Hence, quantification theory, according to Peirce, is not a matter of an extension of formal vocabulary, but an expansion into territory that is qualitatively different from what Aristotelian logic covers.
As a matter of fact, an extension like (2.5a) and (2.5b) gives the handle to the -variables generalisation of the Gambier system (2.6).
This group also includes orphan drugs based on existing approved therapies, such as celecoxib and sildenafil, for which development was only a matter of an indication extension.
Yet, however strange it may seem in view of his identification of matter with extension, Descartes offered nonetheless a fully developed theory of smallest particles.
In metaphysics, he provided arguments for the existence of God, to show that the essence of matter is extension, and that the essence of mind is thought.
He held to Descartes's views that the essence of matter is extension; that the essence of mind is thought; that material substance and mental substance are essentially, and really distinct; that mind and body interact; that while humans have souls, brutes and other living things are mere machines; and that material things operate by means of moving parts according to the laws of motion.
Matter, with its properties of extension, impenetrability, etc., cannot be conceived as producing thought.
Accordingly, Descartes attempted to broaden the limits of knowledge by proving to his own satisfaction that God exists; that the standard for knowing something is having a "clear and distinct" idea of it; that mind is more easily known than body; that the essence of matter is extension; and, finally, that most of his former beliefs are true.
For Descartes argued in his 1644 Principles of Philosophy (see Book II) that the essence of matter was extension (i.e., size and shape) because any other attribute of bodies could be imagined away without imagining away matter itself.
