Prior to accompanying me on this intellectual journey, providing some definitions of philosophical concepts and terms is crucial. While I will be defining various concepts in detail in future posts, this post will serve as a foundation for a common understanding in rational discourse.
A proposition is an indicative, meaningful sentence that has a truth value of either true or false.
“The cat is on the mat.”
“Everything that begins to exist has a cause.”
“Libertarian free will does not exist.”
Intension and Extension
In the ancient past, people did not know that the evening star (which was called Hesperus) and the morning star (which was called Phosphorous) were in fact one and the same thing — the planet Venus. Thus, the propositions
Hesperus is the second planet from the Sun
Phosphorous is the second planet from the Sun
are both validated by one and the same fact — Venus being the second planet from the Sun; they both refer to exactly the same things. But a question arises: Does this mean the two propositions are actually one and the same proposition?
Philosophers, in puzzling over questions like this, have introduced a useful dichotomy between the intension (or sense or connotation) and the extension (or reference or denotation) of a proposition. Extensionally (in the case above) the propositions are equivalent, for they are about exactly the same things in the world. However, they differ intensionally. One could believe one without believing the other, if, like the ancient Greeks, one did not know that Hesperus and Phosphorous were identical. Thus, two propositions may be extensionally equivalent but intensionally distinct. Propositions, then, are individuated by their intensions.
An important note concerns what is called intensional contexts (or referentially opaque contexts, or oblique contexts). In such contexts one can no longer swap extensionally equivalent (co-referring) expressions in a proposition without potentially changing its truth value. An example of this is shown below:
Patrick believes that Mark Twain wrote The Adventures of Tom Sawyer
Patrick believes that Samuel Langhorne Clemens wrote The Adventures of Tom Sawyer
We can suppose that the first is true and the second false, despite the fact that Mark Twain and Samuel Langhorne Clemens are numerically identical.
Neither, in intensional contexts, can one infer the existence of the entities mentioned. For example, it may be true that
Children believe in the Easter Bunny
But it does not follow that the Easter Bunny exists.
This will all be highly relevant when we explore Descartes’ arguments for substance dualism in the future.
“An argument is a set of propositions, one of which is the conclusion and the others premises, in which the premises taken together are intended as providing a reason for accepting the truth of the conclusion (where reason here is intended in the sense of rational justification)” (American Philosophical Association).
Arguments can usually be spotted by premise and conclusion indicators. For example:
[premises] therefore [conclusion]
[premises] so [conclusion]
[premises] thus [conclusion]
[premises] hence [conclusion]
[conclusion] since [premises]
[conclusion] follows from [premises]
[conclusion] because [premises]
There are two components to a good argument: the premises must be true, and they must provide sufficient support for affirming the conclusion. The latter concerns the argument’s structure (and whether or not is valid), while the former determines whether or not an argument is sound (provided that it is, indeed, valid).
There are, roughly, two general types of arguments. First, the premises, if true, might render the conclusion probable. These kinds of arguments are called inductive arguments. Deductive arguments, on the other hand, are such that the truth of the premises guarantees the truth of the conclusion. Abductive arguments, which are inferences to the best explanation, can be considered a sub-category of inductive arguments.
An argument is valid if and only if it is impossible for the premises to be true and the conclusion false. An argument is sound if and only if it is valid and its premises are true. Now, with all this terminology, it can be difficult for some to keep track of which terms apply to which concepts. So, to recap: propositions are true or false; sets of propositions are consistent or inconsistent; (deductive) arguments are valid or invalid, sound or unsound.
Truth is a complex subject matter, one that has been a central issue in philosophy for quite a long time.
The following short summary is from the American Philosophical Association:
“Correspondence theories of truth take truth to consist in the relation of a proposition to the world—in particular to its correspondence to the facts. A proposition is true if the facts really are as it says they are. “The cat is on the mat” is true if and only if the cat really is on the mat.
Coherence theories of truth, on the other hand, take the truth of a proposition to consist in its relation to other propositions—in particular in its coherence with a set of propositions. The coherentist about truth maintains that truth is an internal feature of systems of propositions. The only mark of truth is whether a proposition coheres with the other propositions in the system: if it does not one may reject the proposition as false, or adjust the system by rejecting some of the other propositions in the system as false.”
In the following posts, I will provide even more crucial philosophical terminology that will aid in one’s precision and clarity in thinking, as well as enhance one’s ability to analyze and evaluate arguments. I hope you can join me!