With a relational view of the human being, i.e. the basic condition that people always enter into relations of dependence, there is no contradiction between. This diagram shows the contradictory relationships between categorical propositions in the square of opposition of Aristotelian logic. In classical logic, a contradiction consists of a logical incompatibility between two or more. Propositions are contradictory when the truth of one implies the falsity of the other , Lastly, two propositions are said to stand in the relation of subalternation.

While they cannot both be true, they can both be false, as with the examples of "all planets are gas giants" and "no planets are gas giants.

Propositions are subcontrary when it is impossible for both to be false. Because "some lunches are free" is false, "some lunches are not free" must be true. Note, however, that it is possible for corresponding I and O propositions both to be true, as with "some nations are democracies," and "some nations are not democracies.

And Not But: Celebrating Contradiction in Relationship | HuffPost Life

Lastly, two propositions are said to stand in the relation of subalternation when the truth of the first "the superaltern" implies the truth of the second "the subaltern"but not conversely. A propositions stand in the subalternation relation with the corresponding I propositions. The truth of the A proposition "all plastics are synthetic," implies the truth of the proposition "some plastics are synthetic.

Consequently, the falsity of an I or O proposition implies the falsity of the corresponding A or E proposition, respectively. However, the truth of a particular proposition does not imply the truth of the corresponding universal proposition, nor does the falsity of an universal proposition carry downwards to the respective particular propositions. The presupposition, mentioned above, that all categories contain at least one thing, has been abandoned by most later logicians.

Modern logic deals with uninstantiated terms such as "unicorn" and "ether flow" the same as it does other terms such as "apple" and "orangutan".

When dealing with "empty categories", the relations of being contrary, being subcontrary and of subalternation no longer hold. S1 and S2 are assigned from these classes.

This also applies to the primitive formulas. Thus by definition our formula is not a tautology. Post observed that, if the system were inconsistent, a deduction in it that is, the last formula in a sequence of formulas derived from the tautologies could ultimately yield S itself. As an assignment to variable S can come from either class K1 or K2, the deduction violates the inheritance characteristic of tautology, i.

From this, Post was able to derive the following definition of inconsistency without the use of the notion of contradiction: A system will be said to be inconsistent if it yields the assertion of the unmodified variable p [S in the Newman and Nagel examples].

In other words, the notion of "contradiction" can be dispensed when constructing a proof of consistency; what replaces it is the notion of "mutually exclusive and exhaustive" classes.

An axiomatic system need not include the notion of "contradiction". Some dialetheistsincluding Graham Priesthave argued that coherence may not require consistency.

Square of Opposition

Contributors control their own work and posted freely to our site. If you need to flag this entry as abusive, send us an email. Nature abhors a vacuum, or so they say. Similarly, human beings abhor contradiction, particularly in the context of relationships.