WHAT IS LOGICAL TRUTH?
Logical truth is a concept in logic and philosophy that refers to statements or propositions that are true solely based on their logical structure, regardless of the content or subject matter. In other words, a logical truth is true because of the relationships and rules that govern its logical form, and it would remain true under any interpretation or substitution of its terms.
An example of a logical truth is the law of identity, which states that “A is A,” where “A” represents any entity or proposition. This statement is true regardless of the specific content of “A,” as it simply asserts that something is identical to itself. Another example is the tautology “A or not-A,” which means that either a proposition “A” is true, or its negation “not-A” is true. This statement is true under all possible interpretations of “A.”
Logical truths are often contrasted with empirical truths, which are true based on observation and experience rather than their logical structure. Empirical truths can be subject to change as new evidence becomes available, whereas logical truths are considered universally and necessarily true because of their logical form.
In formal logic, logical truths can be demonstrated using a system of symbolic notation and rules of inference, such as propositional logic or predicate logic. These systems provide a rigorous framework for understanding and analyzing the logical structure of statements and arguments.
How logical truth and logic in general relates to the concept of necessary existence of non-nothingness?
The relationship between logical truth, logic in general, and the concept of necessary existence of non-nothingness can be explored from several perspectives.
One argument is that the principles of logic, such as the law of non-contradiction and the law of identity, are necessary truths that follow from the existence of non-nothingness. The law of non-contradiction, for example, holds that something cannot both be and not be at the same time and in the same respect. This principle is seen as a necessary truth because it is impossible to conceive of a situation in which something both is and is not at the same time and in the same respect.
Similarly, the law of identity holds that something is identical to itself. This principle is also seen as a necessary truth because it is impossible to conceive of a situation in which something is not identical to itself.
The principle of non-contradiction: One of the most fundamental logical truths is the principle of non-contradiction, which states that a proposition and its negation cannot both be true at the same time and in the same respect. This principle is often invoked when discussing the concept of necessary existence of non-nothingness. Since the idea of absolute nothingness is self-contradictory, the necessary existence of non-nothingness is posited to avoid this contradiction.
Logical necessity: Logical truth and necessity are closely related concepts. A logical truth is a statement that is true in all possible worlds or interpretations solely based on its logical form. Similarly, when discussing the necessary existence of non-nothingness, we are considering a form of metaphysical necessity, which means that non-nothingness must exist in all possible worlds to avoid the contradiction of absolute nothingness. The concept of necessity thus links logical truth and the necessary existence of non-nothingness.