Examples 7.6 Indirect Proof Again, like conditional proof, an indirect proof is a method for deriving conclusions. This method works in the following way: we'll assume the opposite of the conclusion we're trying to derive, and then see whether we can
Examples 4.5
The Traditional Square of Opposition
Key: Contradictory = opposite truth value Contrary = at least one is false (not both true) Subcontrary = at least one is true (not both false) Subalternation = truth flows downward, falsity flows up
Notes 5.2 Venn Diagrams are the easiest way for determining validity in categorical syllogisms. All you have to do is put three circles together as follows:
Now, the procedure is simply to transfer the content of the premises to the circles and see
Examples 7.3 Rules of Replacement! The first 8 rules were technically rules of inference. That is, given a few premises (maybe only one), you could infer some other particular premise (or conclusion). Here the idea is that you can replace a premise w
Notes 6.4 Truth Tables for Arguments In order to test for validity in an argument using truth tables, all we have to do is the following: 1. Symbolize the argument (if necessaryit won't always be on the test) to represent the simple propositions. 2.
Examples 6.5 Indirect Truth Tables These things are useful, but not somewhat tricky to catch on to. The basic idea is as follows: instead of doing an entire truth table for an argument with lots of components and lots of premises, we'll just do a sho
Notes 6.1 So we should have gotten the point now that the validity of a deductive argument depends entirely on the form of an argument. But language, of course, can obscure the form of argumentand this is why weve been analyzing more normal language
Examples 7.5 Conditional Proof So, here's not another rule, but a method for obtaining conclusions in a proof sequence. It works, in theory, like the following: imagine that you have a conclusion to derive that's a conditional (say, A E). What this c
Examples 7.1 Natural Deduction, the topic we'll be concerned with for the next bit of the course, is the most efficient method for establishing validity (the thing we're most concerned with in logic). Here, we derive a conclusion of an argument from
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Examples 7.4 Rules of Replacement II . . . Transposition (Trans) (A B) : (~B ~A)
This one ought to make sense if you think about it for a second. If it's true that `If it rains, then the game is cancelled, then it certainly has to be true that `If t
Exercises 1.4
Some definitions you need to know: Valid deductive argument: a deductive argument where it is impossible for the conclusion to be false given the truth of the premises. Invalid deductive argument: a deductive argument in which it is po
modus ponens (MP) ~F (G H) ~F GH modus tollens (MT) (D v F) K ~K ~(D v F) hypothetical syllogism (HS) A (D F) (D F) ~H A ~H disjunctive syllogism (DS) U v ~(W X) ~U ~(W X) Simplification (Simp) PQ P ~(E v F) (E v F) v (N (N K) ~M (R S) (C v K) ~M (C
Notes 5.3
Generally, the Venn Diagram method is OK for assessing validity. But, to sort of supplement that method for examining validity we can add the following rules. First, we should remind ourselves of distribution of terms. Remember the followi
Examples 6.3 Truth Tables for Propositions So, 6.2 gave us truth functions for all of the operators we use. Now, we're going to implement those functions on whole propositions with multiple operators. We then stand in a position to note similarities
Notes 4.2 Quality the quality of a categorical proposition depends on its being affirmative or negative. Affirmative: "All S are P", "Some S are P" Negative: "No S are P", "Some S are not P" Quantity the quantity of a categorical proposition depend
5.1 Notes In general, a syllogism is simply a deductive argument consisting of two premises and a conclusion: If you don't know what a syllogism is, then you shouldn't be able to graduate. You don't know what a syllogism is. Therefore, you shouldn't
Notes 4.4 Consider the statement "No dogs are cats". Basically, this statement says that no members of the dog class are included in the class of cats. But the statement "No cats are dogs" says exactly the same thing. So these two statements have the
Study Guide for 4th Exam
First of all, know all of the little definitions for things on 6.1. These will be your multiple choice questions. As always, they will count for big pointsso make sure you're confident with them. Some examples would be: kno
Exercises 3.2 Fallacies of Relevance
Appeal to Force: when the arguer uses potential harm or violence as evidence for their conclusion. (Secretary to boss) I deserve a raise in salary for the coming year. After all, you know how friendly I am with yo
Exercises 3.1
Informal Fallacies
This may be the most useful part of the course, because informal fallacies are perhaps the most pervasive fallacies you'll see. They can be tricky to figure out, but we need to start by separating the formal from inf
Examples 7.2 More Rules of Replacement!
Constructive Dilemma (CD) (P Q) (R PvR QvS S)
Here's a short English equivalent, though, admittedly, we don't use it much: If it rains then the game is cancelled, and if I miss the game then I'll be unhappy.