8/15/06
The computer support for the exercises in Tutorial 1 can either be by 'applet' , as in the original, or by downloadable program. If your browser or computer is not working properly with the applets, you could try the alternative approach of using the downloadable program offered here.
You should now and do Sentential Exercise 1 (Propex1).
You can work on the exercise which is reproduced below.
Help with Tutorial 1 Alternative Exercises
[You do not require the Deriver program to do Exercise 1.]
Are each of the premises of the following arguments true, or are they false? What is the truth value of the conclusions? Is each argument valid or is it invalid?
Take note of the fact that many combinations are possible. For example, that an argument is valid does not mean that its premises are true (nor does the truth of an argument's premises mean that the argument is valid) ... One combination is impossible--which one is that?
(You should be able to make your mind up about the truth or falsity; judging validity (in the technical logical sense) is more difficult, after all it is the aim of this course to teach you how to do this, and we are only on Tutorial 1; however, if you understand the definitions given in the Tutorial you should be able to make a reasonable attempt.)
a)
Phoenix is in Arizona,
San Franciso is in California.
Therefore
Los Angeles is in California.b)
Phoenix is in Arizona,
San Franciso is in California.
Therefore
Phoenix is in Arizona and San Franciso is in California.c)
Phoenix is in California,
San Franciso is in Arizona.
Therefore
Phoenix is in California and San Franciso is in Arizona.d)
Phoenix is in California and San Franciso is in California.
Therefore
San Franciso is in California.
a)
Phoenix is in Arizona, (True)
San Franciso is in California. (True)
Therefore
Los Angeles is in California. (True)
(Invalid)b)
Phoenix is in Arizona, (True)
San Franciso is in California. (True)
Therefore
Phoenix is in Arizona and San Franciso is in California. (True )
(Valid argument)c)
Phoenix is in California, (False)
San Franciso is in Arizona. (False)
Therefore
Phoenix is in California and San Franciso is in Arizona.(False )
(Valid argument)d)
Phoenix is in California and San Franciso is in California. ( False)
Therefore
San Franciso is in California.( True)
(Valid argument)
(The impossible combination mentioned earlier is all the premises true and the conclusion false in a valid argument (for if all the premises are true and the conclusion false then it is possible for all the premises to be true and the conclusion false at one and the same time and that means that the argument is invalid).)
[You are now going to start interacting with the Deriver program. In particular you will be needing to use parts of this Web page as input to Deriver. Basically there are two ways of doing this. First, simply copy and paste what you want into the Deriver's Journal. (When you look at Deriver, there is a 'Palette' of logical symbols for your use, and, below the palette, is the 'Journal' where you can enter text.) Second you can often shorten this just by copying what you want (without pasting it). When Deriver is working it will go looking in sensible places for input from you, and if you have selected and copied part of a Web page, it will take that as input.]
The program knows of four atomic sentences and has itself adopted the following conventions regarding them
The sentence 'Philosophy is hard' is symbolized by 'H'.
The sentence 'Philosophy is interesting' is symbolized by 'I'.
The sentence 'Logic is hard' is symbolized by 'L'.
The sentence 'Logic is interesting' is symbolized by 'M'.
Form a view as to how the program will symbolize the following sentences, then ask it to do so. First check that Propositional Level is chosen under the Semantics Menu. Then symbolize by selecting the sentence, copying your selection (using the Edit Menu on your Web Browser or suitable key combinations) and, in Deriver, clicking To Symbols (under the Semantics Menu). When you have symbolized the sentences, ask the program to translate them back by selecting each symbol and clicking To English (also under the Semantics Menu).
Symbolize
a) Logic is hard.
b) Philosophy is interesting.
c) Philosophy is hard.
[This exercise is trivial from the point of view of logic, no doubt you can do it in an instant in your head. But you are also learning here how to use the computer program. And later exercises will have more challenging logic.]
Copy and paste this into the Deriver's Journal. [When you look at Deriver, there is a 'Palette' of logical symbols for your use, and, below the palette, is the 'Journal' where you can enter text.]
In this exercise you must chose how you are going to symbolize the sentences. The program knows of the three sentences above, but that is all. Tell the program how you are going to do it by selecting
remember sentence (<english in here>) <capital in here>
and clicking 'Do Command' from the Actions Menu. For example, the program does not know of the sentence 'Capital punishment deters killers' (*if you want to check on this ask the program to symbolize a) below, you will find the program cannot do so.*), now select
remember sentence (Capital punishment deters killers) D
and click Do Command-- the program learns the sentence (*if you want to check on this ask the program to symbolize a) below , you will find that the program symbolizes it.*).
First tell of your conventions
remember sentence (Capital punishment is justified) <capital-here>
remember sentence (Capital punishment is inhuman) <capital-here>
remember sentence (Capital punishment is cheap) <capital-here>
then symbolize, asking the machine to translate back and forward for you.
a) Capital punishment deters killers.
b) Capital punishment is justified.
c) Capital punishment is inhuman.
d) Capital punishment is cheap.