The second rule of validity that relates to the distribution of terms is this:
A valid syllogism must distribute the middle term in at least one premise.
This syllogism, for example, breaks this rule: Continue reading Undistributed Middle
Monthly Archives: October 2015
Illicit terms
In my last post I promised to explain the reasoning behind the rules of validity that relate to the distribution of terms. Recall that a term is distributed in a statement when it refers to the entire extension of the term. This implies, as we saw, that the subjects of universal statements and the predicates of negative statements are distributed.
One related rule of validity says this:
A valid syllogism must distribute in its premise any term distributed in the conclusion.
This syllogism, for example, breaks this rule: Continue reading Illicit terms
Distributed Terms
A term is distributed in a statement when the statement makes some claim about the entire extension of the term. For the four types of categorical statements, the highlighted terms are distributed, as shown in this simplified square of opposition:
All S is P No S is P
Some S is P Some S is not P
You should discern two patterns to help you remember which terms are distributed: Continue reading Distributed Terms
Fixing a counterexample
Mr. Nance,
One of my students came up with a counter-example for OAO-1 (#6 Quiz 9) in class yesterday:
Some fish are not cats.
All catfish are fish.
∴ Some catfish are not cats.
Because of subimplication “NO catfish are cats” is true, would this counterexample be incorrect since “some catfish are not cats” is implied to be true as well? We had several class examples so by the end of the class, we were all a bit bogged down.
Thanks for your help! Continue reading Fixing a counterexample
Logic and the GOP debate
Mr. Nance,
Since this is an election year, can you help us with some real life examples on how we can best apply the tools of logic? For example, when I watch the presidential debates, they speak much faster than I can analyze what they said, since it is at such a rapid pace, to test for validity.
A real-life enthymeme
Mr. Nance,
An article included said of the following argument, “That’s a syllogism without a minor premise”:
“[P]olitical decisions in the modern world often concern how to deploy science and technology, so people well-trained in science and technology will be better prepared to make those decisions.”
I would like to give this to my students to work on, but I can’t seem to translate Jacob’s rendering into terms that work formally. Do you have time to take a look?
All the Best. Continue reading A real-life enthymeme
One Lesson Logic Students Must Learn!
The most important concepts to understand in Formal Logic is the concept of validity. All logic students should memorize and come to understand these three different (but related) ways of defining validity:
- In a valid argument, the premises imply the conclusion
- In a valid argument, if the premises are true, then the conclusion must be true.
- If an argument has true premises and a false conclusion, then it is invalid.
#14 – On Logic
“The worse your logic, the more interesting the results you obtain from it.” – Lord Russell
“Against logic there is no armor like ignorance.” – Laurence J. Peter
“You can’t be very good at philosophy if you’re very bad at logic” – Peter Kreeft
Fitting Words!
“Given the state of our culture, we should want our sons and daughters to be dangerous in the right cause, to possess effective weapons against the enemies of God and His people and know how to use them, because sometimes, fitting words are fighting words.”
– Fitting Words: Classical Rhetoric for the Christian Student
Syllogism challenge
Some time ago on this blog, I challenged my readers to translate this syllogism from Quintilian into standard categorical form, and to determine its validity:
“Virtue is the only thing that is good, for that alone is good which no one can put to a bad use: but no one can make a bad use of virtue.”
Let’s see what we can do. The word “for” is a premise indicator, so the conclusion is the first statement. Re-arranging into standard order, we get: Continue reading Syllogism challenge