Skills to be acquired in this tutorial:
To start learning how to symbolize propositions using predicate logic.
There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Beryl is wise.
is valid. Yet if we try to analyse this at a propositional level we find that 'Beryl is a philosopher' is an atomic proposition (which might be symbolized by A) and 'All philosophers are wise' is also an atomic proposition, different from the first one (and so might be symbolized by B), and the conclusion 'Beryl is wise' is an atomic proposition different from the other two (and could be symbolized by C); so the apparent logical form of the argument, as judged by propositional logic, is
A, B ∴ C
which is an invalid form.
Obviously what is needed here is a more careful look at the structure of the propositions which make up the argument. And predicate logic is the tool for this.
The task of this second part of the course is to learn the symbolization techniques, the semantics, and the new rules of inference, for predicate logic. Then we will be in a position to make informed judgements about a wider range of arguments.
In predicate logic, 'atomic' propositions are analysed at a finer level. A proposition like 'Beryl is wise' is not just something which is true or is false; rather it is something with a structure... there is a thing, Beryl, which has the property of being wise.
To symbolize at predicate logic level, entities like Beryl are symbolized by constant terms which are lower case letters from the beginning of the alphabet ('b' would be fine for Beryl) and properties are symbolized by upper case letters ('W' would be fine for '..is wise'); and the two are put together by writing the property first followed by the individual it applies to. The result, using the conventions mentioned here, is
Beryl is wise
would be symbolized by
Exercises to accompany Predicate Tutorial 1
It is usual to analyse an argument using only propositional logic or only predicate logic-- you do not mix up the two levels on one argument. We now move on to predicate logic...
Exercise 1 (of 4):
(*Note that English grammar is a context sensitive grammar and this means that no computer program can deal with it correctly in its entirety. This program makes simplifications and trims English down to a basic core 'near-English' which a computer can manage. For example, one simplification is not paying a lot of attention to having verbs agree properly with their subjects-- for the computer we write 'John goes' and 'John and Jill goes'. No doubt you will seized with a warm and humourous feeling when reading some of these sentences (all students of logic experience this at some time or another). The point of it is to convey how grammatical structure transforms into logical structure and the intermediate near-English helps in this . *)
Exercise 2 (of 4):
[This is a Video, click the Play button to view it..]
Exercise 3 (of 4):
Exercise 4 (of 4):
If you decide to use the web application for the exercises you can launch it from here Deriver [Gentzen] — username 'logic' password 'logic'. Then either copy and paste the above formulas into the Journal or use the Deriver File Menu to Open Web Page with this address https://softoption.us/test/easyDeriver/CombinedExercisesEasyDGentzen.html .
You may need to set some Preferences for this.
- you can check that the parser is set to gentzen.