SSH 105 Lecture Notes - Lecture 6: Modus Ponens, Hypothetical Syllogism, Deductive Reasoning
19 Jun 2018
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Lecture 5/6
Review: Deductive arguments
- A deductive argument intends to provide logically conclusive support for the conclusion
- Goal is- if premise is true, conclusion must be true
- Suppose lawyer stands up at trial and says ladies and gentlemen’s if you look at the
evidence you will see that my client is not guilty
Validity
Conclusion would have to be true too
Conclusion logically follows from the premises
The conclusion is guaranteed to be true as well
Argument pattern- common structure
Universal Modus Ponens
- Related to modus ponens
- As and Bs stand for characteristics
- If everything in the world has feature a has feature b- suppose that’s true
- Suppose x has feature a
- Then it is true that x also has feature b
- Regular modus ponens has conditionals
Universal modus Tollens
- Suppose everything in the world that has characteristic a has characteristic b, suppose x
does not have characteristic b- that means x should also not have characteristic a
Universal hypothetical syllogism
- Cross out B and B and go straight to As are Cs
Universal ruling out
- Suppose that absolutely nothing that has characteristic a has b- and X is A therefore X is
not B
- Valid
Invalid patters
- Invalid because it is not distinct to Abdul
- First claim is all about groups of students, second claim says Abdul is not in the group-
the first two claims even if they’re true does not mean that the claim is true
- It does not say students are the only ones hardworking
Validity
- Special relationship between premises and conclusions
Entirely possible to look past words at the logic
find more resources at oneclass.com
find more resources at oneclass.com
Inductive arguments
- Premises/data in weather forecast intend to make the conclusion likely
- Goal is not to show that given some data there is only one possible conclusion, shows
that given some evidence/premises a certain conclusion is likely
- Likely and probability is most important
- Ladies and gentlemen of the jury, given the evidence it is very likely that my client is
innocent
Cogent
- Not valid but premises give good reason for conclusion
- If premises are true, conclusion is not certain but likely
- Suppose these 2 things are true-
- Likely that Mary’s health will improve- it is not guaranteed because it say’s tends
- Not a valid piece of reasoning- not certain
- It is not valid because conclusion is not guaranteed when the premise is true
- It is cogent because if premise is true, conclusion is likely
Non-cogent argument
- Does not make it likely that Jim is corrupt because it say’s a few/some- that by itself does
not make it likely that he is corrupt
- Not valid because statement three is not absolutely correct
- Not cogent because even if premise is true, it does not make the conclusion likely
Slide 15
- Cogent argument because if premise is true, conclusion is likely
The cogency test
- Cogency test we start with our imagination and say to ourselves let’s pretend these are
true and lets ask our self what does it mean to the conclusion- if it is likely it is cogent if
it is not likely it is non-cogent
A cogent argument can have
- Figure out if an argument is cogent by applying cogency test
- If it is true that most pigs can fly, if it is true that Jim is a pic then it is probably true that
Jim can fly
- We don’t need to know is premises are true or false but can still figure out if an argument
is cogent
Some common patterns of cogent arguments
- Not guaranteed that Kraay is nice even if the premises are true- but it is agreed that is
likely that Kraay is nice
Some common patterns of non-cogent arguments
- Non-cogent because PhD is not limited to just professors
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
A deductive argument intends to provide logically conclusive support for the conclusion. Goal is- if premise is true, conclusion must be true. Suppose lawyer stands up at trial and says ladies and gentlemen"s if you look at the evidence you will see that my client is not guilty. The conclusion is guaranteed to be true as well. Then it is true that x also has feature b. If everything in the world has feature a has feature b- suppose that"s true. Suppose everything in the world that has characteristic a has characteristic b, suppose x does not have characteristic b- that means x should also not have characteristic a. Cross out b and b and go straight to as are cs. Suppose that absolutely nothing that has characteristic a has b- and x is a therefore x is not b. Invalid because it is not distinct to abdul.
