Logic And Ontology

In today’s time, logic is the study of formally valid inferences. An argument is formally valid if the conclusion necessarily follows from its premises. Logic is the study of truth, in this case, formal truth, which is concerned with the preservation of truth value. Logic does not concern itself with material truths because the latter is considered to be the domain of empirical sciences, and thinking by itself does not advance our knowledge of the world.

Logic abstracts from all content and considers the form of thinking alone. This does not necessarily mean that logic is a part of psychology because empirical psychology does not inform us about the nature of thinking itself. So logic à la Frege considers thoughts to be objective but not in the sense that they can be found within the spatio-temporal world like a tree or a chair. Thoughts are objective because different people can have the same thought. Modern logic, however, brackets the question of the ontology of thoughts. It takes expressions of a language, specifies their logical form in a mathematical formula language, and establishes relations of derivability or logical consequence. Its formal results can be valid whether we subsequently interpret the expressions as representing Fregean thoughts, propositions of some other kind, or contents explained through linguistic and inferential practices.

So, if the philosophical question is what it is that we understand when we understand an expression in a language, then modern logic does not raise, much less try to answer that question. Philosophers in the analytical stream do consider the question; some take the content of thinking to be propositions, some analyze propositions in terms of possible worlds, and others use an inferential-role semantics. But strictly, this is not what modern formal logic is concerned with. The question is nevertheless important if we need to understand what ‘understanding’ is and what it is that is understood. Logic then has become a formal representation of thought but does not tell us about the nature of thinking itself.

There are other non-psychological approaches to logic; one is à la Wittgenstein, which considers logical truths to be tautologies, and the other is Kantian. Kant considers logic to be a priori, and the concepts or categories of thinking are derived from the underlying principle ‘I think’. Logic can advance our knowledge through determining the possibility of synthetic a-priori judgments, but it requires the intervention of intuition to do so. The pure concepts of understanding have a formal function of organizing the data or the manifold of intuition, and without the latter they cannot lead to cognition. Note that Kant and, to a lesser extent, Frege are concerned, within logic, with the question of cognition: how do we think about the world, how are these thoughts true or false, what does it mean to understand or cognize the world, what concepts are implicated in this process, what is the content of thinking, does thought have a distinctive content of its own or is it dependent on sense-perception for a content, what is a concept, how do we form judgments, how do we draw an inference, what makes an inference true or false, what is the nature of an explanation? When it is said that the role of logic is formal, in Kant, it does not mean that he is concerned only with formal truths in the modern sense. He goes beyond general logic to transcendental logic, which studies the possibility of experience itself. The project of understanding the possibility of synthetic a-priori truths is the same as the question of the material validity of inference - what makes our thoughts about the world true, not just formally true but materially true because we are investigating the relation between thought and reality.

Logic, then, at the very least, cannot be reduced to empirical psychology because the latter cannot answer the philosophical questions we raised above, as a matter of fact it presupposes an understanding of what thinking is. Psychology cannot tell you the difference between a thought like ‘2+2=4’ and ‘the grass is green’; we differentiate the former from the latter in terms of necessity or concept containment, but the distinction is drawn in logic rather than in psychology. Psychology can describe mental processes but cannot explain norms for correct reasoning because the latter are concerned not only about how we do reason but how we should reason. Psychology itself has serious limitations. If we probe into the subject matter of psychology, we find that it necessarily depends on other sciences for its object of study. I will make my point thus: in probability calculus, there is a gambler's fallacy. As a psychologist, you can investigate the bias that leads to this fallacious reasoning, but you cannot, by studying what is inside the skull of the human being, decide that what the person is doing is a form of fallacious reasoning. My point is: a) psychology can study cognitive biases, but it cannot tell whether or not they are biases without appealing to another science; b) how can we regard some thought to be biased or a fallacy by appealing to these internal states alone?

Logic, then, is the study of thought and the content of thoughts, and in this sense it is the study of knowledge itself. This requires that we abstract from everything empirical to concentrate on thinking alone, and so empirical psychology does not inform us about the nature of thought itself. Let us now consider how thought is related to reality. We saw that the Kantian answer is that logic can advance our knowledge of the world through the mediation of intuition, but it cannot lead us to knowledge of things-in-themselves. Logic is the science of valid thought, and the validity of thinking requires finding what is true in the object itself. What corresponds to thought within the object is thought itself, or it is the content of thinking itself hidden behind a sensuous garb. These contents we understand in terms of categories of thought - essences-accidents, substance-attribute, whole-parts, cause-effect, relations, necessity-possibility, etc. How do we know these categories apply to reality? For Kant, this is itself subject to proof, while in earlier times this correspondence of thought and reality is what made proof itself possible.

We find that in Ancient times the status of Aristotle’s Categories was debated, and the latter was found insufficient for informing us about the nature of reality itself. The basic idea was that logic, as the study of words and concepts, presupposes metaphysics and so cannot ground metaphysical knowledge. It is the Forms that make meaningful speech or language possible, and so the intersection between thought and reality cannot be found at the linguistic level. Forms that explain what it is for a thing to be or what is true in the object are considered in Platonism to be the objects of divine intellect. This inspired the Medieval definition of truth, where being and truth are convertible - adaequatio rei et intellectus, or truth is the adequacy of intellect and being.

Consider if I were to find a set of rules of grammar that are common to all languages and if I can give a reason why these rules must necessarily be found within any language in order for it to be considered a language, then I have given sufficient grounds for distinguishing grammar from non-grammar. This amounts to a philosophical cognition. Similarly, within Metaphysics, when philosophers try to understand the meaning of being, they are in search of that characteristic which allows us to differentiate being from non-being necessarily. Platonists found the answer in the unity that a thing possessed, which made it the one thing it is; i.e. it made a ‘horse’ a horse, allowing us to distinguish it from non-horses. This unity that made it one thing then is what corresponds to the essence or the true thought of the horse. This unity does not come from a combination of material parts but from the Form, and Forms are the objects of pure thought. Since embodied beings cannot elevate themselves to pure thinking, they must use the method of dialectics to hypothesize Forms, and this method seeks to find the patterns that allow distinct things to be regarded as in a respect the same. The Form of piety, for example, would explain which different actions should be considered pious, and someone who understood the Form of piety understood how to classify actions as pious and distinguish them from non-pious ones. The Forms grounded the possibility of regarding different things as the same and so made valid knowledge possible too. They grounded the possibility of meaning too because without the a-priori content of thinking we would not have a meaningful world at all.

The important point is this: human beings are rational animals, and it is because of our rationality that we have religion, philosophy, science, mathematics, morality, and politics. The concepts of truth and falsehood, good and bad, rights and duties are impossible without reason. There would be no such thing as objective truth or objective morality without reason because objectivity comes from rationality. To say that these concepts are objective is to say that, at a deeper level, our rationality connects us to the world; it does not dictate our every move, but it makes engagement with a meaningful world possible for us. Now consider someone who believes that concepts and reality are separate from each other but still believes that we can have ideas of truth, morality, and politics without it, say, in a non-conceptual way of knowing things. To use the previous example of grammar, I can modify the list of rules, subtract some if required, but if someone says that a sentence can be grammatical even if it does not conform to any rules of grammar whatsoever, then all that can be said is that such a person does not really understand what he is talking about. The same is the predicament of those who separate concept and reality sharply and then try to escape the ensuing scepticism by appealing to non-conceptual or intuitive ways of knowing. Even for Kant, it is thought which informs us what is true in an intuition; by itself, intuition leads only to silence. Silence, however, is not a substitute for truth.

At a deeper level, then we can say that logic, as the study of human rationality or thought itself, becomes the same as the study of metaphysics or the science of being qua being.