THE PROPOSITIONS
CONCEPT.- They are language expressions or assertive sentences that are characterized by having the property of being true (T) or false (F), but never true and false simultaneously.
1. THEY ARE INFORMATIVE EXPRESSIONS.- They use descriptive language of reality. (Description of objects, facts or phenomena)
Example: Peru is located in the central and western part of South America.
2. THEY LACK AMBIGUITY.- Because they have the property of being true or false, but not both at the same time.
Example: The ant is an invertebrate animal (V)
Cusco is the folkloric capital of Peru (F)
3. THEY ARE RELATING.- Because they have the quality of uniting each other, through their truth or falsehood. True propositions must generate true propositions, while false propositions must generate false propositions.
– All mammals are vertebrates (V), consequently dogs are vertebrates (V).
– No religious person is idealist (F), therefore no Catholic is idealist (F).
EXPRESSIONS THAT ARE NOT PROPOSITIONS
to. Grammatical phrases, because they do not affirm or deny something: hungry dogs.
b. Directive expressions: retreat! Shut up! Etc.
c. Desiderative expressions or wishes: how I would like to be a doctor!
d. Interrogative expressions: Is it true that cigarettes cause cancer?
and. Exclamatory expressions: how hungry I am! how cold!
F. Expressions of doubt: it would change life
g. The famous expressions: “I only know that I know nothing”
h. Expressions or open statements: x + 3 > 7
TYPES OF PROPOSITIONS
According to the structural criterion, the propositions can be:
A) ATOMIC OR SIMPLE PROPOSITIONS
B) MOLECULAR OR COMPOUND PROPOSITIONS
A) ATOMIC PROPOSITIONS.- They have a single subject and a single predicate, lack linking terms and cannot be disaggregated into simpler propositions.
Example: The neuron is a nerve cell.
Man is a rational animal
B) MOLECULAR PROPOSITIONS.-They are built from simple propositions, have a linking term and can be disaggregated into simple propositions.
Example: Gold is a metal and helium is a gas.
If it is hot then the temperature will rise
SUBDIVISION OF ATOMIC AND MOLECULAR PROPOSITIONS
1) ATOMIC OR SIMPLE PROPOSITIONS.- They may be:
a) Predictive Propositions.- They state a quality or characteristic of a specific object or entity. These propositions include a subject and a predicate.
University It is a research center.
Subject predicate
b) Relational Propositions.- They include correlated subjects.
Iquitos is larger than Tumbes
H.H
2) MOLECULAR OR COMPOUND PROPOSALS.- They may be:
a) Conjunctive Propositions.- They are those that use the linking term “and”. Equivalent expressions are also used: “with”, “in addition”, “both___ and ___”, “also”, “however”, “at the same time”, “and”, “equally”, and others. Example:
Logic is a formal science and physics is a natural science.
b) Disjunctive Propositions.- They are those that use the linking term “o”, exceptionally “u”. These propositions are of two types:
Inclusive or Weak Disjunctions.- When the two alternatives proposed can be fulfilled at the same time, or only one. Example:
Water produces snow or steam.
Exclusive or Strong Disjunctions.- When it admits compliance with only one proposed alternative.
Roberto is healthy or sick
c) Conditional Propositions.- They divide the proposition into two: the Antecedent and the Consequent. The connective or linking term “if” is placed in front of the antecedent, while the link “then” is placed in front of the consequent.
If you practice logic then you will pass the course
Consequential Antecedent
I will have colic yes I eat excessively
Consequent Antecedent
Similar or equivalent link terms can be Direct or Indirect.
Direct Indirect
Antecedent_______Consequent Consequent________Antecedent
Therefore since
Consequently since
Then if
Therefore because
Hence when
d) Biconditional Propositions.- They use the double condition “if and only if” as a term, and their equivalent linking terms can be: “then and only then”, “when and only when”, “because and only because”; and others.
I will travel to France if and only if I get a visa.
e) Negative Propositions.- They use the adverb “no” or similar terms. Negation is a special logical constant. When denying a Simple Proposition the terms are used; “no”, “never”, “never”, and the like; but when the negation affects a Compound Proposition, the terms are used: “it is false that”, “it is impossible that”, “it is not true that”, “it does not happen that”, “it does not happen that”; and others.
Lima is not the capital of France
It is impossible for the sun to rise and not have clarity.
SYMBOLIZATION OF PROPOSITIONS
SYMBOLIZATION OR FORMALIZATION.- It is a logical procedure that consists of transferring propositions from ordinary language to symbolic or formal language.
ELEMENTS OF SYMBOLIZATION.- Three elements are required: Variables, Propositionals, Propositional Operators and Grouping Signs.
1) Propositional Variables.- They are the symbols that replace simple propositions. Lowercase letters are used starting with the letter p, q, r, s, t,….
2) Propositional Operators.- They are the symbols that replace the linking or logical connective terms. These might be:
a) Monadic Operator.- It has only one link and its effect is to the right. It is necessarily placed before the negated proposition. The only monadic operator is negation.
The moon is not a star -p
b) Binadic or Dyadic Operator.- It has double range and its effect is to both sides. It is placed in the middle of the affected compound proposition. All operators are Binadic except for the negative operator.
Physics and chemistry are sciences p/q
p/q
There are multiple operator symbolization systems. We will address two
3) Signs of Grouping.- It is used to clarify the Hierarchy of operators. Auxiliary points are used or simply: parentheses, brackets, keys, bars, etc. The hierarchy will be as follows:
The parentheses ( ) will have a lower hierarchy compared to the brackets and braces.
The brackets Yo and They will have a higher hierarchy than parentheses but a lower hierarchy than braces.
The keys [
] They are the dominant ones, they have a higher hierarchy than parentheses and brackets
] They are the dominant ones, they have a higher hierarchy than parentheses and brackets
Example: If you study or work then you will be successful
p OR q. ®. r
