lecture 5 (reasoning) Flashcards
inductive force? 2
- an argument is inductively forceful if, given true premises, the conclusion is more likely to be true than false
- argument is not deductively valid
inductive vs deductive reasoning? 2
- Deductive reasoning leads to a conclusion that must be true if the premises are true
- inductive reasoning leads to a probable conclusion based on the premises
How is probability explained in relation to inductive reasoning? 1->3; +1
- Probability can be explained through proportion, frequency, or rational expectation
- It reflects how entitled a person is to believe a conclusion based on the evidence
What does it mean if the conditional probability of C relative to P is greater than 1/2 but less than 1?
It means that the argument is inductively forceful, making the conclusion more likely to be true than false based on the premises
inductive soundness?
An argument is inductively sound if it is inductively forceful and its premises are actually true, although the conclusion may still be false
what is a statistical syllogism?1 + e.g
- when a general statement is applied to a specific case
- example:
P1: 60% of the PVV staff like blond hair
P2: Bobette is a PVV employee
C: Bobette likes blond hair
What is an inductive generalization? 1+e.g
- reasoning from specific instances to make a general conclusion
- example:
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
How to evaluate
inductive
generalisations? 2
- check how representative the sample is
- more representative sample makes the conclusion more likely to be correct, increasing the inductive force of the argument.
inductive analogy? 1+e.g
- similarities between two specific things are used to draw a conclusion
- example:
P1: Snowflakes are unique and exquisite.
P2: Children are unique and exquisite.
P3: Snowflakes lose their uniqueness in the classroom.
C: Children lose their uniqueness in the classroom.
How do you evaluate inductive analogies? 3
- quantity (more similarities, fewer differences),
- relevance (how relevant the similarities and differences are)
- weight (the predictive value of each)
what is abduction? 1+e.g
- choosing the explanation that best predicts or explains the observed facts
- example:
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
How do we evaluate abduction?
by considering the predictive power of one explanation over others
How does adding evidence strengthen an inductive argument?
The conjunction of two pieces of evidence (B and C) typically provides stronger support for a conclusion than either piece of evidence alone
How can an inductive argument be converted into a deductive one? 1+e.g
- By adding a connecting premise that makes explicit the basis for the inductive principle
- inductive argument:
P1) All of the observed samples of jackdaws are monogamous
C) All jackdaws are monogamous. - converted into deductive argument:
P1) All of the observed samples of jackdaws are monogamous.
P2) If all of the observed samples of jackdaws are monogamous, then all jackdaws are monogamous
C) All jackdaws are monogamous
What makes an argument with “probably” still deductive?
when the word “probably” is explicit in both the premise and the conclusion, making the argument deductive but uncertain.
why is the argument P1: Most Americans are people who were born in America. P2: Most people who were born in America are white C: Most Americans are white. neither deductively valid nor inductively forceful?
the argument incorrectly assumes proportions, and half of a half results in a proportion much lower than “most” (less than 1/4)
What happens to probability in extended arguments?
The conclusion of a probabilistic argument can serve as a premise in further arguments, with the qualifier “probably” carrying over
What steps should you follow after reconstructing an argument? 3
- Check if it is deductively valid
- If not, check if it is inductively forceful
- If forceful, check the truth of premises to assess soundness
Degree of rational expectation? 1+2+2
- Validity & force are properties of whole arguments, not of individual propositions
- Objective probability is about the state of the world (frequency or proportion)
- Subjective probability is about your beliefs about the state of the world
- Degree of rational expectation: the degree to which you’re entitled to believe something, given the evidence you have
- If 50% this happens than 50% that happens -> 25%, so not forceful
How do you calculate the probability of independent events?
The probability of both events A and B happening is the product of their probabilities: Pr(A and B) = Pr(A) × Pr(B)
How do you calculate the probability of a disjunction of events?
Pr(A or B) = Pr(A) + Pr(B) − Pr(A and B)
What is conditional probability and how is it calculated?
- Conditional probability, Pr(A|B), is the probability of A given B
- calculated as Pr(A and B) / Pr(B)
OR
Pr(A|B) = Pr(B|A) x Pr(A) all divided by P(B)
conditional probability and forcefulness?
forcefulness argument doesn’t change once you’ve calculated the conditional probability, what changes is to what extent you believe that premise is true.
sensitivity vs specificity? 2
- sensitivity: how well a test can identify as positive the individuals that possess the condition being measured
- specificity: how well a test can identify as negative the individuals that do not possess the condition being measured
base rate?
the probability of a condition or characteristic existing in the population prior to the test being taken
true positives and negatives, and false positives and negatives?
- true positive (TP): when a test correctly identifies as positive the existence of the condition
- False positive (FP):
when a test result is positive but the condition is not present - True negative (TN):
when the test correctly identifies as negative the absence of a condition - False negative (FN)
when a test result is negative but the condition is present
what is the positive predictive power and how do you calculate it? 2
- the probability of when a test result is positive it is a true positive
- positive predictive power = true positives/(true positives + false positives)
what is the negative predictive power and how do you calculate it? 2
- the probability of when a test result is negative it is a true negative
- negative predictive power = true negatives/(true negatives + false negatives)
