Chapter 7: The Philosophy of Probability Flashcards
The Interpretations of Probability
Objectivism
Subjectivism
Epistemtic Approach
Objectivism
probability statements refer to facts/claims of External World.
(Ex. Probability that coin will land heads up, is a claim about the coin’s propensity to land on heads every other flip).
Subjectivism
probability statements refer to the speaker’s degree of belief about something.
Epistemic Approach
probability statements refer to the degree of support one statement gets from another statement.
3 Versions of Objectivist Interpretation
1) Classical Interpretation
2) Frequenistic Interpretation
3) Propensity Interpretation
Classical Interpretation
Probability = Number of Favorable Cases / Number of possible cases
Regarding the classical interpretation, the only reason that a you would propose that a ____________ of ____________ rolls/tosses will definitely occur is if you’ve observed a ____________ that would make you think that. But this is _________ because your aim was to actually find ______________ using the __________ of rolls/tosses.
combination; equipossible; probability; circular; probability; combination
Problem with the Classical Interpretation
- What if your probabilities aren’t equally possible cases?
When the number of all possible outcomes is infinite, the favorable outcome will always be zero (ration between finite number : infinity = 0)
The Frequency Interpretation
Probability = Total number of positive events / Total number of trials.
Frequency Interpretation is always defined relative to some _____________ _______________ (the relevant total number of ___________).
reference class; trials
Problem with Frequency Interpretation (See Notes)
In deciding what is the relevant reference class
(whether that’s the combination of two [or more] trials, or deciding between separate trials).
The Frequency Interpretation comes into even more trouble if the event for which we are trying to decide among the ______________ ______________ is ____________, such that there’s only ___________ event (trial).
reference classes; unique; one
Venn’s Idea of the Frequency Interpretation
- Frequency Interpretation would only work if the number of total trials was infinite.
- Should distinguish between the limiting frequency and frequency observed.
Limiting Frequency
Total number of positive events (out of total number of trials) that we would get if one and the same experiment was done infinitely many times.
Frequency Observed
Total number of positive events (out of total number of trials) observed from a limited total number of trials.