Statements on the Square of Opposition

Recently I discovered a link to a device very similar to the Semiotic Square. I immediately became interested in disproving the logical device's purported logical validity.

Here is what I wrote in criticism (note especially the second paragraph):

[At Left: The Square of Opposition, which I intend to criticize, and Below: the Categorical Deduction diagram that I mean to defend].

[In reference to the Square of Opposition,] The graphical design alone is one of the simplest symbols in philosophy, logic, symbolics, and semiotics: it simply means 'modifying something', and in my view it is a rather incomplete notion of coherence. For example, if we have the categories they grant of 'None', 'All', 'Some', and 'Some not', we could add 'ambiguously some', 'ambiguously all' 'arbitrarily some' 'arbitrarily all' etc. This shows a clear pattern of incoherence in the formula, since in my view, although arbitrariness and ambiguity might apply to all cases, they are themselves in some sense, opposites. In other words, how do we know that 'some' are not 'all' by qualification, let alone whether ambiguous cases are arbitrated on the level of 'everything' versus on the level of 'nothing'? There is a deep need to find exclusion, a tool the square of opposition does not use well. Where is the logic? It is a little unfair, but I think the answer is categorical deduction, using opposites.


On the other hand [still referring to the Square of Opposition as opposed to Categorical Deduction], I can see how the diagram is inspired to create an exclusive set, it's just that it takes a kind of spiral pattern which does not easily return to its point of origin. Performing a categorical deduction on the set, we would conclude that 'Something is not nothing where everything is something' OR 'Something is not something where everything is nothing'. I'm afraid these statements do not hold up, because 1. In the first statement, it is the wrong kind of conservatism. We shouldn't need to prove everything is true to prove SOME things are true. 2. In the second case, instead of being conservative, it is the wrong type of generalization. There is no necessary connection between irrationalist statements of contradiction and the abnegation of all properties. Indeed, irrational properties may exist, under the right semantic conditions. So, the square of opposition rests on two fallacies, namely A. generic assumptions and B. A specific form of the fallacy of Affirming the Consequent. Added to this is the reality that I've virtually invented the complexity of the diagram in order to analyze it. Remember, the categorical deduction diagrams are different, even if they seem more simple, they usually involve more substantive data (i.e. opposite words), and a more coherent---perhaps the only simple and coherent----logical method.

Alternate method: Re-arranging the Square of Opposition to fit the standard of categorical deduction arguably yields the order (All, None, Not Some, Some), because the alternate order (All, None, Some, Not Some) yields trivial cases (1. Everything is nothing that is not something, and 2. Everything that is not something is not something,) , and the alternate order (All, Some, Not Some, None) does not complete a cycle, and amounts to quantification (what I call the quantification fallacy, a case in which data cannot return to itself or self-reflect, due in this case to beginning with everything and ending with nothing). Accepting the chosen order, the categorical deduction is different, but I suspect it is equally problematic due to the flawed choices. 1. Everything is nothing when something is not something, and 2. Everything is something when something is not something. Instead of being trivial, this example is purely relativistic, and in a coherent context, that doesn't hold up. The categorical deduction is neither relative, nor trivial, nor problematic, and so it must be the method that is preferred.

----Nathan Coppedge

Originally comments on Facebook.com/dimensionism

In response to the SEP: http://plato.stanford.edu/entries/square/