Module 4 Notes - Probability & Inductive Reasoning (9/26)

To-Do List:

  • Precis 4

  • Group Discussion 1st reply

  • Group Discussion 2nd reply

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:

    1. The way the world is (e.i. sets of facts)

    2. The evidence we have that the event in question will occur (e.i. sets of data)

    3. 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