in terms of psychology or the senses i guess). gusto, I hoped for some debate because i'd like to learn more about this topic. As far as i know, though, quite a few philosophers believe numbers to be objective entities that are mind-independent. I intuit the opposite, but i could always go either way. -doug-
2/17/05 3:09 PM
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DonnaTroy
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Edited: 17-Feb-05
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ONE dog is an objective entity... and if you have a pack of hounds after you, you are in big trouble, even using your martial arts skills. ;-)
2/17/05 3:10 PM
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DonnaTroy
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Edited: 17-Feb-05
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Besides, animals use to have the sense of numbering, counting their nestlings.
2/17/05 11:17 PM
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vermonter
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Edited: 17-Feb-05
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Donna, I'm not saying that one dog and one dog don't make two dogs, but rather that there is no abstract entity {1} or an abstract entity {+} such that {1} added to {1} is exactly the same as a third abstract entity {2}. -doug-
2/17/05 11:37 PM
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Dory
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Edited: 17-Feb-05
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If logical expressions arent real, what is real? Would you please describe what you mean by that term. I mean, they are real logical expressions.
2/18/05 8:23 AM
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DonnaTroy
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Edited: 18-Feb-05
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Well, doug, it is your option to live in denial. ;-)
2/18/05 2:22 PM
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vermonter
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Edited: 18-Feb-05
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Dory, I think the goal of one particular project is to reduce math TO logic, which in turn will be reduced to sense experience, and otherwise material things. I'm also not saying that "the story of math doesn't exist" rather that "there is nothing such as the number one, to which a single apple, orange, or what have you, personifies. There are just apples and oranges." Try to imagine what the number one is. You can't (and no i don't mean a character that represents it EG '1'). You may think of a singular object, but not an actual number that the object is an example of. -doug-
2/18/05 7:16 PM
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Dory
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Edited: 18-Feb-05
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Doug, Math as an ideal type has no physical existence. I think we can agree on this. Do they have some real nonphysical existence?
2/18/05 7:44 PM
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vermonter
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"Do they have some real nonphysical existence? " I don't think they do. Some people do, though. This is one of my weakest topics though! -doug-
2/18/05 11:06 PM
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Dory
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Edited: 18-Feb-05
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How would you determine a real nonphysical existence? (By you here, I dont mean a general you, I mean you in particular.) I assume a body and a spirit, I think you called this the dualistic position between materialism and idealism, based on my presupposition of the God of the Bible. 1 Corinthian 15:45-50 And so it is written, The first man Adam was made a living soul; the last Adam [was made] a quickening spirit. Howbeit that [was] not first which is spiritual, but that which is natural; and afterward that which is spiritual. The first man [is] of the earth, earthy: the second man [is] the Lord from heaven. As [is] the earthy, such [are] they also that are earthy: and as [is] the heavenly, such [are] they also that are heavenly. And as we have borne the image of the earthy, we shall also bear the image of the heavenly. Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption."
2/19/05 3:34 PM
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Dogbert
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Edited: 19-Feb-05
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The most popular arguments for the existence of mathematical objects are so called indispensabilty arguments. The idea is that if we need any entities in our major scientific theories, we should admit their existence. So we should assume the existence of genes, atoms and electricity. But we need mathematical objects like numbers in that theories too, so they exist too. There are several approaches to attack that view: 1. Harty Fields argues that one really doesn't need math for science. To make his point he has shown how to do Newtonian physics without talking about mathematical objects. Mathematical objects are only used as pragmatic tools. Math is about truth preserving transformations of scientific statements. 2. If we use standard set theory, it is not uniquely determined what the mathematical objects are. There are for example two major approaches to treat numbers as sets (of sets of s...) due to Zermelo and von Neumann. So one cannot really say what sets the numbers are. That arfument is due to Paul Benacerraf. 3. One can take another approach to realism. That is one can use a different criteria for why objects should exist or not. For further reading

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