Venn Diagrams and the Modern Square of Opposition

Held that universal propositions about existing things have existential import- open to existence-only differs from Boole in A and E propositions -particular propositions make a positive assertion about existence

Held that universal propositions about existing things have NO existential import-closed to existence-particular propositions make a positive assertion about existence All S are P= no members of S are outside PNo S are P= no members of S are inside PSome S are P= at least one S exists, and that S is a PSome S are not P= at least one S exists, and that S is NOT a P

-has exactly 2 terms -left circle represents subject term, right circle denotes predicate term

Shading and Xs are used-shading an area means that particular area is empty shading always used in A and E propositions- placing an X means at least one thing exists in that area X always used in I and O propositions

Asserts no member of S is outside P- represented in a venn diagram by shading all of the S area that lies outside of P circle-says nothing about existence since no X exists

Asserts no members of S are inside P-represented by shading S circle that lies inside P circle-says nothing about existence since no X exists

Asserts that at least one S exists and and that S is also P- represented by placing an X in area where S and P circles overlap X represents an existing thing that is both an S and P

Asserts that at least one S exists and that S is NOT a P- represented by placing an X in part of S circle that lies outside the P circle-X represents an existing thing that is an S but not a P

Represents contradictory pairs of 4 different types of categorical propositions according to BooleA-O are contradictory relation statements - will have opposite truth values (if A is said to be true it follows that O will be false) E-I are contradictory relation statements -will have opposite truth values

-Given the truth value of an A-O proposition nothing can be concluded of E-I (E-I not necessarily true of false)
- Given truth value of E-I proposition nothing can be concluded of A-O.

An argument having a single premiseex. assume O premise true- compute truth value of corresponding A proposition - by contradictory relations A is false- this would make conclusion true and argument valid

According to Boole, an argument that is valid is considered unconditionally valid because they are valid regardless of whether terms refer to existing things

Statements having this form are equivalent to the statement "All S are P" is FALSE

If an A proposition exists with an E proposition - E has undetermined truth value because nothing can be concluded about E from A- This being the case makes the conclusion invalid

Using letters to represent the terms draw a diagram for premise and conclusion. (one for each)- If information expressed by conclusion diagram is contained in premise diagram it is said to be VALID- If NOT, it is INVALID