1. INTRODUCTION TO LOGIC

Logic

* Deals with ==distinguishing correct from incorrect reasoning==. Logic aims to make a system to @@evaluate arguments@@ and $guide us to construct our own arguments.$

What is logic used for?

To ==distinguish correct from incorrect reasoning==. Logic aims to make a system to @@evaluate arguments@@ and $guide us to construct our own arguments.$

Thinking

* ==Thoughts or ideas,== but not connecting them.
* They are @@merely reiterating@@ facts or ideas.

Reasoning

The ==linking together of thoughts or ideas== to make @@inferences@@ or @@arguments@@.

Inference

One proposition (conclusion) is @@based on some other proposition/propositions. (premises)@@

Premise

Proposition as a support to ==prove the conclusion acceptable.==

Conclusion

Proposition affirmed or accepted ==based on the premises.==

Statement

* A sentence that has a ^^truth value^^ (either %%true%% or ==false==)
* Usually a ^^declarative sentence^^

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Ex. The sky is cloudy.

* It doesn’t matter if this is true or false. It is still a statement.

Proposition

* ==Meaning or info content== of a statement
* One proposition may be expressed in different statements, but one statement cannot be expressed in different propositions.

Statements and Propositions…

Can be ==simple== or @@compound@@

Simple

==Do not contain any other simple statements== as components.

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Ex.


1. The Philippines is known to be a good travel destination.
2. The Philippines has had the highest discovery rate of new species within the last 10 years.
3. The Philippines has a deeper volcano.
4. The official language of the Philippines is Filipino.

Compound

Contain at least one simple statement as a component.

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Ex.


1. %%Mayon volcano is the world’s most perfect cone-shaped volcano,%% ==while== ^^Mt. Apo is the highest peak in the Philippines.^^
2. %%The Philippines has had the highest discovery rate of new species within the last 10 years,%% ==but== ^^we seemed to fail in conserving them.^^
3. %%The Philippines has a decade volcano%% ==and== ^^a number of famous mountains as well.^^
4. ==While== %%we recognize many regional languages,%% ^^the official language of the Philippines is Filipino.^^

The two kinds of logical reasoning

Deductive and Inductive

Deductive Reasoning

* ==Necessary== reasoning
* Arranged from @@general to specific@@
* General premise and ends with a specific conclusion

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Ex.


1. All students with a valid ID have access to the library.
2. Archer is a student with valid ID.

∴ Therefore, Archer has access to the library.

Inductive Reasoning

* ==Probabilistic== reasoning
* Could be false…
* Arranged from @@specific to general@@ ideas.
* Starts with $specific premises$ and ends with a $general conclusion.$

Ex.


1. Observing that every time you eat peanuts, you develop a rash.

∴ You then conclude that you are allergic to peanuts.

What makes a valid argument?

When it has a ==correct form.==

* When it has an incorrect form, it is invalid.

What makes a sound argument?

When it is ==valid and true.==

* When it is valid but not true or both is false, then it is unsound.

What makes a rational argument?

When it is ==sound and useful== for real life and other things.

* Proving whether an argument is rational or irrational is @@subjective@@. It is difficult to determine an argument’s rationality in general when there are many types of arguments.