Popper’ın Aksiyomatik Olasılık Kuramı ve Değer-Atama Problemi

Date

2018-12-01

Author

Demir, Mehmet Hilmi

Metadata

Show full item record

Item Usage Stats

117
views

0
downloads

In the standard theory of probability, developed by Kolmogorov, the concept of conditional probability is defined with what is known as the ratio formula: the probability of A given B is the ratio between the probability of A and B and the probability of B, i.e. P(A|B)= (P(AB))/(P(B)). Clearly, this ratio is not defined when the probability of the condition, P(B), is 0. According to Popper, this problem, which is known as the zero-denominator problem, shows a serious conceptual shortcoming of the standard Kolmogorovian theory of probability. In order to overcome this shortcoming, Popper developed an alternative axiomatic theory of probability where conditional probability is taken as primitive. It should be noted that this axiomatic probability theory is different than and independent from Popper’s philosophy of probability which is based on the propensity approach. Popper claims that his axiomatic theory is a better fit for the use of probability in the philosophy of science and statistics. Based on this claim, it is often stated that Popper’s theory is conceptually superior to Kolmogorov’s theory. The ultimate aim of this paper is to evaluate this claim by analyzing Popper’s axiomatic theory within the context of the zerodenominator problem.

Subject Keywords

Zero denominator problem, Hájek, Kolmogorov, Popper, Conditional probability

URI

https://hdl.handle.net/11511/80754
https://dergipark.org.tr/tr/download/article-file/622426

Journal

BEYTULHIKME-AN INTERNATIONAL JOURNAL OF PHILOSOPHY

Collections

Department of Philosophy, Article

Suggestions

OpenMETU
Core

Popper's Axiomatic Probability System and the Value-Assignment Problem Demir, Mehmet Hilmi (2018-12-01) In the standard theory of probability, developed by Kolmogorov, the concept of conditional probability is defined with what is known as the ratio formula: the probability of A given B is the ratio between the probability of A and B and the probability of B, i.e. P(AIB)=(P(AB))/(P(B)). Clearly, this ratio is not defined when the probability of the condition, P(B), is o. According to Popper, this problem, which is known as the zero-denominator problem, shows a serious conceptual shortcoming of the standard Ko...
On the generating graphs of the symmetric and alternating groups Erdem, Fuat; Ercan, Gülin; Maróti, Attila; Department of Mathematics (2018) Dixon showed that the probability that a random pair of elements in the symmetric group $S_n$ generates $S_n$ or the alternating group $A_n$ tends to $1$ as $n to infty$. (A generalization of this result was given by Babai and Hayes.) The generating graph $Gamma(G)$ of a finite group $G$ is defined to be the simple graph on the set of non-identity elements of $G$ with the property that two elements are connected by and edge if and only if they generate $G$. The purpose of this thesis is to study the graphs ...
Use of probability hypothesis density filter for human activity recognition Günay, Elif Erdem; Akar, Gözde; Demirekler, Mübeccel; Department of Electrical and Electronics Engineering (2016) This thesis addresses a Gaussian Mixture Probability Hypothesis Density (GMPHD) based probabilistic group tracking approach to human action recognition problem. First of all, feature set of the video images denoted as observations are obtained by applying Harris Corner Detector(HCD) technique following a GMPHD lter, which is a state-of-the-art target tracking method. Discriminative information is extracted from the output of the GM-PHD lter and using these, recognition features are constructed related to ...
Orthogonal polynomials and moment problem Topkara, Mustafa; Aytuna, Aydın; Department of Mathematics (2004) The generalized moment of order k of a mass distribution sigma for a natural number k is given by integral of lambda to the power k with respect to mass distribution sigma and variable lambda. In extended moment problem, given a sequence of real numbers, it is required to find a mass distribution whose generalized moment of order k is k'th term of the sequence. The conditions of existence and uniqueness of the solution obtained by Hamburger are studied in this thesis by the use of orthogonal polynomials det...
A multilevel structural model of mathematical thinking in derivative concept Özdil, Utkun; Ubuz, Behiye; Department of Secondary Science and Mathematics Education (2012) The purpose of the study was threefold: (1) to determine the factor structure of mathematical thinking at the within-classroom and at the between-classroom level; (2) to investigate the extent of variation in the relationships among different mathematical thinking constructs at the within- and between-classroom levels; and (3) to examine the cross-level interactions among different types of mathematical thinking. Previous research was extended by investigating the factor structure of mathematical thinking i...

Citation Formats

M. H. Demir, “Popper’ın Aksiyomatik Olasılık Kuramı ve Değer-Atama Problemi,” BEYTULHIKME-AN INTERNATIONAL JOURNAL OF PHILOSOPHY, pp. 455–469, 2018, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/80754.