Syllogistic logic

Invented by Aristotle. It features arguments using “all”, “no” and “some”. Syllogisms are vertical sequences of one or more wffs in which each letter occurs twice and the “letter for a chain”.

There are three parts to an arguments in syllogistic logic.

1. Major Premise - All men are mortal
2. Minor Premise - Socrates is a men
3. Conclusion - Socrates is mortal

Instead of words, you use representative letters. You usually substitute the word for the first letter.

We have specific vocabulary used for syllogism:

1. All
2. No
3. Some
4. Is
5. Not

You combine the letters represent q thing with these words, you get the following stuffs called Well-Formed Formulas - wffs

8 possible forms

• all A is B
• no A is B
• some A is B
• some A is not B
• x is A
• x is not A
• x is y
• x is not y

Wffs

• no P is C
• some F is H
• p is w
• all R is B

Non-Wffs

• w leads to h

• only e is n

• k if n

• most R is L

  Because these use language that isn’t limited to Wffs

Capitalisation:

• Some are capitalised and others aren’t.
• In each wff, there are 2 letters
• If the wff begins with a word such as some, all, or no, then both letter gets capitalised.
• Else / If the wff begins with a letter, then the first letter is lower case.
  • Second Letter:
    • If the represented term is GENERAL(a so and so, adjectives and verbs), use a CAPITAL letter
    • If it is specific(the so and so, this so and so and proper names), use a lower case letter.

Example

1. No penguins live in Kansas - no P is L

Validity test - Star method:

Output

1. No rabbits eat meat - no R* is E*
2. Bugs Bunny is a rabbit - b is R
3. Bugs Bunny doesn’t eat meat - b* is not E

• Next underline any letter that is distributed - if it occurs just after all or anywhere after no or not
  • Ex: all B is C, no T is W, h is not F, p is k.
• Next we need to star* certain letters:
  • Star premise letters that are distributed and conclusion letters that aren’t distributed.
• Is the every capital letter starred exactly once(small letter can be starred any number of times) and Is there exactly ONE star on the right hand side?
  • If yes to both, the syllogism is valid.