Introduction.

Many times a complex argument presented by a Philosopher can be distilled to a more simple form which allows one to both understand it better and critically examine it's crucial premises and assumptions.

Take for instance a famous argument by William Paley which we will read during Week Four of this class. His basic argument goes something like this:



An instrument like a watch is so complex that it is almost impossible that it should come about by chance.
Furthermore, watches have a purpose, and one could discover that purpose even if they had never seen a watch, simply by observing the watch.
Humans seem to exhibit more complexity than a watch (Paley uses the design of the human eye as an example), and if it is nearly impossible that a watch should come into being by chance, then it should be even more so for humans.
Humans too seem to have a purpose (albeit more complex) just like watches.
Either things come about by chance or design.
It seems very unreasonable to assume that humans came about by chance.
Therefore the most rational explanation for humans is that they were created with design.
Things that are created with design have a designer.
The designer of Humans is called "God "

Hopefully students will be able to see that the above argument is invalid, which only means that even if all the premises are true, the conclusion that humans were designed and that designer is God, could still be false. Actually this type of argument is an argument from analogy, all of which are invalid. But as I noted earlier , invalid arguments are quite common, and some come very close to guaranteeing the truth of their conclusions. What is left up to the reader is to determine just how strong the conclusion is. In doing so, it helps to uncover which premises are the least likely to be true, and if the conclusion drawn from those premises is the most reasonable.

Of course, we ourselves many times do not have to identify the weak premises or suspect inferences, other Philosophers have done that for us! For example, Richard Dawkins makes the case in his book, "The Blind Watchmaker" that natural processes can account for the complexity and "design" found not only in humans but in all biological life forms. We will read his essay during Week Four also, but the important part here is to note that if Dawkin's claim is correct, then that casts doubt on Paley's premise that "things that are created with a design have a designer" - and once that claim is weakened, then it directly weakens the conclusion that depends on it, that God is the designer of humans!

To make matters worse (or perhaps better, depending on your perspective) a central claim in yet another argument concerning God and Human design (The Problem of Evil) will simply assume that the claim that a Designer did indeed design humans is true. Then the further claim will be made that humans are imperfect in their design (they are subject to disease, deformities, uncontrollable rages, carelessness, and the list will go on) so that the nature of the Designer is that either it is limited in ability to design a better human, or worse, the designer must want to design humans (and for that matter the world) imperfectly, making the nature of the designer more akin to a cosmic masochist than a loving Deity.

That is the nature of Philosophy - arguments! Of course, that should not be seen as a bad thing, since debate and analysis have overthrown some fundamentally wrong views of the universe in favor of more correct views - this progress over time has led to a truly amazing revolution about what is known about the world and the Universe we live in and eventually launched a whole new discipline distinct from what was once called Natural Philosophy - that discipline today is know as Science in all its many forms. Our first reading deals with Renee Descartes, a central figure in Philosophy, known for both his Philosophical works as well as his Mathematical genius, and the author of the famous adage, "I think, therefore I am" - We will examine and debate his arguments and conclusions soon.

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Assignment:

To sharpen your logical skills, I present below some simple arguments.

Assume all the premises are true (even if you disagree with them, you must assume they are true)

Answer the following questions about each argument, and explain your answer.

1. On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)

2. If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.

[Here just a reminder: with invalid arguments it is possible to come up with counter-examples that will make a weak conclusion stronger, which is just as important to take into consideration as making a strong conclusion weaker!]

Please note, I have placed an italicized "therefore" in front of all conclusions. In real life, the conclusion is usually understood and not necessarily followed by the word, "therefore".

And finally, assume word meaning continuity - in other words, assume that the same word in different sentences has the same meaning.

Here are two examples:

A.

If it rains, then the streets get wet.

It rains

Therefore the streets are wet

This argument is valid, and on the assumption of true premises, there is no way that the conclusion could be false. Furthermore it has the valid form:

If P, then Q

P

Therefore Q

 

B.

If it rains, then the streets get wet.

It did not rain.

Therefore the streets did not get wet.

This argument is invalid, since even on the assumption of true premises, one could add an additional premise which does not change the truth of the existing premises.

à "There was a snow storm last night which melted during the day, leaving the streets wet"

If this additional premise were true, the original premises can be true as well, but the conclusion that the streets are NOT WET would now be false. Hence the argument is invalid.


Homework TITLE: Valid/Invalid Informal Analysis


1.
The capital of Massachusetts is Boston.
Boston is the home of the Boston Red Sox.
Therefore, the capital of Massachusetts is the home of the Boston Red Sox.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)


b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.




2.
This is a large hat.
Someone is the owner of this hat.
The owners of large hats are people with large heads.
People with large heads have large brains.
People with large brains are highly intellectual.
Therefore, the owner of this hat is highly intellectual.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)




b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.




3.
Every horse that has ever been observed has had a heart.
Therefore, every horse yet to be observed will have a heart.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)




b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.





4.
Malaria is caused by a parasite that lives in mosquitoes that inhabit tropical regions throughout the world.John has malaria.
Therefore he must have recently been in a tropical country.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)




b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.




5.
If it rains hard and long in the Tucson area, then the washes fill with water.
The Tanque Verde wash near Tucson is full of water.
Therefore it must had rained hard and long in the Tucson area.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)




b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.




6.
IF this stuff turns litmus paper pink. then it is an acid.
IF this stuff is an acid, then you don't want to drink it.
This stuff does turn litmus paper pink.
Therefore, you don't want to drink this stuff.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)




b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.





7.
I once had a bad case of the flu, and took zinc supplements and felt better the next day.
Therefore, zinc supplements help alleviate the flu.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)




b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.




8.
If Descartes thinks, then he must exist.
Descartes is not thinking
Therefore he does not exist.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)




b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.




9.
Kaiser Permanente, one of the nation's largest managed care organizations, has ordered its pharmacies to stop dispensing Bextra, an arthritis and pain drug made by Pfizer that some tests have indicated may increase the risk of heart attacks and strokes.
 Therefore, one should not take Bextra.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)




b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.




10.
If water is boiled at 212 degrees, then all harmful organisms will be killed.
We boiled this water at 212 degrees.
Therefore there will be no living harmful organisms in the water.

a)  On the assumption of true premises, must the conclusion be true if the premises are true (in other words, is the argument valid?)




b)  If the argument is invalid (which means the conclusion could be false even with all true premises)- come up with a counter-example (premise) such that if the new premise were true, the truth of the original premises does not change, but the conclusion to the argument is no longer guaranteed.