Tutorial 3: Sentences and Truth
6/8/07 10Software
Skills to be acquired in this tutorial:
To learn how compound sentences are true or false depending on the truth or falsity of their component sentences.
6/8/07 10Software
To learn how compound sentences are true or false depending on the truth or falsity of their component sentences.
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 ...'
'⊃' which translates back to 'if... then ...'
'≡' which translates back to '... if and only if ...'
8/29/06
Your browser does not support html5 video.
-->
[This is a film-- press the 'play' symbol.]
9/1/12
Symbolizing compound sentences. 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.
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.
To become familiar with the notions of argument, valid, invalid, premise, and conclusion. To learn how to symbolize atomic sentences.
Bergmann[2004] The Logic Book Chapter 1
The main role of logic is to assess arguments-- to say whether an individual argument is valid or whether it is invalid. In logic, arguments are taken to consist of two components--premises, and a conclusion.
For example,
Indicative sentences in a natural language, English, for instance, are either true or false. For example, 'There are 35 State Governors in the U.S.A.' is an indicative sentence (which happens to be false).
Indicative sentences can be atomic or compound. 'There are 35 State Governors in the U.S.A.' is an atomic sentence; whereas 'There are 35 State Governors in the U.S.A. and there is one President of the U.S.A. ' expresses a compound sentence composed of two atomic sentences (one false one and one true one).
Welcome!
These web pages provide an introduction to logic to the level of Propositional and Predicate Calculus.
The focus of the program is on arguments and the question of whether they are valid. Arguments have the form <list of premises> ∴<conclusion>. An argument is valid if and only if it is not possible for all its premises to be true and its conclusion false at one and the same time; an argument which is not valid is invalid.
8/29/06
Your browser does not support html5 video.
-->
[This is a film-- press the 'play' symbol.]
10Software
Hausman[2007] Logic and Philosophy Chapter 7
We will certainly wish to discuss the truth and falsity of formulas with quantifiers in them.
Let us start with an Interpretation
Interpretation 1
Universe= {a,b}
F={a}
6/21/07
This video uses '&' as the logical symbol for 'and'.