Download PDF by Dirk van Dalen: A Blaricum Topology for Brouwer

By Dirk van Dalen

Does your homeland have any mathematical vacationer sights equivalent to statues, plaques, graves, the cafd the place the well-known conjecture used to be made, the table the place the recognized initials are scratched, birthplaces, homes, or memorials? have you ever encountered a mathematical sight in your travels? if that is so, we invite you to undergo this column an image, an outline of its mathematical importance, and both a map or instructions in order that others may possibly stick with on your tracks.

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2) T h e s e r e m a r k s are e x t r a n e o u s to the m a i n lines of the work. Peirce is m e r e l y p o i n t i n g o u t that the f r e q u e n c y i n t e r p r e t a t i o n of the probability of an event as the ratio of cases in which the e v e n t holds to all cases w h e t h e r it holds or not is n o t the only perfectly n e a t way of int e r p r e t i n g probability. O n e could start by using, instead of probability, the ratio of favorable to u n f a v o r a b l e cases, the ratio of u n f a v o r a b l e to favorable cases, or the log of either.

The opening section of this paper includes a clear statement of Peirce's aim to construct a logical calculus of inference of wide scope: I think there can be no doubt that a calculus, or art of drawing inferences, based upon the notation I am to describe, would be perfectly possible and even practically useful in some difficult cases, and particularly in the investigation of logic. (Peirce 1870, p. 28) Peirce emphasized the word "investigation," m e a n i n g here research into logic itself, as opposed to applications of logic elsewhere.

A s s u m i n g that these are all p r o p e r t i e s of e l e m e n t s of a fixed set, this is e q u i v a l e n t to Boole. , x is a cardinal n u m b e r ) , t h e n Peirce's l a n g u a g e of p r o p e r t i e s is b e t t e r because it is m o r e g e n e r a l . T h e idea of equality of p r o p o s i t i o n s u n d e r a probability i n t e r p r e t a t i o n is clear: b o t h p r o p o s i t i o n s are assigned the same probability based on the probability a s s i g n m e n t to p r o p o s i t i o n a l letters used.

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A Blaricum Topology for Brouwer by Dirk van Dalen


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