PHIL 1000 - Argument Forms Handout
In class we discussed both inductive and deductive arguments. I wanted to provide a quick recap and
overview of what we went over, along with some specific argument forms.
Inductive Arguments
• Inductive arguments move from the particular to the general. In other words, inductive arguments
generalize from experience.
• Inductive arguments lead to conclusions that are probable rather than certain.
• Inductive arguments can be either strong or weak (strong when there is a greater probability, weak
when there is less).
Examples:
a) I’ve eaten clams 50 times, and every time I have gotten sick. So clams make me sick.
This looks like a pretty strong inductive argument. It is still, like all inductive arguments, only a
probable conclusion (a “guess”). Who knows, maybe every time you ate clams you had not washed
your hands or some such thing and were infected in some other way. But the argument is a strong one
since you are appealing to quite a few experiences. If you had only appealed to one or two experiences,
the argument would be much weaker.
b) I have eaten dinner over at Jenny’s house twice, and both times the food has been just awful.
Jenny is a horrible cook.
Again, an inductive argument. The argument begins with an appeal to particular experiences and then
draws a very general conclusion. In this case, though, the argument is weak. Generalizing from just two
experiences does not give us very high probability. Maybe Jenny just had some bad luck with recipes
those two times.
Deductive Arguments
• Deductive arguments move from the general to the particular.
• Deductive arguments lead to conclusions that are certain and necessary.
• Deductive arguments are either valid or invalid, sound or unsound.
A deductive argument is valid if the conclusion necessarily follows from the premises. the deductive
argument is invalid if the conclusion does not follow from the premises. The validity has nothing to do
with the truth of the premises. Instead it is a question of the form of the argument. Obviously valid
arguments are what you are striving for.
Once you have a valid argument, the next question is whether the propositions/premises are true. If all
the premises of a valid argument are true, then the argument is “sound.” In that case, not only does the
conclusion follow from the premises, but you know for certain that the conclusion is true.
PHIL 1000 - Argument Forms Handout
Deductive Argument Forms and Examples:
Modus Ponens
Valid Form: If P then Q. P
Therefore Q.
If my friend gave birth, she must be a woman. My friend did give birth.
Therefore she must be a woman.
In this case, the P term is “my friend giving birth” and the Q term is being a woman. These arguments are not always worded with “if then” propositions. Take this example: All Frenchman enjoy wine. Francois is French. Therefore Francois enjoys wine.
In this case, the P term is “all Frenchman” and the Q term is “enjoy wine”. In the second premise, the P
term is affirmed in the case of Francois. And so it must then necessarily follow that Francois loves wine.
Sometimes, though, one can construct a modus ponens argument such that it is invalid, that is, that the
conclusion does not necessarily follow. This is what an invalid modus ponens argument would look like:
Invalid Form:
If P then Q Q
Therefore P
For example:
If you are a fish, then you live in the water. Flipper lives in the water.
Therefore Flipper is a fish.
But the conclusion does not necessarily follow from the premises. Even though the two premises are
true, it is not true that Flipper is a fish. After all, it is not only fish that live in the water.
Modus Tollens
Valid Form:
If P then Q.
not Q
Therefore not P.
PHIL 1000 - Argument Forms Handout
If the battery were dead, then the car would not start. The car is starting.
Therefore the battery is not dead.
In this case, the P term is “dead battery” and the Q term is “car starting”. The conclusion necessarily
follows.
Again, these arguments do not always use the explicit “if then” structure. Take this example:
Mountaineers are always very fit. But I am not fit, so I am not a mountaineer.
Sometimes, though, one can construct a modus tollens argument such that it is invalid, that is, that the
conclusion does not necessarily follow. This is what an invalid modus tollens argument would look like:
Invalid Form: If P, then Q
not P
Therefore not Q
For example:
If I owned a hotel, then I would be rich. I don’t own a hotel.
Therefore I am not rich.
But the conclusion here does not follow. After all, not all rich people own hotels. In other words, I could
be rich while still not owning a hotel.
For these next two, I am going to let you sort out the terms for yourself.
Disjunctive Syllogism
Either P or Q Not Q Therefore P.
Either we should save our money or pay to renovate our house. We cannot afford to renovate our house.
Therefore we should save our money.
Hypothetical Syllogism
If P then Q
If Q then R Therefore if P then R
PHIL 1000 - Argument Forms Handout
If I get an A on my final, then I will get an A in the class.
If I get an A in the class, I will have a 3.5 GPA average for the semester.
I got an A on my final, and so I will have a 3.5 GPA average for the semester.
Finally, to tidy things up here a bit, I will simply provide a list of these 4 valid forms of deductive
arguments.
Modus Ponens
If P then Q. P
Therefore Q.
Modus Tollens
If P then Q.
not Q
Therefore not P.
Disjunctive Syllogism
Either P or Q Not Q Therefore P.
Hypothetical Syllogism
If P then Q
If Q then R Therefore if P then R