converse
→ “围着灶台转”，“话题围绕着……展开”
converse (adj.)
"turned about, transposed, reciprocal," 1560s, originally mathematical, from Latin conversus "turned around," past participle of convertere "to turn about, turn around, transform," from assimilated form of com "with, together" + vertere "to turn" (from PIE root *wer- "to turn, bend"). From 1794 as "opposite or contrary in direction." Related: Conversely.
converse (n.1)
1550s, originally in mathematics, from converse (adj.). From 1786 as "thing or action that is the exact opposite of another." As an example, Century Dictionary gives "the hollows in a mold in which a medal has been cast are the converse of the parts of the medal in relief." Chaucer [乔叟] has in convers, apparently meaning "on the other side."
converse (v.)
from Latin conversari "to live, dwell, live with, keep company with," passive voice of conversare, literally "to turn round with."
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of the original statement.
Let S be a statement of the form P implies Q (P → Q). Then the converse of S is the statement Q implies P (Q → P). In general, the truth of S says nothing about the truth of its converse, unless the antecedent P and the consequent Q are logically equivalent.
For example, consider the true statement "If I am a human, then I am mortal." The converse of that statement is "If I am mortal, then I am a human," which is not necessarily true.
On the other hand, the converse of a statement with mutually inclusive terms remains true, given the truth of the original proposition. This is equivalent to saying that the converse of a definition is true. Thus, the statement "If I am a triangle, then I am a three-sided polygon" is logically equivalent to "If I am a three-sided polygon, then I am a triangle", because the definition of "triangle" is "three-sided polygon".
Going from a statement to its converse is the fallacy of affirming the consequent. However, if the statement S and its converse are equivalent (i.e., P is true if and only if Q is also true), then affirming the consequent will be valid.
Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dark,") and invalidly inferring its converse ("The room is dark, so the lamp is broken,") even though the converse may not be true. This arises when a consequent ("the room would be dark") has more than one other possible antecedents (for example, "the lamp is not plugged in" or "the lamp is in working order, but is switched off").
Converse errors are common in everyday thinking and communication and can result from, among other causes, communication issues, misconceptions about logic, and failure to consider other causes.
The opposite statement, denying the consequent, is a valid form of argument. In propositional logic, modus tollens (/ˈmoʊdəs ˈtɒlɛnz/) (MT), also known as modus tollendo tollens (Latin for "mode that by denying denies") and denying the consequent, is a deductive argument form and a rule of inference. Modus tollens takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
六级/考研单词: converse, reciprocal, mathematics, assimilate, contrary, dictionary, hollow, mold, medal, dwell, passive, literal, logic, reverse, constituent, implicit, equivalent, mortal, mutual, thereby, triangle, affirm, valid, confuse, necessity, infer, plug, issue, deduce, negate
浙公网安备 33010602011771号
