La intertextualidad y la semiótica social

So far we have pointed out that Russell and Cotnoir have slightly different presuppositions when it comes to what they take logic to be. But what about the epistemology of logic? Here, prima facie both authors do not have to take clear stances. After all, logical as well as formalizability nihilism are concerned with the very possibility of logic itself and not with our knowledge of it. However, in the following, I will draw some skeptical ideas from the discussion of both versions of nihilism above: Even though the arguments of both Cotnoir and Russell did not establish their respective version of nihilism we might have to accept some skeptical lessons from their ideas.

We concluded the section on Russell’s nihilism with an open issue: I have argued against Russell’s motivation for universalism and, especially, her alleged counterexamples to our most basic laws. However, it is not clear at all where the boundary between models that pick out cases and models that do not lays. So, even if the possibility of logical nihilism by means of Russell’s monstrous models is blocked there is still an issue of logical skepticism, i.e. if we are not able to determine the set of cases then we cannot know the extension of our logical consequence relation. The only thing we might have

3.3. AND HOW CAN WE KNOW OF IT?

established is that conjunction elimination and the law of identity should be covered by this relation. Thus, Russell’s argument for nihilism can be rather seen as an expression of this form of skepticism: If we want to have more laws of logic then we have to find some criterion by which we can determine the set of cases.7 _{One could take some of the}

arguments presented by Etchemendy (1990) as a predecessor of this form of skepticism: the semantic definition of logical consequence does not tell us by itself what the laws of logic are since, as Tarski already realized, it does not fix the set of cases. Thus, the semantic definition does not provide us with firm grounds to decide disputes about which logical laws are valid in full generality. To conclude, I would like to point out that this general lesson is in line with other works by Russell (2014; 2015; 2018) which are, rather, concerned with the epistemology of logic. This open end of our discussion of nihilism can be seen as one of the central question of her writings in this area.

Cotnoir poses his formalizability nihilism as an answer to certain troubles of the philos- ophy of language. As he puts it, there are a lot of troubles which we run into when trying to give a formal account of natural language consequence. Since these problems are so overwhelming there are abductive grounds to accept formalizability nihilism as a unified solution to all of these problems. I think the last chapter has shown in how far this idea is misguided: Cotnoir’s diagnosis that it is our attempt of formalization that produces these problems gets it wrong. However, just as in the case of Russell’s nihilism one can easily make a transition towards seeing Cotnoir’s original motivation as a basis for skepticism with regards to logic: the vast mass of problems which we run into in our logical inquiries makes a positive outlook quite implausible. My argumentation of the second chapter has merely provided grounds to believe that this is not an issue of formalization. Cotnoir’s negative meta-induction, however, stands as it is: If we share his negative outlook on the debates on the semantic paradoxes, universal quantification or vagueness then we should also accepts his pessimism. Thus, one could say that even though Cotnoir’s and Russell’s nihilisms are quite different, they are still in alignment with respect to the skeptical up- shots which I have made out in their position: Our attempts to give an account of logical consequence have failed since no satisfying answer to the different paradoxes is at hand.

Last, it makes sense to point towards the difference between these two skeptical lines of thought: Russell points towards the general inconclusive reasons we have when we are only considering the semantic definition of logical consequence. Cotnoir, on the other hand, takes other reasons into consideration: The “correct logic” is the one that does not fall into the numerous paradoxes and problems which he draws attention to. These consideration, however, lead to a negative result: There does not seem to be a satisfying answer to these issues. Further, one could bring the two versions of skepticism into a

7_{One could take this as the general lesson which Russell intends with her “nihilism”. After all, she}

says that even if her monstrous models are too outrageous to be accepted some minimal logic that would survive the collapse arguments against logical pluralism would not be satisfying on its own.

3.3. AND HOW CAN WE KNOW OF IT?

common story: If we try to give further arguments to determine which logic is the correct one, i.e. answering the russellian skepticism, we will probably draw attention to the paradoxes and problems to discern different logics from each other. Then, however, we should at some point be facing cotnoirian skepticism since no account presents a satisfying answer to the paradoxes.