PHIL2420 Lecture Notes - Lecture 9: Mathematical Proof, Models 1, Statistical Inference
1 Jun 2018
School
Department
Course
Professor
PHIL 2420
Critical Thinking
May 10, 2018
WEEK 9
Reasoning and Argument
Where should the armor go?
• Abraham Wald – Jew, refugee that went to the West
• Manhattan project – where they built the atomic bomb
• Military wanted to lower risk of planes being shot down
• Limitations on armor
• Data on lane damage
• More armor the plane has, less maneuver, slower flies
o More chances of being in range of bullet
• Can’t arm whole plane, need to find places where best to put armor
• Wald – put armor where holes are
Take Home Lesson 7 – Survivorship Bias
Concentrating on people or things that made it past some selection process and
overlooking those that did not. They don’t make them like they used to.
EXAMPLE: Plane with bullet holes
• Don’t infer that those cars were made better before
• Count the number of cars that did last
• Stock broker, choosing the stock
7 Step Scheme for Analyzing Scientific Results
• What you choose as your null hypo is important – will determine range of
possibilities for result
Reasoning – providing reasons for your statements
Why use reasoning?
1. Providing reasons justifies statements
2. Reasoning can expose mistakes
a. If you only express opposing opinions, you don’t get anywhere
b. Need to explain why
3. Reasoning facilitates critique
4. Providing reasons can move discussion forward
a. Can identify points of agreement and disagreement if both attack where
real problem is
Reasoning as a Recursive Process
find more resources at oneclass.com
find more resources at oneclass.com
• When you want to support a position, you provide reasons for it
• The you can provide reasons for the reasons, and so on
Formally, reasoning proceeds through the construction of arguments.
Persuasion is an attempt to convince others that what you say is true.
Purpose of an Argument
1. To attack or defend an opinion
2. For justifying judgments
a. Make a decision
A research report can be seen as an argument.
Argument – infers a conclusion from a set of premises (reasons)
• Good argument = premises support conclusion effectively
• Logicians evaluate arguments on the basis of their structure alone
An argument is either inductive or deductive on the basis of form alone.
• All A’s are B. x1 is an A. Therefore, x1 is B.
• X1 is A, X2 is A, X3 is A. Therefore, all A’s are B’s.
Types of Arguments
1. Inductive
a. Allows us to generalize on the basis of empirical data
b. Truth of premises support the truth of its conclusion
c. Usually what philosophers are interested in
d. Draws general conclusions from particular facts
e. The premises of inductive arguments support the conclusion, but not with
necessity.
i. S1 is white, S2 is white, S3 is white. Therefore, all swans are white.
f. Conclusions are not logically guaranteed from the premises, so induction
can’t give 100% certainty.
g. The stronger the evidence supporting an inductive argument, the more
reliable its conclusion will be.
h. Sampling – only gives you correlations, used to evaluate experiment about
causes
i. Random sampling needs clear hypothesis
ii. Sample must not be biased
iii. Larger the sample, better the data (Law of Large Numbers)
iv. Need a good method (survey design, outcome parameters)
i. Analogy – modelling
i. X is similar to Y. X has property P. Therefore, Y also has property
P.
ii. Scientific models
1. Models has assumptions
2. Designed with purposes
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Take home lesson 7 survivorship bias overlooking those that did not. (cid:1688)they don"t make them like they used to. (cid:1689) Concentrating on people or things that made it past some selection process and. Example: plane with bullet holes: don"t infer that those cars were made better before, count the number of cars that did last, stock broker, choosing the stock. 7 step scheme for analyzing scientific results: what you choose as your null hypo is important will determine range of possibilities for result. Reasoning as a recursive process: when you want to support a position, you provide reasons for it, the you can provide reasons for the reasons, and so on. Formally, reasoning proceeds through the construction of arguments. Persuasion is an attempt to convince others that what you say is true. Purpose of an argument: to attack or defend an opinion, for justifying judgments, make a decision. A research report can be seen as an argument.
