Propositional Logic: Introduction

http://www.criticalthinkingtutorials.com

This is the introduction to a video tutorial series titled "Basic Concepts in Propositional Logic", which you can preview and purchase at the link above.

List of Tutorials in this Course

Introduction

Part 1: Compound Claims
1.1 Conjunctions (A and B)
1.2 Disjunctions (A or B)
1.3 Conditionals (If A then B)

Part 2: Contradiction and Consistency
2.1 Contradictories (not-A)
2.2 Contradictories vs. contraries
2.3 Contradictions (A and not-A)
2.4 Consistent vs. inconsistent sets of claims

Part 3: Contradictories of Compound Claims
3.1 not-(not-A)
3.2 not-(A and B)
3.3 not-(A or B)
3.4 not-(If A then B)

Part 4: Ways of Saying "If A then B"
4.1 A if B
4.2 A only if B
4.3 A if and only if B
4.4 A unless B
4.5 The contrapositive: If not-B then not-A
4.6 (not-A) or B
4.7 Necessary and sufficient

Appendix: Categorical Claims and Their Contradictories
1. Categorical vs propositional logic
2. All A are B
3. Some A are B
4. Only A are B
5. Square of Opposition

Category:

Education

Tags:

• logic
• propositional logic

[SteveShaw008]

@ 2:06. "John is" is also a propositional claim, that is, in addition to "wearing a red coat" and "stolen a jeep."

[PhilosophyFreak]

@SteveShaw008 Mmm... "John is" is not a propositional claim. Nor is "wearing a red coat" or "stolen a jeep". Only when you put a subject term and a predicate term together do you get a proposition that makes an assertion that could be true or false (which is the defining characteristic of a proposition).

[SteveShaw008]

@PhilosophyFreak That should read: "John is wearing a read coat" and "John has stolen a jeep," two propositional claims. "John is" could mean "John exists," another propositional claim. Otherwise, you risk making P. Coffey's mistake, one of several that Wittgenstein listed in his review of Coffey's book (1913): "III [6] He confounds the copula is with the word is expressing identity. (The word is has obviously different meanings in the propositions—Twice two is four and Socrates is mortal.)"

[PhilosophyFreak]

@SteveShaw008  That's good, I wasn't thinking along those lines! (Neither would most intro texts, though, so I don't feel too bad :) )

[meeene4]

Nice video, I am studying this and am only confused on one thing, syntactic and semantic sequents, when something syntactically and semantically entail another, I don't get that.

[PhilosophyFreak]

@meeene4 That is a tricky distinction. Basically, semantics is about meaning (which in this case is about whether a given proposition is true or false), and syntax is just about the formal rules for manipulating symbols. Semantic entailment involves questions like "If A is true and B is true, does C have to be true?". Syntactic entailment is about what you can derive from the inference rules. There's a close overlap but they are distinct concepts of entailment.

[August1977]

I cannot believe there's not an easier way to define these concepts

[tolsonw]

good stuff

[PhilosophyFreak]

@xXHellScreemXx  Yep. At least, computer programming is usually based on Boolean logic, and Boolean logic is just a form of propositional logic. DeMorgan's rules, for example, are basic theorems of propositional logic, but every computer science student knows them.

[xXHellScreemXx]

isnt that computer science?

[onoringo]

nice visual and great fresher; hope there are more and hope it breaks down how to breakdown real world arguments and to build some others (e.g., in research papers)