por what is the modus putting ponens?
He modus putting ponens It is a type of logical argument, of reasoned inference, belonging to the formal system of deduction rules of the well-known propositional logic. This argumentative structure is the initial pattern that is transmitted in propositional logic and is directly related to conditional arguments.
The argument modus putting ponens It can be seen as a two-legged syllogism, which instead of using a third term that serves as a link, rather uses a conditional statement with which it relates the antecedent element to the consequent element.
Leaving conventionalisms, we can see the modus putting ponens as a procedure (modus) of the rules of deduction, that by means of the assertion (putting) of an antecedent or reference (a previous element), manages to assert (you put) to a consequent or conclusion (a later element).
This reasonable formulation starts from two propositions or premises. It seeks to be able to deduce through these a conclusion that, despite being implicit and conditioned within the argument, requires a double affirmation —both of the term that precedes it and of itself— in order to be considered a consequent.
origins
This affirmative mode, as part of the application of deductive logic, has its origins in antiquity. It appeared from the hand of the Greek philosopher Aristotle of Stagira, from the 4th century BC. c.
Aristotle raised with the modus ponens —as it is also called— to obtain a reasoned conclusion through the validation of both a precedent and a consequent in a premise. In this process, the antecedent is eliminated, leaving only the consequent.
The Hellenic thinker wanted to lay the foundations of descriptive logical reasoning in order to explain and conceptualize all the phenomena close to the existence of man, the product of his interaction with the environment.
Etymology
He modus putting ponens has its roots in Latin. In the Spanish language its meaning is: «a method that affirming (asserting), affirms (asserts)», because, as previously stated, it is made up of two elements (an antecedent and a consequent) affirmative in its structure.
Explanation
Generally speaking, the modus putting ponens correlates two propositions: a conditioning antecedent called «P» and a conditioned consequent called «Q».
It is important that premise 1 always has the conditional form “if-then”; the «if» goes before the antecedent, and the «then» goes before the consequent.
Its formulation is as follows:
Premise 1: If «P» then «Q».
Premise 2: «P».
Conclusion: “Q”.
examples
First example
Premise 1: «If you want to pass tomorrow’s exam, then you must study hard.»
Premise 2: «You want to pass the exam tomorrow.»
Conclusive: «Therefore, you must study hard.»
second example
Premise 1: «If you want to get to school fast, then you should take that road.»
Premise 2: «You want to get to school fast.»
Conclusive: «Therefore, you must take that path.»
third example
Premise 1: “If you want to eat fish, then you must go buy in the market”.
Premise 2: “You want to eat fish”.
Conclusive: «Therefore, you must go buy in the market.»
Variants and examples
He modus putting ponens It may present small variations in its formulation. The four most common variants with their respective examples will be presented below.
variant 1
Premise 1: If “P” then “¬Q”.
Premise 2: «P».
Conclusion: “¬Q”.
In this case the symbol “¬” resembles the negation of “Q”.
First example
Premise 1: «If you keep eating that way, then you won’t achieve your goal weight.»
Premise 2: «You keep eating that way.»
Conclusion: «Therefore, you will not achieve your ideal weight.»
second example
Premise 1: «If you keep eating so much salt, then you will not manage to control hypertension.»
Premise 2: «You keep eating so much salt.»
Conclusion: «Therefore, you will not manage to control hypertension.»
third example
Premise 1: “If you are aware of the path, then you will not get lost”.
Premise 2: «You are aware of the path.»
Conclusion: «Therefore, you will not be lost.»
Variant 2
Premise 1: If “P”^“R” then “Q”.
Premise 2: “P”^.
Conclusion: “Q”.
In this case, the symbol «^» alludes to the copulative conjunction «y», while the «R» comes to represent another antecedent that is added to validate «Q». That is, we are in the presence of a double condition.
First example
Premise 1: «If you come home and bring popcorn, then we will watch a movie.»
Premise 2: «You come home and bring popcorn.»
Conclusion: «Therefore, we will watch a movie.»
second example
Premise 1: «If you drive drunk and looking at your cell phone, then you will crash.»
Premise 2: «You drive drunk and looking at your cell phone.»
Conclusion: «Therefore, you will crash.»
third example
Premise 1: «If you drink coffee and eat chocolate, then you are taking care of your heart.»
Premise 2: «You drink coffee and eat chocolate.»
Conclusion: «Therefore, you are guarding your heart.»
Variant 3
Premise 1: If “¬P” then “Q”
Premise 2: “¬P”
Conclusion: «Q»
In this case the symbol “¬” resembles the negation of “P”.
First example
Premise 1: «If you didn’t study vowel concurrencies, then you will fail the linguistics exam.»
Premise 2: «You did not study vowel concurrences.»
Conclusion: «Therefore, you will fail the linguistics exam.»
second example
Premise 1: «If you don’t give your parrot food, then it will die.»
Premise 2: «You do not give food to your parrot.»
Conclusion: «Therefore, he will die.»
third example
Premise 1: «If you don’t drink water, then you will get dehydrated.»
Premise 2: «You don’t drink water.»
Conclusion: «Therefore, you will become dehydrated.»
Variant 4
Premise 1: If “P” then “Q”^“R”
Premise 2: “P”
Conclusion: “Q”^“R”.
In this case, the symbol «^» alludes to the copulative conjunction «and», while the «R» represents a second consequent in the proposition; therefore, an antecedent will be affirming two consequents at the same time.
First example
Premise 1: «If you were good to your mother, then your father will bring you a guitar and its strings.»
Premise 2: «You were good to your mother.»
Conclusion: «Therefore, your father will bring you a guitar and its strings.»
second example
Premise 1: «If you are swimming, then you will improve your physical resistance and lose weight.»
Premise 2: «You are practicing swimming.»
Conclusion: «Therefore, you will improve your physical resistance and lose weight.»
third example
Premise 1: “If you have read this article in Lifer, then you have learned and are more prepared”.
Premise 2: «You have read this article in Lifer.»
Conclusion: «Therefore, you have learned and are more prepared.»
modus ponensa path to logic
He modus ponens represents the first rule of propositional logic. It is a concept that, based on premises that are simple to understand, opens the understanding to deeper reasoning.
Despite being one of the most used resources in the world of logic, it cannot be confused with a logical law; it is simply a method for the elaboration of deductive evidence.
By removing a judgment from the conclusions, the modus ponens Avoid agglutination and extensive concatenation of elements when making deductions. For this quality it is also called «separation rule».
He modus putting ponens It is an indispensable resource for the full knowledge of Aristotelian logic.