In the following few lessons, we will be going over some fundamental principles of reasoning, which are sometimes called “laws of thought.” Note, however, that these “laws” don’t work like the laws of physics. That is, a law of science describes events (e.g., Newton’s Second Law of Motion says that the net force of any object will be equal to the object’s mass times its acceleration); if an event turns out differently than a law of science predicts, then we know the problem is with the law, and not with the universe’s objects. By contrast, the laws of thought propose a standard for thought; when our actual reasoning practices depart from them, the problem is with our reasoning practices, not the law. (A tentative analogy might be pursued here with societal laws, like “Every car must stop at a red light”. When a car runs a red light, we don’t say that our law didn’t accurately predict this instance, and then discard it. We keep the law: the problem is with the car!). Nevertheless, the principles expressed in these laws of thought are so basic to reasoning that some philosophers have argued that, if one were to deny some or all of them, we couldn’t reason at all. These include:
These are considered to be fundamental principles upon which much of philosophical reasoning is based.
This lesson will focus on the Principle of Non-Contradiction, which itself was given in three separate formulations by Aristotle: the metaphysical formulation, the doxastic formulation, and the semantic formulation
Metaphysics is a field of philosophy, originally referring to those Aristotelian works that “come after physics”. Metaphysics deals with general and fundamental questions about the nature of reality beyond just the laws of physics. While the metaphysical form of the principle may seem like a complex and convoluted statement, all that it really says is that something cannot have a property and not have the same property in the same respect — where the expression ‘in the same respect’ specifies the conditions in which that property applies.. This stipulation is necessary insofar as a property might apply under some conditions, but not others. For example, the same blizzard wind can be cold for Noah and not
cold for Jane, or the same blizzard wind can be cold for Noah now, but not cold for Noah an hour ago. When we specify, however, that the same wind cannot be cold and not cold for the same person or at the same time, then we see that the wind cannot be cold and not cold for Noah now.
“Doxastic” means “of or relating to belief or opinion”. Accordingly, the second version of the principle can be interpreted in either of two ways:
(i) as a statement about the psychological capabilities of the mind,
or
(ii) as a declaration of what it is rational to believe in general.
While the metaphysical formulation of the Principle of Non-Contradiction purports that it is impossible for objects themselves to hold and not hold the same property under the same conditions, this doxastic formulation concerns whether we, as rational thinkers, are ever justified to (or even able to) believe that the same object can hold and not hold the same property under the same conditions. More simply, the metaphysical formulation deals with how an object actually is while the doxastic formulation deals with how we can and should understand the object.
Activity: Discuss with a partner which of these two interpretations is more warranted? Can either of you think of reasons to favor one over the other? Why might they both be true, even if Aristotle meant one or the other?)
‘Semantics’ refers to a field of linguistics (and oftentimes, philosophy as well) that examines the meaning of linguistic units, which is often closely tied to the truth-conditions of that unit. The Semantic Formulation of the principle refers to the idea that no two contradictory propositions can be true or false at the same time. Take, for instance, the propositions: “New York is a city” and “New York is not a city.” According to the Semantic Principle of Non-Contradiction, one of these must be true and the other must be false. It cannot both be the case that New York is a city and that New York is not a city. Likewise, it cannot both be false that New York is a city and that New York is not a city.
The Semantic Formulation differs from the first two formulations insofar as it captures the logical sentiment behind them. The first two formulations state principles about the possibility of objects to be X and not-X at the same time or principles about whether a subject is ever justified to believe that an object to be X and not-X at the same time. The Semantic Formulation simply reflects these two principles in their application to logic.
Activity: Test the claim that this version of the principle “can be viewed as nothing more than an extension of the first” by trying to think of some examples where the first version is violated but not the third, or vice versa. If you are able to come up with one, share your reasoning with the class.