Intensional science

The word intension is not as well-known as its homophone intention. The word intension denotes the intrinsic meaning of a word, also called the comprehension or connotation. It contrasts with the extension, which denotes the range of applicability or objects to which the word refers, also known as the denotation. For example, the intension of “boat” is “a small vehicle for mobility on water” but the extension is the particular boat or boats that are included such as canoes, kayaks, rowboats, etc.

In physical science the extension particularly refers to the primary qualities of size, shape, and number which belong to physical matter independently of an observer. Modern science focuses on the extensional side of things and is less interested in the intensions associated with them. This is the basic reason why modern science lacks meaningfulness; it has little to say about intensions.

Is there a kind of science that is interested in the intensional side of things? Yes, but it is considered primitive by modern science. This can be explained by the inverse relation between the intension and the extension of words: as the intension expands and becomes more specific, the extension gets smaller and as the intension contracts into one more general, the extension gets larger. For example, the extension of “boat” covers all the boats in the world but the extension of the more specific term “speed boat” covers only boats which are built for speed.

Extensional science privileges a theory with a larger extension over one with a smaller extension. But an intensional science would privilege a theory with a larger intension, which means a smaller extension. For example, a geocentric theory is considered primitive by extensional science but its small extension would not be a disadvantage to an intensional science. The value of a theory would depend more on how meaningful it is.

This makes intensional science very strange from the modern perspective which so values large extensions. It does however lead to a reevaluation of traditional theories or narratives, which may have deep intensional aspects. For example, consider cosmology in the ancient Near East:

Sumerian cosmology became the foundation of many Near Eastern concepts. The Sumerians speculated that the major components of the universe were heaven (a vaulted, hollow space) and earth (a flat disc) which existed, immovably, in a boundless sea from which the universe had come into being. Between heaven and earth was the atmosphere, from which the sun, moon and stars were fashioned. The separation of heaven and earth and the creation of the planets were followed by plant, animal and human life. Invisible, immortal gods guided and controlled this universe, according to prescribed rules. [A New Dictionary of Religions, edited by John R. Hinnells, Blackwell, 1995.]

Again, this is very primitive from the extensional perspective. It doesn’t mention the earth’s rotation about an axis, its orbit around the sun, the distance to the stars, etc. But it fits the everyday world we live in, which is not a world of light-years and large masses; it’s a world with the earth’s surface below and a curved space above. And it’s part of a narrative about who is behind the universe and why it exists. Extensional science has nothing to offer on that subject.

This leads to consideration of the book of Genesis in the Hebrew Bible. There certainly are similarities between the Genesis narrative and the Sumerian cosmology. Their extension is minimal but their intension is part of a narrative about the meaning of the universe. The Genesis narrative contains many subtleties noted by commentators over the centuries. It repays close study and meditation. It is part of the Bible, which is certainly a very profound book, and for a large portion of humanity is Holy Scripture.

A mature intensional theory would correspond to reality in its own way. All traditional narratives are not equally valid. Criteria need to be developed to privilege the better ones. Insofar as intensional and extensional theories overlap, they should be consistent with one another. Modifying an extensional theory for intensional reasons would no doubt be controversial.

Which is better, extensional or intensional science? Neither. They both have their places. Extensional science is well suited for studying the furthest stars, the possibility of interplanetary travel, and more mundane tasks such as building roads and bridges. Intensional science gives us a meaningful understanding of the universe, tells us who is behind it, why it exists, and why we’re here. We need both.