هومن محمد قربانیان

In his famous 1985 article “What the Tortoise Said to Achilles”, Lewis Carroll offers a regress that suggests we could never reach the conclusion of a deductive argument. In that story, logical rules are conditional propositions that adding them to an argument never provides enough reason to infer the conclusion. For example, when we are to use modus ponens, “if (if P then Q) and (P) then (Q)”, the rule itself does not justify us in a way that we could follow (Q) from (if P then Q) and (P) as the premises. Here, we follow a path that in Ethics is called non-cognitive moral expressivism. According to logical expressivism, logical inferences are not just mental states without any consequences, but we should consider logical facts and rules of logic as some dispositions that create capabilities for making inferences from premises. 

Methods and Material:

The method of research here is based on content analysis and logical inference. First, the main problem is established, and then I tried to apply the solution introduced in Ethics for the same problem in Logic. In the end, I concluded that disposition could serve as a good reason to reach the conclusion in arguments.

It seems as if we should have a principle that makes whoever faces an argument draw the conclusion. In the philosophy of Ethics, these principles are usually expressed by “ought”, so in logic, we should express inferential rules, such as MP, as follow:- Everyone that believes P and if P then Q ought to believes Q too.The normativity of logical rules is defended by some famous philosophers such as Wittgenstein and Ryle. Wittgenstein believes rules of inference cannot be true or false, since they are just like instructions or commands that we must follow like instructions in a handbook. What I added here is that these instructions themselves could make the mind move in a certain direction without any need for other reasons. Ryle believes that logical rules are not some sort of knowledge of facts, but actually, are “how-to-act” or knowledge of performance; in other words, we should explore the issue at hand in practical wisdom rather than theoretical wisdom. When we know a logical rule, we know how to act in a certain way, not that this knowledge is an extra premise that should be added to the argument.Boghossian suggests this idea that passing through one piece of information to another one does not need further belief to justify this move. Logical dispositions, when we try to have a valid inference, make the logical move from premises to the conclusion possible. As Wittgenstein put forward in his Philosophical Investigations, acting according to logic is like following some rules, and our knowledge about these rules is dispositional: “When I obey a rule, I do not choose. I obey the rule blindly”. In this way, logic is internally sufficient and justified. Logical internalism explains this idea as follow:- Beliefs, in their propositional form, do not motivate to act.Logical rules motivate to act according to them.
Therefore, logical rules are not beliefs in propositional form.The conclusion introduces a simple form of logical non-cognitivism that suggests knowledge of logic is not knowledge about facts, but rather logic contains norms that lead agents to infer properly.

As the result, the solution for Carroll`s puzzle suggested here is that we should consider logical principles as dispositions that guide us in our mental movements; logical principles, in this way, are not some sort of beliefs that represents facts. In articulating this solution, we use a theory in the philosophy of ethics that considers moral judgments as non-cognitive mental states. In logical non-cognitivism, logic is a handbook for deducing. Also, according to logical internalism, non-propositional rules of logic are enough to entail the conclusion and there is no need to add other premises to the argument. Logical expressivism is an approach in the epistemology of logic that regards logic as a self-sufficient knowledge and as a prerequisite for any rational activity.Basic principles and rules of logic should not be presented as descriptive propositions. The justification of inferential rules is based on their normativity. All our knowledge is not objective and descriptive, but some part of it is normative and how-to-do norms. It is clear that this picture of logic is not realistic and logical expressivism should be considered an antirealist theory and must be interpreted in this way: logic is not trying to paint a picture of the word, rather it is the precondition for any objective knowledge about the world.

The Liar Paradox is a self-reference sentence that arrives at a contradiction by reasoning about its self. Some philosophers, like Tarski, have tried to solve this paradox by using formal languages instead of natural languages. Some others consider this riddle as a problem for natural languages. The minimalist theory of truth, presented by Paul Horwich, consider truth only as a logical tool in language and not a deep concept that need philosophical reflection. According to Horwich, we can explain all the occurrences of true predicate in sentences by our natural tendency to accept the Equivalence Schema. He proposes if we eliminate the problematic and self-reference sentences from instantiations on Equivalence Schema then we can be free of the liar paradox. As I show in this article, this solution leads to a defective conception of true predicate and is inconsistent with the main idea of the minimalist theory of truth .

According to the deflationary theory of truth, to assert that a proposition is true does not add any properties to that proposition. However, most of the theories of content and meaning take the concept of truth as a fundamental semantic concept and define other semantic concepts, such as meaning, according to it. In this article, we tried to show how it is possible to substitute the verification conditions instead of the concept of truth and justify the objective and social aspect of propositions through the users of a language. Also, we tried to show how semantic properties of the logical operators could be explained according to the deflationary conception of truth. Logical operators act as connectives for complex contents and without a deflationary explanation of their rule in sentences or arguments, our survey would be incomplete. Here we explained this rule according to the syntax of formal logic and accepted the equivalence schema as a universal proposition.