# modus ponens



## TETRAKTYS

hi

mi nature languaje is spanish, so excuse me if my english is not nice


what does it mean in latin the prahse or words?:  modus ponens

i found it in a phrase that says: " .... that is behind the "modus ponens..."


greetings


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## Stoicorum_simia

It's a term in logic, for the type of argument 'If p, then q; p; therefore q'. (Maybe logicians could finesse that?) Short for _modus ponendo ponens_, 'method which lays down (=asserts) by laying down'.


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## JLicharson

In English, this sort of argument is often called a 'tautology', i.e., an argument that depends on at least one of its own suppositions.


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## Stoicorum_simia

JLicharson said:


> In English, this sort of argument is often called a 'tautology', i.e., an argument that depends on at least one of its own suppositions.


That may be so in logic, but it should be noted that tautology has another and commoner meaning, which is repetition of the same point or definition in different language. In which sense it is somewhat derogatory, which is not the case with the usage in logic I suppose.


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## Forero

Context would help work out what the intended meaning is, but essentially _modus _(_ponendo_)_ ponens_ reaches the conclusion that a certain thing is true from the knowledge that something else is true under the assumption that the latter thing invariably implies the former.

For example, if we can assume that all red apples are ripe, then any time we encounter a red apple, we can conclude (from that assumption and knowledge of that encounter) that we have found a ripe apple.

I would guess that what is referred to as "behind the _modus ponens_" is some assumption about an inevitable conclusion.


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## brian

La traducción en español sería: _modo que afirmando afirma._ (Si P entonces Q; P. Entonces Q.)

P.S. En este foro se puede escribir en cualquiera lengua, inclusive el español.


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## berndf

In classical logic, a deduction is valid only if it can be reduced to an established deduction rule or syllogism. In this respect the modus ponens is not a tautology but a rule to establish tautologies. Modern propositional logic defined tautologies via truth tables and syllogisms have lost their paramount importance in logic.

For the most basic syllogisms in propositional logic (in predicate logic you have more) you have a complex premise (a theorem) and an atomic premise. The latter can be either affirmative (_ponendo_) or negating (_tollendo_) arriving at a positive (ponens) or a negative (tollens) conclusion. Hence you have four basic syllogisms:
_Modus ponendo ponens_: If A then B; A; hence B.
_Modus ponendo tollens_: Not both A and B; A; hence not-B. 
_Modus tollendo ponens_: A or B; not-B; hence A.
_Modus tollendo tollens_: If A then B; not-B; hence not-A.

The most important of the four are the _modus ponendo ponens_ and the _modus tollendo tollens_ which are often shortened to _modus ponens_ and _modus tollens_ respectively.

Concerning the grammar of _modus ponendo ponens_: It means _[the] mode [which is] out-of-affirming affirming _where _ponendo_ is an ablative gerund and _ponens_ a nominative present participle.


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## Outsider

These terms from classical logic are usually left in Latin, in Spanish too.  _Modus ponendo ponens._


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