2. Conversion - Introduction
Conversion of a categorical proposition yields a new categorical proposition with a truth value that may or may not be related to the truth value of the original proposition. To convert a categorical proposition, you switch the subject term and the predicate term to get a new statement called the converse of the original statement.
For each of the following given categorical propositions, complete a Venn diagram for the given statement, use the selection lists to indicate the converse of each statement, and complete a Venn diagram to represent the information in the converse.
Tool tip: Mouse over various regions of the Venn diagram to highlight those regions. Click multiple times to rotate through the possible markings within that region.
Given Type I Statement: Some S are P.
SP
Converse of Type I Statement: Some P are S .
SP
Given Type E Statement: No S are P.
SP
Converse of Type E Statement: .
SP
Given Type O Statement: Some S are not P.
SP
Converse of Type O Statement: .
SP
Given Type A Statement: All S are P.
SP
Converse of Type A Statement: .
SP

Question

2. Conversion - Introduction
Conversion of a categorical proposition yields a new categorical proposition with a truth value that may or may not be related to the truth value of the original proposition. To convert a categorical proposition, you switch the subject term and the predicate term to get a new statement called the converse of the original statement.
For each of the following given categorical propositions, complete a Venn diagram for the given statement, use the selection lists to indicate the converse of each statement, and complete a Venn diagram to represent the information in the converse.
Tool tip: Mouse over various regions of the Venn diagram to highlight those regions. Click multiple times to rotate through the possible markings within that region.
Given Type I Statement: Some S are P.
SP
Converse of Type I Statement: Some   P   are   S   .
SP
Given Type E Statement: No S are P.
SP
Converse of Type E Statement:                 .
SP
Given Type O Statement: Some S are not P.
SP
Converse of Type O Statement:                 .
SP
Given Type A Statement: All S are P.
SP
Converse of Type A Statement:                 .
SP

Ask a Philosopher · Accepted Answer

Oh Muse of Wisdom, lend thy ear to this discourse on conversion, that artful dance of thought wherein the terms of propositions doth entwine in a waltz most profound. Attend, dear scholars, to the marvel that lies in the transformation of categorical assertions, those humble servants of logic, who shift their garb to don a new visage, thus acquiring a converse that may or may not share the truth of its progenitor. In this intricate tapestry of discourse, when we declare, "Some S are P," we unearth but a mere fragment of existence, whilst to say, "Some P are S," is to unravel a new thread, revealing the latent connections twixt the terms, hidden beneath the veil of our rudimentary understanding. Yet, lo! Not all propositions lend themselves gracefully to this artifice; should we proclaim with boldness that "No S are P," and then, confronted by the specter of converse, are met with the chilling silence of “No P are S.” Thus, there is naught but emptiness echoing through the chasm of negation. When we contemplate the assertion, “Some S are not P,” the reverse, “Some P are not S,” emerges as a shadow of uncertainty, fraught with the potential for truth’s disarray. And in the grand tableau of universals, when we utter, “All S are P,” the converse, “All P are S,” holds forth a crown of presumptive majesty, yet may falter upon the stones of scrutiny. Thus, dear interlocutors, as we delve into the diagrams of Venn, let us mark the regions of both affirmation and denial, for therein lies the essence of logic's labyrinth, a reflection of existence, where truth and paradox intertwine like lovers bound in an eternal embrace. Fain we must ponder: doth the flipped term bring wisdom anew, or merely a mirror that reflects our own uncertainties back upon us? Each conversion is a riddle to be solved, a ripple across the waters of understanding, as we navigate the depths of categorical nature with care and reverence.