## Lecture 6

**How Truth-Functional Connectives Work (pages 154–155)**

I would like you to have memorized the truth tables for **conjunction**, **inclusive disjunction**, **negation**, and** conditional**. See notes on Lecture 5 for these truth tables.

In this section, we’ll explore the concept of a truth-functional connective. In the next section, we’ll give you a taste of how to test for validity using all that we’ve learned in Lesson 4 as background. Lesson 6 gets into more detail and considers application to real-life examples, as, up until now, we’ve been dealing with simple sentences and silly examples. We’re using these simples and sillies because the real world is messy (and hence harder to symbolize and test for validity). So we’re starting slow and easy (i.e., simple and silly). The authors make two points about connectives (page 155): first, the connectives are used to construct new propositions from old ones; second, the truth value of the new proposition is determined by the truth value of the original propositions plus the rules of connection. That is why we call the connectives truth-functional connectives. To see how this works, page 155 takes you through a whole bunch of examples of how to determine the truth or falsity of new propositions that are built up from old propositions using the connectives we’ve already learned.

This section is easy once you realize that the authors are assigning the truth value for each variable (which represents any proposition), and then all you are asked to do is determine the truth value of the entire proposition. If you don’t understand by now that propositions are simply sentences with true or false values (something we discussed in Lesson 3), then you need to review! So, for example, if your eye scans page 155 and detects a list of a bunch of symbols “A & B True,” etc., and you

are confused about how the authors could ever determine that these propositions are true or false, then read the paragraph before, where they already assign true to propositions A and B and false to G and H.

Go through the example on page 155.

## Practice Questions

The following are practice questions over the material covered in Week 1. They may represent potential exam questions. You are not required to answer these questions and turn them in, but feel free to leave your answer in the comments.

1. Matching

a. Ethos 1. Reason

b. Pathos 2. Authority

c. Logos 3. Emotion

2. Fill in the blank

An argument is a __________ series of _________________ that are intended to give ________________ for another ____________________.

3. Short answer.

Bob gives a poor argument in support of his position, and Alice says, “your argument is simply false.” Suppose Bob’s argument is:

1. All planets are massive enough to clear their orbits. (this is true)

2. Pluto is not a planet. (this is true)

3. Therefore, Pluto is not massive enough to clear its orbit. (this is true)

Here’s Neil DeGrasse Tyson trying to justify why he demoted Pluto from Planethood.

But these investigative journalists suspect something more sinister…

That’s right… Neil deGrasse Tyson actually commandeered the Large Hadron Collider, launched it into deep space, and Pluto was history…

Ahem. What should Alice have said to Bob, and explain the difference to her.

## Reading Assignment 8/29-9/02

Week 2: 08/29/11-09/02/11

*Understanding Arguments*, Chapter 3, pp. 51-75.

Suggested Exercises:

Exercise *IV*, pg. 61.

Lecture Topics:

(08/30) Tuesday’s Lecture Topic: Validity, Conditionals

(09/01) Thursday’s Lecture Topic: Validity (cont.), Soundness

## Lecture Two

August 25, 2011

Announcement: https://logicandreasoning1200.wordpress.com/ Has the syllabus, class notes, extras. Blackboard only for grading.

Review:

At this point you should:

a. have looked at the syllabus

b. know the difference between rhetoric and philosophical argumentation.

Today: What does it mean for philosophical arguments to be logos based?

Chapter One: pp. 3,4.

* Monty Python Skit:

A. Defn of “argument”: “An argument is a connected series of propositions that are intended to give reasons for another proposition.”

Defn of “proposition”: “Propositions are sentences or statements that have truth value (either true or false).”

Two types of propositions: “conclusions”, “premises”. Conclusion is the proposition that you want to prove to be true. Premises are the propositions that provide reasons to believe the conclusion.

For next time, read Chapter Three.

## Welcome to the blog

This is the official blog corresponding to Philosophy 1200 *Logic and Reasoning* for the Fall of 2011.