Philosophy
Asadollah Fallahi
Abstract
Recently, Morteza Hajhosseini (2023) published his second edition of the book (2017) Two Non-Classical Logic Systems, A new Outlook on Elements of Logic, where he developed various non-standard logical systems based on specific philosophical foundations. His systems consist of the following five:
A ...
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Recently, Morteza Hajhosseini (2023) published his second edition of the book (2017) Two Non-Classical Logic Systems, A new Outlook on Elements of Logic, where he developed various non-standard logical systems based on specific philosophical foundations. His systems consist of the following five:
A truth-functional propositional system,
A non-truth-functional propositional system,
Adding the non-truth-functional implication of the second system to the whole first one,
Adding the truth-functional conjunction and disjunction of the first system to the whole second one,
Combining the whole two systems into a new comprehensive propositional.
In other papers, I reported extensively Hajhosseini’s logical systems and criticized them from a formal point of view only (Fallahi 2023a, 2023b, 2023c, 2023d). In a fifth paper, I regarded historical aspects of Hajhosseini’s logical systems and his claims of innovation (Fallahi 2023e). In the sixth paper, I delved into his epistemological incentives and showed that he confused logical and epistemological purposes (Fallahi 2023f). In this paper, eventually, I seek to criticize the philosophical foundations for Hajhosseini’s logical systems.
Some of the philosophical foundations of these logical systems are mentioned with some brief descriptions as follows:
Axioms and postulates are different.
What is to be used in logic are the axioms, not the postulates.
According to Hajhosseini, axioms and postulates are different from each other, and it is axioms that are useful for logic, not postulates; therefore, logical systems should have axioms and not postulates. I show that the traditional distinction between axioms and postulates is an epistemological one and is not useful for logic.
Hajhosseini considered postulates also to be different from logical truths and theorems. Although the difference of axioms/postulates with respect to theorems can be accepted in a way, the difference of axioms/postulates with respect to logical truths is not very acceptable because the axioms/postulates are true in all models and a fortiori, they are to be considered logical truths.
Also, Hajhosseini’s arguments that axioms cannot be deduced from other theorems are epistemological arguments and not logical ones. Also, Hajhosseini’s claim that the axioms are not even based on themselves is a claim that conflicts with some of Hajhosseini’s other words. Also, his claim that adding axioms or inconsistent propositions does not make arguments incorrect or invalid is in conflict with the definitions of "correctness" and "validity" in the book.
It is impossible to infer a formula and its negation from the same premises.
Hajhosseini’s arguments that impossible premises do not entail a proposition as well as its negation are epistemological arguments and not logical ones.
A contrafactual conditional is actually a bi-conditional.
Hajhosseini uses his logical systems to explain contrafactual conditional, but what I understand from his explanations, it seems to me that he interprets them as biconditionals. However, interpreting the counterfactual conditional as a biconditional is not consistent with the commonplace counterfactual conditional examples.
Many well-formed formulas in mathematical logic are not meaningful.
Hajhosseini claims sentences such as “if I am typing then two is even”, although well-formed in modern logic, are meaningless. It should be noted that the well-formed formulas of the language of the modern logics (both classical and non-classical) are all meaningful. The most that can be said about them is that some of them are very complicated or (very) false, but complicatedness—or even falsehood—does not mean meaningless. Also, some of these complex formulas are not logical theorems or logical truths, but some of them are even contradictory to logical theorems and therefore are logical falsehoods, but these do not mean nonsense.
The antecedent and consequent of a conditional must be consistent.
This is familiar under the name “Boethius rule” in the history of logic, which Hajhosseini named it “Hajhosseini's rule”. I think it is generally incorrect and must be conditioned by "consistency of the antecedent", otherwise it conflicts with numerous examples of conditionals whose antecedent and consequent are incompatible.
Natural intuition (= our innate intuition of natural language) is the only (or the most important) criterion for evaluating logics.
Hajhosseini has claimed in many places that his systems agree with intuition; and as a result, the existing classical and non-classical logics are all counter-intuitive. I show that the concept of "intuitiveness" is not so simple and accessible that he claims for himself with such intensity and severity and with this abundance and denial for others. I put forth the possibility that perhaps the logical concepts used (including, the concept of "implication" and "inference") are fundamentally vague and indeterminate, and the intuitions of classical and non-classical logicians, including Hajhosseini himself, are a kind of conventional but unconscious precision and not Intuition in the strict sense of the word. Despite such a possibility, one should be much more cautious in using the word "intuitive".
Classical logic assumes that “rationality” is included in “extensionality”.
Hajhosseini claims that the classical logic intentional or non-truth-functional languages are rational ones. I show that this philosophical premise of "confining “rationality” in “extensionality”" has not been well explained in the book and has not been referred to the sources in classical logicians’ works.
Implication must be explained by causation.
Contrary to this, I show that the analysis of the metaphysical issue of "causation" has nothing to do with the logical issue of "implication" and the two should not be compared. For example, circularity is impossible in "causation" but possible in "implication". Of course, when metaphysical causation is established, logical implication is also established, but the opposite is not true because every proposition implies itself, but it is not its own cause. Also, the implication can be symmetric but causation is not.
Traditional logic as a source of inspiration.
Hajhosseini often refers to traditional logic as if it were his source of inspiration. But it is debatable because the difference between the viewpoints of traditional logicians is so wide and surprising that without extensive familiarity with the history of traditional logic, it is impossible to understand that most of the objections of the new logic to the traditional logic were already raised in the traditional logic itself.
