Autosave: 2022-12-21 05:34:20

Logic/General_concepts/Logical_consistency.md

@@ -38,7 +38,7 @@ $$
 \{P \lor Q, Q\}
 $$
 
-### Truth-table
+### Truth table
 
 $ \{P, Q\} $ form a consistent set because there is at least one assignment when both propositions are true. In fact there are two (corresponding to each disjunct) but one is sufficient.
 
@@ -52,14 +52,14 @@ F	F					F               F
 
 ## Derivation
 
-> In terms of logical derivation, a finite $\Gamma$ of propositions is **inconsistent** in a system of derivation for propositional logic if and only if a proposition of the $P & \sim P$ is derivable from $\Gamma$. It is **consistent** just if this is not the case.
+> In terms of logical derivation, a finite $\Gamma$ of propositions is **inconsistent** in a system of derivation for propositional logic if and only if a proposition of the form $P \& \sim P$ is derivable from $\Gamma$. It is **consistent** just if this is not the case.
 
 In other terms, if you can derive a contradiction from the set, the set is logically inconsistent.
 
-A [contradiction](Logical%20truth%20and%20falsity.md#logical-falsity) contradiction has very important consequences for reasoning because if a set of propositions is inconsistent, every and all other propositions are derivable from that set.
+A [contradiction](/Logic/General_concepts/Logical_truth_and_falsity.md#logical-falsity) has very important consequences for reasoning because if a set of propositions is inconsistent, any other proposition is derivable from it.
 
-![proofs-drawio-Page-5.drawio 3.png](../img/proofs-drawio-Page-5.drawio%203.png)
+![](/img/derivation_from_contradiction.png)
 
 _A demonstration of the the consequences of deriving a contradiction in a sequence of reasoning._
 
-Here we want to derive some proposition $Q$. If we can derive a contradiction from its negation as an assumption then, by the [negation elimination](Negation%20Elimination.md) rule, we can assert $Q$. This is why contradictions should be avoided in arguments, they 'prove' everything which, by association, undermines any particular premise you are trying to assert.
+Here we want to derive some proposition $Q$. If we can derive a contradiction from its negation as an assumption then, by the [negation elimination](/Logic/Proofs/Negation_Elimination.md)) rule, we can assert $Q$. This is why contradictions should be avoided in arguments, they 'prove' everything which, by association, undermines any particular premise you are trying to assert.

Logic/General_concepts/Logical_indeterminacy.md

@@ -1,10 +1,12 @@
 ---
 categories:
-  - Mathematics
-tags: [logic]
+  - Logic
+tags: [propositional-logic]
 ---
 
-The vast majority of sentences in natural and formal logical languages are neither [ logically true](Logical%20truth%20and%20falsity.md#logical-truth) or [\| logically false](Logical%20truth%20and%20falsity.md#logical-falsity). This makes sense because sentences of this form are all either tautologies or contradictions and as such do not express information about the state of events in the world. We call sentences that are neither logically true or logically false, logically indeterminate sentences.
+# Logical indeterminacy
+
+The vast majority of sentences in natural and formal logical languages are neither [logically true](/Logic/General_concepts/Logical_truth_and_falsity.md#logical-truth) or [logically false](/Logic/General_concepts/Logical_truth_and_falsity.md#logical-falsity). This makes sense because sentences of this form are all either tautologies or contradictions and as such do not express information about the state of events in the world. We call sentences that are neither logically true or logically false, logically indeterminate sentences.
 
 ## Informal definition