- What is a proposition?
- Proposition in philosophy
- Proposition in logic
- Simple and compound statements
- Proposition in mathematics
We explain what a proposition is, its meaning in philosophy, logic and mathematics. Also, simple and compound propositions.
What is a proposition?
A proposition, in general terms, is something that is proposed. That is, it is an equivalent expression of a simple sentence assertive, a prayer in which it is affirmed that something is, that something exists or that it has a certain characteristic. Therefore, it can be judged as true (if it agrees with reality) or false (if it does not).
It is a term widely used in different contexts of knowledge, such as certain formal disciplines (logic, math) wave linguistics and the philosophy. The idea is that, taking different propositions as antecedents, it is possible to obtain certain conclusions, and furthermore, the procedure through which we have obtained them can be carefully studied.
In any case, a proposition must be understood as a chain of signs that belong to the same language, whether they are sounds or characters (in a natural language) or signs and representations (in a formal language).
Whereas, in colloquial language, a proposal is understood as a proposal: an invitation that we make to another or others and that can be accepted or rejected.
Finally, we must not confuse a proposition with a preposition. The latter is just a grammatical category, that is, a type of words, which have a more or less obvious grammatical meaning, and which serve to establish relationships between things. Examples of prepositions are: de, para, contra, entre, por, sobre, bajo, en, etc.
Proposition in philosophy
Within the field of philosophical debate, there is talk of a proposition to refer to a mental act through which a judgment regarding reality is expressed in a specific language, allowing to establish a relationship of some kind between a subject and a predicate determined.
In this sense, the proposition should not be confused with the sentence by which it is expressed, since the same judgment can be expressed through different sentences, as in:
- Ana is a woman.
- Ana is not a man.
Proposition in logic
Logic studies the relationships between propositions and the reasoning mechanisms that allow us to arrive at one from another. In themselves, propositions differ from judgments, since the former propose something about reality and the latter affirm or deny something of it. That is, propositions are the logical product of judgments.
Formal logic represents propositions through letters of the alphabet, in order to study the logical connections between them abstracted from their semantic content: “if p then what”.
From this relationship, then it can be determined in which cases the content expressed is true, and in which cases it is false, through the so-called "truth tables", which assign true (V) or false (F) values to the established relationship, to study its possible outcomes.
Simple and compound statements
Logic classifies propositions into two types: simple and compound, depending on their conformation.
- Simple propositions. They are those that are composed of a subject and a predicate directly related, without factors of negation (no), conjunction (and), disjunction (or) or implication (if ... then) appear. In sentence terms, they correspond to simple sentences without subordinates. For example: "The dog is black."
- Compound propositions. They are those of a complex type, which incorporate additional elements through negation, conjunction, disjunction or implication factors, and which in sentence terms consist of sentences with subordinate and other components. For example: "If the dog is black, the dog is neither blue nor red."
Proposition in mathematics
Since mathematics is a formal language very close to logic, its approach to propositions is not too different, with the exception that it uses numbers, variables and mathematical signs to express the relationship and connections between the terms of a proposition. or of one with others. Thus, mathematical propositions also affirm or deny something, establishing a connection that can be judged as true or false.
For example, the expression 4 + 5 = 7 affirms a formal relationship between these quantities, which in this case can be considered as false, since its resolution indicates that 4 + 5 = 9. However, despite being false, it can be stated , that is, it can be proposed.
Mathematical propositions can be made more complex by incorporating variables, like equations, expressing relations of possibility and variation. For example, in the expression x = 3y + z the meanings of true or false will depend on the values we assign to the variables, although their proportion and their meaning will remain the same no matter what.