Symbolic Logic Operators | ||
Connective | Symbol | Formal Name |
Not | ~~ | Negation |
And | &n | Conjunction |
Or | Ú? | Disjunction |
If ...then | É? | Conditional |
...if and only if... | º? | Biconditional |
ARGUMENT = STATEMENT SUPPORTED + SUPPORTING EVIDENCE |
ARGUMENT = CONCLUSION + PREMISES |
The CONCLUSION is true because the PREMISES are true. |
Your First Step In Evaluating An Argument Must Be To Examine Its Premises To Determine Whether They Are Empirical Or Conceptual. |
The CONCLUSION is (presumed) true because the PREMISES are true. |
Determining the truth or falsity of its Premises is the essential step at the heart of the process of determining the validity and soundness of Arguments. |
Deductive Arguments are always either completely Valid or Invalid, with no middle ground. |
Deduction Begins With The General (The Rule) And Ends With The Specific. |
Induction Proceeds From The Specific (The Observation) To The General. |
Deductions Are Always Certain! |
Inductions Are Always Uncertain, to Greater Or Lesser Degree! |
Statements Can Be True Or False, But They Can’t Be Valid Or Invalid In The Sense These Terms Are Used In Logic. |
Arguments Can Be Valid Or Invalid, But They Can’t Be True Or False. |
And | ||
Statement A | Statement B | A & B |
T | T | T |
T | F | F |
F | T | F |
F | F | F |
Or | ||
Statement A | Statement B | A Ú B |
T | T | T |
T | F | T |
F | T | T |
F | F | F |
Not | |
A | ~ A |
T | F |
F | T |
If - Then | ||
T | T | T |
T | F | F |
F | T | T |
F | F | T |
If And Only If (= Iff) | ||
Statement A | Statement B | A iff B |
T | T | T |
T | F | F |
F | T | T |
F | F | T |
The Four Syllogism Figures | ||||
1st | 2nd | 3rd | 4th | |
Major | MP | PM | MP | PM |
Minor | SM | SM | MS | MS |
Conclusion | SP | SP | SP | SP |
Unconditionally Valid Syllogisms | |||
AAA | EAE | IAI | AEE |
EAE | AEE | AII | IAI |
AII | EIO | OAO | EIO |
EIO | AOO | EIO | - |
Conditionally Valid Syllogisms | ||||
Figure 1 | Figure 2 | Figure 3 | Figure 4 | Required Conditions |
AAI EAO |
AEO EAO |
- | AEO | S Exists |
- | - | AII EAO |
EAO | M Exists |
- | - | - | AAI | P Exists |