Help for Remaining Propositional Games
Topic
Logical System
propositional
Tutorial 4: Arguments and searching for a counter example
Topic
Logical System
9/16/12
Skills to be acquired in this tutorial:
To learn how to symbolize arguments, and how to judge whether they might be invalid using truth-table methods.
Why this is useful:
We wish to appraise arguments, to do this we have to symbolize them first. Judging the invalidity of arguments by truth-table methods is not particularly important, but it does help to develop skills involving truth and lists of formulas.
Help with Tutorial 3, if you need it
Topic
Logical System
8/29/06
Tutorial 3 The Main Connective Applet
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Supplementary: The Paradoxes of Material Implication
Topic
Logical System
1/24/06
The problem or issue here lies with the truth table for the conditional (or material implication) ⊃
Tutorial 3: Propositions and Truth
Topic
Logical System
9/15/12
Skills to be acquired in this tutorial:
To learn how compound propositions are true or false depending on the truth or falsity of their component propositions.
Review
Topic
Logical System
There is the idea of setting up a code or convention or dictionary between atomic propositions and capital letters.
There are compound propositions, each of which has a main connective which connects its components.
There are five propositional logical connectives:
'∼' which translates back to 'it is not the case that...'
'∧' which translates back to '... and ...'
'∨' which translates back to '... or ...'
'³' which translates back to 'if... then ...'
'≡' which translates back to '... if and only if ...'
Help with Tutorial 2
Topic
Logical System
8/29/06
Tutorial 2 Example: How Experts Symbolize
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[This is a film-- press the 'play' symbol.]
Tutorial 2: Symbolizing compound propositions
Topic
Logical System
9/1/12
Skills to be acquired in this tutorial:
Symbolizing compound propositions. Learning about logical connectives, and the notion of the main connective. Recognizing different constructions in English which have the same underlying logical form. Paraphrasing the English into a standard form.
Why this is useful:
It is the next step in learning how to symbolize. Main connectives are very important-- they are central to symbolization, they are central to the semantics, and they are central to derivations.
Symbolizing Compound Propositions I
Topic
Logical System
8/25/12
Not all propositions are atomic propositions. Consider the proposition asserted by 'It is not the case that in 2011 the United States had a female President'. This is a true proposition, yet it is not an atomic one. It is made up of the atomic proposition 'in 2011 the United States had a female President' (which is false) and negation (expressed by 'It is not the case that...'), and the resulting compound proposition, which is the negation of a false proposition, is true.
There are several types of compound proposition.