MODUS PUTTING PONENS: EXPLANATION AND EXAMPLES - PHILOSOPHY - 2024

The modus ponendo ponens 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 guideline that is transmitted in propositional logic and is directly related to conditional arguments.

The argument modus ponendo ponens can be seen as a two-legged syllogism, which instead of using a third term that serves as a link, rather uses a conditional sentence with which it relates the antecedent element with the consequent element.

Aristotle, father of philosophical logic

Leaving conventionalisms, we can see the modus ponendo ponens as a procedure (modus) of the deduction rules, which through the assertion (putting) of an antecedent or reference (a previous element), manages to assert (ponens) 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 de Estagira, from the 4th century BC. C.

Aristotle proposed with the modus ponens -as it is also called- 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, product of his interaction with the environment.

Etymology

The modus ponendo 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 consists of two elements (an antecedent and a consequent) affirmative in its structuring.

Explanation

In general terms, the modus ponendo ponens correlates two propositions: a conditioning antecedent called "P" and a conditioned consequent called "Q".

It is important that premise 1 always has the conditioning form "if-then"; the "if" is prior to the antecedent, and the "then" is prior to 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 the exam tomorrow, 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 must take that path."

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 should go shopping at the market."

Premise 2: "You want to eat fish."

Conclusive: "Therefore, you must go buy in the market"

Variants and examples

The modus ponendo ponens 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 reach your ideal 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 won't be able to control your hypertension."

Premise 2: "You keep eating so much salt."

Conclusion: "Therefore, you will not be able to control hypertension."

Third example

Premise 1: "If you are aware of the road, then you will not get lost."

Premise 2: "You are watching the road."

Conclusion: "Therefore, you will not get lost."

Variant 2

Premise 1: If “P” ^ “R” then “Q”

Premise 2: “P” ^

Conclusion: "Q"

In this case, the symbol "^" refers to the copulative conjunction "and", while the "R" comes to represent another antecedent that is added to validate "Q". That is, we are in the presence of a double conditioner.

First example

Premise 1: "If you come home and bring some popcorn, then we'll see a movie."

Premise 2: "You come home and bring popcorn."

Conclusion: "Therefore, we will see 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 watching 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 taking care of 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 did not study vowel concurrences, then you will fail the linguistics test."

Premise 2: "You did not study vowel concurrences."

Conclusion: "Therefore, you will fail the linguistics test."

Second example

Premise 1: "If you don't feed your parrot, then it will die."

Premise 2: "You don't give your parrot food."

Conclusion: "Therefore, he will die."

Third example

Premise 1: "If you don't drink water, then you will become 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 "^" refers 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 practicing swimming, then you will improve your physical resistance and lose weight."

Premise 2: "You are swimming."

Conclusion: "Therefore, you will improve your physical resistance and lose weight."

Third example

Premise 1: "If you have read this article in Lifeder, then you have learned and are more prepared."

Premise 2: "You have read this article in Lifeder."

Conclusion: "Therefore, you have learned and are more prepared."

The modus ponens represents the first rule of propositional logic. It is a concept that, starting from simple premises 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 of producing deductive evidence.

By removing a sentence from the conclusions, the modus ponens avoids the extensive agglutination and concatenation of elements when making deductions. For this quality it is also called "rule of separation".

The modus ponendo ponens is an indispensable resource for a full knowledge of Aristotelian logic.

References

1. Ferrater Mora, J. (1969). Dictionary of Philosophy. Buenos Aires: Hispanoteca. Recovered from: hispanoteca.eu.
2. Modus putting ponies. (S. f.). Spain: Webnode. Recovered from: laws-de-inferencia5.webnode.es.
3. Modus putting ponies. (S. f.). (n / a): Wikipedia. Recovered from: wikipedia.org.
4. Rules of inference and equivalence. (S. f.). Mexico: UPAV. Recovered from: universidadupav.edu.mx.
5. Mazón, R. (2015). Putting ponies. Mexico: Super Mileto. Recovered from: supermileto.blogspot.com.