The Deductive Validity

PHIL 110
Deductive validity
Your task is to construct arguments that fit the common deductively valid forms that you read about in pages 39 - 42 of “How to think about weird things.” Your arguments can be about whatever topic you want, and you can argue for just about any conclusion. Get creative! There is space on this worksheet to type/write in your arguments.
Please do two things for each argument type: 1) Write out your argument in the box on the right, and 2) symbolize your argument in the box on the left. I have included some sample arguments on the last pages of this document, which you can use as a guide.
Modus ponens

If g then h.
g.
Therefore, h.

If you have the correct password, then you can log into the system.
You have the correct password.
Therefore, you can log into the system.

Modus tollens

If m then d.
Not d.
Therefore, not m.

If electorates voted wisely, then the state would have great leadership.
The state does not have great leadership.
Therefore, the electorates did not vote wisely.

Hypothetical syllogism

If w then x.
If x then y.
Thus, if w then y.

If it rains, I will not go to school.
If I do not go to school, I will miss my classes.
Therefore, If it rains, I will miss my classes.

Disjunctive syllogism

Either k or l
Not k.
Therefore, l.

French fries is ether healthy or unhealthy.
But French fries is not healthy.
Therefore, French fries is unhealthy.

Valid generalization

All K’s are M.
This is a K.
Therefore, this is an M.

All mammals have hair
Dolphins are mammals
Dolphins have hair

Examples on next page ➡️
Modus ponens
Using the letters p and q to stand for declarative statements (statements that could be true ...