dorsal/arxiv
View SchemaFinitary and Infinitary Mathematics, the Possibility of Possibilities and the Definition of Probabilities
| Authors | Matthew J. Donald |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306201 |
| URL | https://arxiv.org/abs/quant-ph/0306201 |
Abstract
Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered from the point of view of philosophical idealism. Some of the ways in which infinitary mathematics arises in modern mathematical physics are discussed. Empirical science has led to the mathematics of quantum theory. This in turn can be taken to suggest a picture of reality involving possible minds and the physical laws which determine their probabilities. In this picture, finitary and infinitary mathematics play separate roles. It is argued that mind, language, and finitary mathematics have similar prerequisites, in that each depends on the possibility of possibilities. The infinite, on the other hand, can be described but never experienced, and yet it seems that sets of possibilities and the physical laws which define their probabilities can be described most simply in terms of infinitary mathematics.
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"abstract": "Some relations between physics and finitary and infinitary mathematics are\nexplored in the context of a many-minds interpretation of quantum theory. The\nanalogy between mathematical ``existence\u0027\u0027 and physical ``existence\u0027\u0027 is\nconsidered from the point of view of philosophical idealism. Some of the ways\nin which infinitary mathematics arises in modern mathematical physics are\ndiscussed. Empirical science has led to the mathematics of quantum theory. This\nin turn can be taken to suggest a picture of reality involving possible minds\nand the physical laws which determine their probabilities. In this picture,\nfinitary and infinitary mathematics play separate roles. It is argued that\nmind, language, and finitary mathematics have similar prerequisites, in that\neach depends on the possibility of possibilities. The infinite, on the other\nhand, can be described but never experienced, and yet it seems that sets of\npossibilities and the physical laws which define their probabilities can be\ndescribed most simply in terms of infinitary mathematics.",
"arxiv_id": "quant-ph/0306201",
"authors": [
"Matthew J. Donald"
],
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"title": "Finitary and Infinitary Mathematics, the Possibility of Possibilities and the Definition of Probabilities",
"url": "https://arxiv.org/abs/quant-ph/0306201"
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