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SSR > L5 Ch4 Inductive Force and Probability > Flashcards

L5 Ch4 Inductive Force and Probability Flashcards

1
Q

Summary of WA2 corrections

A
  • P then Q = not Q then not P
  • denying the antecedent (P) does not mean that he consequent (Q) has to be true or false
    > P is false, Q can be either false or true
  • confirming the consequent (Q) does not mean that the antecedent (P) is true or false
    > Q is true, P can be either true or false
  • Unless = if not
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2
Q

what are the general steps of evaluating an argument?

A
  1. develop critical disposition
  2. learn to recognize the elements of an argument
  3. learn to reconstruct arguments
  4. logical assessment
  5. factual assessment
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3
Q

how do we recognize if an argument is valid or not?
(revision)

A
  1. determine whether or not the premises support the conclusion
  2. determine whether all of the premises are true
    = does the conclusion follow logically from the premises?
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4
Q

Inductive force
- what is a forceful argument?

A
  • if the premises were true, the conclusion is likely to be true
  • the likelihood has to be bigger than 50%
  • sometimes we must calculate probability to see if the conclusion is actually likely or not
    ! it is not about the actual truth-value of the premises, it is only about the connection between the premises and the conclusion
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5
Q

what is an example of forceful argument?

A

P1: most students drink tomato juice on Friday mornings
P2: X is a student
C: X drinks tomato juice on Friday mornings

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6
Q
  • what are the most common indicators of probability?
  • what range of probability do they refer to?
A
  • with “most” or “probably”, the probability is usually equal or more than 50%
  • with “some” or “sometimes”, the probability is usually less than 50%
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7
Q

what are the two questions that we need to recognize forcefulness?

A
  • if the premises were true, would the conclusion have to be true as well?
  • if the premises were true, is the conclusion more likely to be true?
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8
Q

what must we pay attention to regarding uncertainty in the arguments?
(TRICKY & important)

A
  • there can be uncertainty in the conclusion of a valid argument!
    > “I will probably throw heads”: valid argument
    > “Probably, I will throw heads”: forceful argument
    → this is because in the second case, “probably” is not part of the conclusion, it is just an indicator that shows that you are somewhat convinced that the statement “I’ll throw heads” is true
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9
Q

what are the kinds of inductive inferences?

A
  • statistical syllogism
  • inductive generalisation
  • inductive analogy
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10
Q

statistical syllogism

A
  • from general to specific
    > P1: 60% of the staff likes blond hair
    > P2: Babette is part of the staff
    > C: Babette likes blonde hair
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11
Q

Inductive generalisation

A
  • from specific to general
    > P1: all psychology students prefer proper dancing
    > P2: most preferences of psychology students are also held by all people
    > C: all people prefer proper dancing
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12
Q

How can we evaluate inductive generalisation?

A
  • how representative is the sample? How comparable is it to the general population?
    > P1: more than 50% of Australians found Pepsi tastier than any other brand
    > C: pepsi is tastier than any other brand
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13
Q

Inductive analogy

A
  • from specific to specific
    > P1: snowflakes are unique
    > P2: children are unique
    > P3: snowflakes lose their uniqueness in the classroom
    > C: children lose their uniqueness in the classroom
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14
Q

how can we evaluate inductive analogies?

A
  • Quantity
    > the more similarities and fewer differences, the stronger the analogy
  • Relevance
    > how relevant the similarities and differences are for the conclusion that is being drawn
  • Weight
    > relative predictive value of each similarity and difference
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15
Q

What is the evaluation of the following inductive analogy?

> P1: firearms are easily available, wanted and dangerous for children
P2: kinder surprises are available, wanted and dangerous for children
P3: kinder surprises are banned from the US
C: firearms should be banned from the US

A
  • Quantity: three similarities between firearms and kinder surprises
  • Relevance: not relevant
  • Weight: not predictive (of why we should ban them)
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16
Q

What is the relevance of the following inductive analogy?

> P1: a car has four wheels
P2: a car can transport people
P3: a handcart has four wheels
C: a handcart can transport people

A

Having wheels is relevant in the judgement about whether it can transport people

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17
Q

What is the evaluation of the following inductive analogy?

> P1: P(insula|X) = high
P2: P(insula|Y) = high
C: X and Y are similar/the same
- “both functions happen in the insula, so they must be connected”

A
  • Quantity: similarity of both functions happening in the insula
  • Relevance: not relevant (the insula could be huge and have lots of functions)
  • Weight: not predictive of similarities
18
Q

Abduction

A
  • inference to the best explanation
  • we must know to what extent that evidence is specific to that hypothesis
    > P1: the candelabra is the murder weapon
    > P2: if the maid is the murderer, then probably the candelabra is the murder weapon
    > C: the maid is the murderer
    → do not invert probabilities! the candelabra could be the murder weapon of the butler as well
19
Q

validity vs force

A
  • validity and force are properties of whole arguments, not of individual propositions
  • conclusion is either true or false, with probability we are just expressing how sure we are of either outcome
20
Q

Objective vs subjective probability

A
  • Objective: about the state of the world
    → frequency or proportion
    > e.g. “the chance of a die having one dot is 1/6”
    > e.g. “45% of september it has rained”
  • Subjective: about your beliefs about the state of the world
    → it could still be informed subjective probabilities using proportions and frequencies
21
Q

Degree of rational expectation

A
  • degree to which you’re entitled to believe something, given the evidence you have
  • part of the subjective probability
  • if assumed the premises were true, how justified are we to believe that the conclusion is rationally true?
  • conclusion is either true or false, but probability expresses how certain we are of either
22
Q

Conjunction
- the “and-rule” of probability

A
  • rules of probabilities used for combining arguments to see how likely conclusion is to be true
    > P1: on most days I eat bananas
    > P2: I probably spray whipped cream in my mouth if I eat a banana
    > C: I spray whipped cream in my mouth
    → we must calculate the comulative probability
    → 50% (most days) of 50% (probably) = 25% (probability overall)
    → argument is not valid, either forceful
23
Q

Proportion

A
  • quantity of how probable something is to happen
  • e.g. most, probably, …
  • e.g. there is a probability of 50% that it’s going to rain
24
Q

Frequency

A
  • how often something usually happens
  • it rains 7 out of 10 days
25
Q

Conversational implicature & probabilities

A
  • “it is probable” is vague, but it is usually used to refer to a state where the probability is substantially higher than 1/2
26
Q

Probability

A

Degree to which it is rational or reasonable to expect that something is true, irrespectively of our opinion and our degree of expectation

27
Q

Conditional probability
- example
- evaluation

A

> P1: 9/10 SSR students are vegetarians
P2: 1/10 non-SSR students are vegetarians
P3: Babetter is vegetarian
C: Babette is an SSR student

  • we are missing base rate of how many SSR students there are in the population
  • we need to know P(SSR|vegetarian)
    → not valid and not forceful
28
Q

conditional probability
- SSR & vegeterianism calculation

A

> P1: P(veggie|SSR)= 0.90
P2: P(veggie|not-SSR)= 0.10
P3: babette is a vegetarian
C: babette is a SSR student
- we are missing P(SSR|veggie)
- we are missing base rate P(A) = all SSR students

29
Q

what is the procedure for calculating conditional probabilities?

A
  • P(A|B) = (P(B|A)xP(A)) / P(B)
  • formula is also in the book during the exam, but we should practice using it to be quicker
30
Q

Evaluate the following argument:
> P1: if you are great, you probably have these 8 traits
> P2: I have these 8 traits
> C: I am great

A
  • not valid
  • not forceful
    > we have: P(8traits|great)
    > we need: P(great|8traits)
31
Q

Solve this probability:
- all succesful people have 8 traits
- 20% non succesful people have 8 traits
- 95% people are not succesful
→ what is the probability that you are succesful (A) given that you have the 8 traits (B)?

A
  • P(A|B) = (P(B|A)xP(A)) / P(B)
    1. P(A) = 5%
    2. P(B) = 100% x 5% + 20% x 95% = 24%
    3. P(B|A) = 100%
    4. (1 x 0.05) / 0.24 = 20.8%
  • frequency trees can help map out all the probabilities
32
Q

Evaluate the following argument:
> P1: I have these 8 traits
> P2: if you have these 8 traits, you’ll probably be great
> C: I am great

A
  • not valid
  • forceful but unsound
  • probability of being great given that you have the 8 traits is 20.8% (<50%)
33
Q

Inductive soundness

A
  • an argument is sound when it is inductively forceful and the premises are true
    ! the truth of the premises make the conclusion probable, but it does not guarantee it
34
Q

Inductive Inference

A
  • premises contain a generalization about a sample of a given population
  • conclusion extrapolates generalization to all the population
    > it sometimes includes extrapolations from the past to the future
35
Q

how can we make an argument more inductively forceful?

A
  • include in the premises all the evidence that would lead us to believe the conclusion to be true
  • we need a representative sample of the population
  • we should add more premises, but it is best to make them explicit when possible (clear connection to other premises)
36
Q

Defeated argument

A
  • despite the force of the arguments, some prior knowledge could lead us to prove that the argument has a false conclusion
37
Q

how can we make an inductive argument, deductive?

A
  • make premises and connections explicit
  • we can use the word “probably” in the conclusion to make the argument valid
  • pay attention to whether the premises are independent or dependent (if dependent, they influence each other’s likelihood)
  • pay attention to the base rate fallacy
    > we can transform a deductively unsound argument to be inductively sound
38
Q

Logical assessment

A
  • check whether argument is deductively valid or inductively forceful
39
Q

Factual assessment

A
  • check whether the argument is sound or not
    → we do this by checking the truth-value of the premises
40
Q

Probability theory

A
  • Conjunction of events: A and B = (A+B) / all outcomes
  • Independent events: A and B = A x B
  • Disjunction of events: A or B = (A + B) / (A and B)
  • Conditional probability: A given B = (A and B) / (B)

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