Module 4 Notes - Probability & Inductive Reasoning (9/26)
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Precis 4
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Inductive Arguments
Defined by their structure
Unlike Deductive, no Inductive Arguments are valid
This means the conclusion will only follow from the premises with some degree of probability ranging from 0-99.99%
Ampliative - Information found in the conclusion that WAS NOT found in the premises (ADD)
Non-Ampliative - Do NOT include any information that was already not in the premises (DOESN’T ADD)
Probability - evaluate the quantifiers to see if the premise is true
For Example: a two sided coin has a 50% of landing heads or tails. (chances/decimals)
Decimals are the most common expression
A probability value will always be equal to 0, 1, or a value in between
Certainty - Objective probability of it happening
Psychological state
The higher the chance, the more probable the claim is (the better)
Probabilities are not always evaluated independently of other considerations
Probabilities are forward-looking (future)
Statistics are backwards-looking (past)
Using Statistical data, we can make a probable claim (Prediction)
Types of Probabilities
Probability - is a measure of the plausibility or likelihood that some event will occur given some set of conditions
The 3 primary sets of conditions are:
The way the world is (e.i. sets of facts)
The evidence we have that the event in question will occur (e.i. sets of data)
Our personal assessment of the events occurrence given the conditions we are aware of
Objective Probability - probabilities associated with (i), interested in chances
E.g. cards, a two-faced coin
Epistemic Probability - corresponds to conditions (ii), the evidence we have that an event will occur
E.g. betting in cards based on what we know
E.g. pulling an ace and asking for the P(Ace), knowing that you just took one out = 5.8%
Subjective Probability/ Credence - corresponds to condition (iii), a measure of how likely you believe/feel it will happen.
Similar to a gut-feeling
Helpful to only focus on epistemic probabilities
Conditional Probabilities
Conditional Probabilities - probabilities that are conditional on other probabilities
Dependent Probabilities - a probability that depends on (is affected by) the probability of another event
Independent Probabilities - a probability that a NOT affected by the probability of another event
| = “given that” in English
The Cost/Benefit Analysis
Diminishing Marginal Value - the quantity of a value thing increases, it’s value to you decreases
Cost/Benefit Analysis - the costs and benefits include the probabilities of different outcomes/ any relevant types of value
Expected Value - What we expect to gain