ARVINDUS

Contemplationam

Self-Reflexivity

SELF-REFLEXIVITY

In this short contemplation we shall go deeper into the concept of self-reflexivity.

Self-reflexivity can be understood as a self-relation. It occurs when a certain given relates to itself. Self-reflexive explications say for instance something about themselves. In Western philosophy this is often seen as problematic because such explications lead to paradoxes, circle reasonings or endless regressions. Sometimes does a self-reflexive explication lead to a paradox. A paradox is an apparent contradiction. Self-reflexive explications can contradict themselves. Take for instance the explication ‘this explication is false’. When this explication is true then it is true that it is false. But if the explication is false then it is true. So with both truth values is the conclusion contradictory to the proposition. Therefore it is paradoxal. Another example is the explication ‘this explication is true’. If this explication is true then it is true and when it is false then it is false. This explication is not paradoxal. However with both truth values is the conclusion equal to the proposition. And this can be considered as a direct circle reasoning. With indirect circle reasonings is the conclusion also equal to the proposition but are between those two still other explications found. This is here not the case and thus regards the aforementioned explication a direct circle reasoning.

To avoid paradoxes and circle reasonings a level differentiation can be applied. In a level differentiation is differentiated between the levels of proposition and of conclusion. The proposition is then put as subject and the conclusion as attribute. For those that are known with the language of logic it can be indicated that ‘e∧¬e’ is absurd but that ‘e∧Ne’ is not absurd. Let us for clarity give an overview as in figure 1.

  Unilevel Multilevel
Proposition Conclulsion Proposition Conclulsion
Paradox Subject This explication is false This explication is true This explication is false  
Attribute   This explication is true
Circle reasoning Subject This explication is true This explication is true This explication is true  
Attribute   This explication is true

Figure 1.

In figure 1 we see how with the paradox on unilevel (one applied level) the explication ‘this explication is false’ as proposition is on the same level contradictory to the explication ‘this explication is true’ as conclusion. However on multilevel (multiple applied levels) is the explication as proposition not contradictory to the explication as conclusion. In this way a paradox is avoided. And in the same way is also a direct circle reasoning avoided with the explication ‘this explication is true’.

The above level differentiation that can avoid paradoxes and circle reasonings does lead however to another problem, namely that of the endless regression. For an explication as conclusion can equally do service as a proposition. And under that proposition then another conclusion is placed, which on its turn can do service as a proposition, and so forth into eternity. The only solution for the above problems lets itself be known in alterity. By simply not relating an explication to itself but to something else are the above mentioned problems easily avoided.