lecture 6 Flashcards
How to find counterexamples to hypotheses of the form: If p, then q?
Find a situation where p is true, but q is false. Thats the only situation where a statement of the form If P, then q is false
What is logic
Logic is related to rationality and argumentation.
According to one definition, to reason rationally is to reason in accordance with principles of logic (and also of probability theory and decision theory)
Focuses on consequence relations, viz. which conclusion(s) follows from a given set of premises in an argument
What is an argument
An argument is a group of statements (= sentences that are either true or false) that include one or more premises cited in support of (i.e. reasons to believe) one conclusion
Example: We should not inflict unnecessary pain on plants, ants fish cows and dogs. after all we should not inflict unnecessary pain on anything with conscious experiences
To reconstruct an argument contained in a passage:
Read the passage carefully
Identify and highlight its main claim
Identify and highlight each individual reason in support of the conclusion
List each individual premise as a single numbered declarative sentence on a separate line
State the conclusion at the bottom, introducing it with “therefore,” or “so,”
To assess whether a conlcusion logically follows from a set of premises in an argument:
Assume that the premises in the argument are true and ask yourself if it is possible for the conclusion to be false, given your assumption about the premises
A conclusion c is a logical consequence of a set of premises X just in case there is no situation in which everything in X is true, but c is untrue
Example: Supplose these statements are all true:
Peter is looking at linda
Linda is looking at henry
Peter is married
Henry is not married
now consider this statement
Someone who is married is looking at someone who is not married
Does conclusion 5 follow from premises 1-4? can you find a possible situation where 1-4 are all true but 5 is false
to make the logic of an argument transparent and enable one evaluate whether and how the arguments conclusion follows from its premises
Identify conclusion and premises in the argument and put the argument in premises-conclusion format
Assume that all the premises in the argument are true, and work out the extent to which they provide good reasons for believe the conclusion is also true
Consider whether all premises are plausible, or some is obviously false, and indicate why/how
The premises-conclusion format example:
The choice by individual consumers to purchase or refuse to purchasae meat has no bearing on what meat producers choose to do with animals. Therefore, anybody should be allowed to eat as much meat as they want.
Premise 1) Individual consumers choices do not make any difference as to what meat producers choose to do with animals
Premise 2) If individual consumers choices do not make any difference as to what meat producers choose to do with animals, then it is okay that anybody eats as much meat as they want
Conclusion: it is okay that anybody eats as much meat as they want
If I assume that the two premises in the argument are true, can I find a situation where the premises are true but the conclusion is false? Do the premises give strong support to the conclusion
The argument we have reconstructed has the following logical form:
premise 1 = P
Premise 2 = IF p then q
Therefore q
This logical form is of that of deductively valid argument,
viz: no possible situation where the conclusion is false assuming the premises are true; so the conclusion logically follows from the two premises
What are some of the roles of deductive logic in science
Hypothesis testing
A normative standard of rationality
ii. Deductive logic in hypothesis testing
hypothetic deductive (HD) method
General pattern of reasoning in HD
Premise 1: If H (&Aux) is true, then I will observe O
Premise 2: I observe not-O
Therefore, H is false (or Aux is false)
An example of everyday life
Suppose your mobile fails to switch on. Your hypothesis is that the batteries are dead.
So, you decide to test whether this hypothesis is true by reasoning thus: “If my hypothesis is true, then I expect my mobile will work properly if I replace the batteries with new ones”
You proceed to replace the batteries. If you observe the mobile works again, then your hypothesis is confirmed. If you observe the mobile still does not work, then your prediction is false, and the hypothesis is disconfirmed
One complication with auxiliary assumptions
Typically, a hypothesis generates an expectation only when given additional, auxiliary assumptions. In such cases when we make a disconfirming observation, we do not know whether the hypothesis or auxiliary assumptions is wrong
An argument:
Premise 1: people do not reason in accordance with what economic models predict
Premise 2: If people do not reason in accordance with what economic models predict, then people are irrational.
Therefore people are irrational.
Is this a good argument
Some reasons to reject or qualify premise 2
Economic models are idealized. Their targets need not be humans in flesh and blood, and their goals need not be to represent human decision making
There is more than one system of logic
Deviations from economic models may indicate that the logic assumed by economists is inadequate to represent human rationality
