Day 2

Context

On this page we continue to focus on conditional arguments and using them to model physical situations.

Explanation

After determining that reasoning is important we will now develop some skill at using logical arguments to describe physical situations.

After this class you should be able to:

• Identify different kinds of arguments.
• Know what premises and conclusions are.
• Identify valid or deductive arguments.
• State what constitutes a sound argument.
• Know the form of a conditional argument.
• Write a conditional argument.

Model

Conditional Arguments

Chapter Two of the text is about logical reasoning. In section B of that chapter it goes through some types of arguments and some definitions of terms we will be using. You should become familiar with that material.

In the end we will be using conditional arguments in this class. This type has been chosen because it makes the connections between the premises and conclusions clear. The form of a conditional argument is:

Premise One:	If A, then B.
Premise Two:	Affirm A.
Conclusion:	Conclude B.

The "A" in the argument is a statement which is like criteria for the condition statement labeled "B". In other words if A is true, then B must also be true. When writing these arguments use the same wording throughout the argument. That is, the A in the first premise should be the same as the A in the second premise and B in the first premise should be the same as B in the conclusion. Properly written conditional arguments are always deductive or valid.

Here is a quick example:

Premise One:	If someone has green eyes, then they have red hair.
Premise Two:	I have green eyes.
Conclusion:	Therefore, I have red hair.

Is this a valid argument?

This argument is written in the correct form and the premises lead to the conclusion, so it is a valid argument. It is also a deductive argument. Valid and deductive mean the same thing.

Is it a sound argument?

To determine if it is sound you must decide if it is deductive and if all of the premises are true. Both conditions must be met to be sound. Another way to ask if it is sound is to ask "Does it lead to the truthfulness of the conclusion." To lead to the truthfulness of the conclusion it must be valid and the premises must be true.

In this case the first premise is questionable. I don't know of any examples, but I don't think that everyone with green eyes has red hair. The second premise is definitely false. I don't have green eyes! This example is not sound.

How about this one? Is it deductive?

P1:	If someone has green eyes, then they have red hair.
P2:	They have red hair.
C:	Therefore, someone has green eyes.

This is a common mistake. It affirms the "B" part of the conditional premise and concludes the "A". There may be other reasons, besides having green eyes, that cause someone to have red hair. This is not deductive. The premises don't lead to the conclusion, so it is not a sound argument either.

If you would like more details about this I have prepared these more detailed pages for another class. There is a practice quiz that may be helpful as well.

Fire

We will now look at several physical phenomena and practice writing conditional arguments. We will start with fire.

To facilitate our discussion we will consider lycopodium powder. Lycopodium powder is a very fine "dust" that comes from a certain kind of moss. When it is placed on a spatula and situated over a Bunsen burner it will start on fire, but it is a slow burn, starting on the edges and top and burning its way to the middle of the pile. But, when it is thrown into the fire it immediately burns in an impressive fireball. Here is a video example.

What is the simplest conditional argument that you could write from your observations?

What are the variables associated with fire? You can think of a variable as anything that could change what you are looking at, in this case fire.

Fundamental variables are variables that must be accounted for regardless of the environment or other factors. What are the fundamental variables for fire?

How could you use the fundamental variables to write a conditional argument?

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Class Homework For This Page
These are the same questions you will find and answer on Canvas.
Don't try to submit them from here.

These questions are from the end of Chapter Two in your textbook.

1. Analyze the following argument (identify the premises and the conclusion). Notice how the structure of the argument can be seen, even if the truthfulness of the premises is unknown or even if the language is unfamiliar.

   A body on which a freely swinging pendulum of fixed length has periods of oscillation which decrease slightly with increasing latitude from the equator to both poles is an oblate spheroid slightly flattened at the poles.

   But the earth is a body on which a freely swinging pendulum of fixed length has periods of oscillation which decrease slightly with increasing latitude from the equator to both poles.

   Therefore the earth is an oblate spheroid slightly flattened at the poles.

   (W. A. Wallace, Einstein, Galileo, and Aquinas: Three Views of Scientific Method)

2. Analyze the following argument (identify the premises and the conclusion). What kind of an argument is this? This argument may have been convincing in the 19th century, but is it convincing today? Explain. Hint: Are there really inhabitants on mars?

   The planet Mars possesses an atmosphere, with clouds and mist closely resembling our own; It has seas distinguished from the land by a greenish color, and polar regions covered with snow. The red colour of our sunrises and sunsets. So much is similar in the surface of mars and the surface of the Earth that we readily argue there must be inhabitants there as here.

   (W. Stanley Jevons, 19th century logician)

3. Does the following argument lead to the truthfulness of the conclusion? Explain.

   P1 If the sun is shining, then the house becomes warm.

   P2 The house becomes warm.

   C The sun is shining.