This document explains the principles of valid and invalid arguments in logic, including the form principle and the use of counterexamples.
Extract
[...] Only when speaking of empiricism would one need to pass to a non-valid argument. In philosophy, one wants valid arguments. - The validity of these arguments rests solely on their form and does not depend on the content (of what is being discussed). When there is the production of an argument, the object of the argument does not prove its validity. But what is the form of the argument? Aristotle emphasizes that the way we write out our reasoning indicates its validity. [...]
[...] not) =Unary connection: applies to a proposition ? p q or = The conjunction (and) =Binary connection: applies to 2 propositions (Attention in the literature unfortunately several symbols are found according to the programmers. The lack of many slides ? check on moodle To be able to ask the truth value of a proposition? With Column laid down: Signature of the expression So: « Jean ne gagne que si Sacha perd » Jean Gagne Sacha loses Sacha loses doesn't mean he doesn't win On doesn't have: (Jean wins and Sacha doesn't lose) ? [...]
[...] When its conclusion really follows/derives from its premises - Invalid ? When its conclusions do not follow/derive from its premises But the true or false conclusion is not the only factor in the validity of the argument. We must also consider the premises. ? Precise Definition: - Valid Argument: ? To hold all its premises as true, we are forced to hold its conclusion as true. ? It is impossible that all its premises be true and its conclusion be false. - Invalid Argument: ? [...]
[...] Conclusion Photo Inference Rules: - Structural Rules: ? rule of repetition ? these are correct rules: they must preserve the true - Connector Rules ? Hat Introduction Rules ? Hat Elimination Rules Deduction: - Premises 1 ? In all cases where the premises are true - Premises 2 - Premises n - ? . And let's use only correct rules (that preserve the true), then - Conclusion ? ? [...]
[...] Not valid (possible to find VVF) Example: On at a time: V - The sun around the earth - The sun turns around Saturn And: V - The sun does not turn around the earth So: F - The sun turns around Saturn Photo With complete evaluations by truth tables: - We have a simple technique to show that an argument is valid/invalid - However, we must be able to highlight the logical form - For now our tool remains limited as we only have signs and tables for and ? Calculation and reasoning: - Validity of an argument: ? until now it is determined by a calculation ? Truth tables evaluation ? Couldn't we also determine it by reasoning? ? Deduction? ? What is a deduction? A sequence of successive steps of reasoning. 1. Premises 2. Premises 7. [...]
