Autosave: 2022-12-21 13:30:04

Logic/General_concepts/Object_language_and_meta-language.md

@@ -28,4 +28,4 @@ When we create an expression in a language we are said to _use_ that language. W
 
 A metalinguistic variable (metavariable for short) is an expression in the metalanguage that is used to talk generally about expressions of the object language. The convention in these notes will be to embolden single letters when these letters are used as metavariables.
 
-For example, instead of saying _'P & Q' is an expression comprising two atomic sentences and a conjunction_ we might say **\*P** is an expression comprising two atomic sentences and a conjunction.\* In this instance **P** is a metavariable in the metalanguage mentioning the expression P & Q in the object language
+For example, instead of saying _'P & Q' is an expression comprising two atomic sentences and a conjunction_ we might say **\*P** is an expression comprising two atomic sentences and a conjunction. In this instance **P** is a metavariable in the metalanguage mentioning the expression P & Q in the object language

Logic/General_concepts/Soundness.md

@@ -1,7 +1,7 @@
 ---
 categories:
   - Logic
-tags: [logic]
+tags: [propositional-logic]
 ---
 
 # Soundness
@@ -32,7 +32,7 @@ ____________________________________________
 
 The difference here is that the premises happen to be true and, given that the argument is valid, the conclusion must also be true. What we have defined here is **soundness**: the argument is said to be sound as well as valid. This is an additional and stronger criterion of evaluation.
 
-> An argument is sound if and only if it is deductively valid and all it's premises are true.
+> An argument is sound if and only if it is deductively valid and all its premises are true.
 
 We must not forget that truth alone is not the sole condition for soundness. We can have arguments whose conclusion and premises are all true without the argument being sound:
 
@@ -45,7 +45,7 @@ ____________________________________________
 (C) London is south of Cambridge
 ```
 
-All sentences are true here but the argument is not deductively valid: the premises are all true but the conclusion is false.
+All propositions are true here but the argument is not deductively valid: the premises are all true but the conclusion is false.
 
 We can also have arguments which are valid but which are not sound:
 
@@ -56,4 +56,4 @@ ____________________________________________
 (C) Vitamin C is harmless
 ```
 
-This argument is valid because we cannot consistently assert the premises and deny the conclusion. In either case, the conclusion can be said to follow from the premises. The problem is that we cannot consistently assert both premises: it is not possible for both sentences to be true at the same time.
+This argument is valid because we cannot consistently assert the premises and deny the conclusion. In either case, the conclusion can be said to follow from the premises. The problem is that we cannot consistently assert both premises: it is not possible for both propositions to be true at the same time.

Logic/General_concepts/Syllogism.md

@@ -1,10 +1,10 @@
 ---
 categories:
-  - Mathematics
-tags: [logic]
+  - Logic
+tags: [propositional-logic]
 ---
 
-In order to make assertions about the relative [consistency](Consistency.md) or inconsistency of a set of propositions we advance arguments. Consider everyday life: if we are having an argument with someone, we believe that they are wrong. A more logical way to say this is that we believe that their beliefs are inconsistent. In order to change their viewpoint or point out why they are wrong we advance an argument intended to show that belief A conflicts with belief B. Or if C is true, then you cannot believe that D.
+In order to make assertions about the relative [consistency](/Logic/General_concepts/Logical_consistency.md) or inconsistency of a set of propositions we advance arguments. Consider everyday life: if we are having an argument with someone, we believe that they are wrong. A more logical way to say this is that we believe that their beliefs are inconsistent. In order to change their viewpoint or point out why they are wrong we advance an argument intended to show that belief A conflicts with belief B. Or if C is true, then you cannot believe that D.
 
 In formal terms **an argument is a set of sentences comprising one or more premises and a conclusion. The conclusion is taken to be supported by the premises.**