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LPS30 Week 1/2 Terms
These are the terms and definitions from Professor Meadows' lectures.
| Term | Definition |
|---|---|
| Premises | A list of propositions ( the reasons). |
| Conclusion | The final proposition. |
| Argument | A connected series of statements intended to establish a proposition. In many cases, an argument will take the form of a list of propositions followed by a final proposition. |
| Validity | An argument is valid if and only if the premises are true then the conclusion must be true. |
| Soundness | An argument is sound just in case it is valid and all of its premises are true. |
| Proposition | A thing we could believe (or disbelieve). We ask whether it would make sense to say you believed it, not whether it's right or not. |
| Deductively Valid | When it is impossible for the premises to be true while the conclusion is false. |
| Abstracts | Replacing words with symbols (p and q). |
| Propositional Form | Found by replacing "sub-propositions" inside a given proposition by letters. The result is said to be the form of the original proposition. |
| Instances | Given a propositional form, we say that a sentence is an instance of that form if we get the sentence (or a sentence with the same meaning) by replacing the single letters by sentences/ |
| Valid Argument Form | If every instance of a given argument form is valid. |
| Propositional Connective | A "piece of language" that allows us to take propositions and connect them to form new propositions, |
| Conjunction (and) | Conjuncts two previous propositions and creates a conjunction as a result. A conjunction is true in case both of its conjuncts are true. |
| Disjunction (or) | Disjuncts two previous propositions and creates a disjunction as a result. A disjunction is true just when at least one of its disjuncts is true. |
| Inclusive | p or q (and possibly both). |
| Exclusive | p or q (but not both). |
| Negation (not) | The original propositions is (sometimes) known as the negand and the new proposition is known as a negation. The negation of a proposition is true in case the original proposition is false. |
| Conditionals (if... then...) | The conditional has an antecedent and a consequent that are both sub-propositions. A conditional is true just when it is not the case that the antecedent is true and consequent is false. |
| Biconditionals | When both the antecedent and consequent can be flipped vice versa and still be true making both sides equal to each other. P ≡q is true just in case it is true that p if q and p only if q. |
| Formula | A meaningful arrangement of symbols will be called a formula. |
| Atomic Formulae | The construction of our abstract language. These atomic formulae might be though of as representing propositions which don't have any parts. |
| Complex | A formula is complex if it is not atomic. |
| Main Connective | The main connective of a complex proposition is the last connective added (so the connective used to form the proposition when the final rule was applied), |
Created by:
villa_melanie
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