The meat of the book, however, is the middle three chapters where he demonstrates how the Simplicity Argument was used to argue for the immortality of the soul, the unity of consciousness, and the identity of the (moral) self with thought. Mijuskovic really shows an in-depth knowledge of early Modern philosophy, appealing to most of the great philosophers of this era and even popular-level writers -- the latter to demonstrate how deeply the argument had permeated society at the time. It's interesting how some thinkers employed the argument for one of its uses but not for the others, like Descartes. He also points out how Locke argued (following Hobbes) that matter may be able to think, and so thought is not necessarily immaterial. But it should be pointed out that Locke argued that thought could not be explained simply as matter in motion: God had to "superadd" thought onto matter in order for the "matter can think" thesis to be possible (on this, see this essay and this essay by Margaret Wilson).
The most interesting of these chapters, for me, was on the unity of consciousness. Mijuskovic summarizes the Simplicity Argument's use here as follows:
The argument from the simplicity of thought and its postulation as the "transcendental" condition for the unity of consciousness most often occurs in opposition to the Epicurean-Hobbesian principle that senseless matter can think; and the argument always refers to the peculiar nature of consciousness and, especially, of selfconsciousness. Thus, for instance, the rationalist tradition involved in this epistemological aspect of the simplicity theory constantly stresses the idea that either all consciousness is actually selfconsciousness; or that there is something special, "rational," about selfconsciousness which essentially distinguishes it from mere sensation, perception, or consciousness. And that even if perception might conceivably be explained on Epicurean grounds, selfconsciousness could never be so understood. Furthermore, unless different "thoughts" or concepts inhered in something essentially unified and simple, they would fall apart and crumble into distinct pieces and a disunity of consciousness would thereby result. But the fact that we cannot divide our idea of, say, blue into pieces as we can partition a blue object demonstrates that there is something different in principle between ideas and objects; and if there were not, stones could think and reason as readily as minds. Thus unless consciousness were unified by something intrinsically simple, and therefore necessarily a unity (for what is simple must be a unity), sensation, perception, cognition, awareness, memory, reason, etc., would all be impossible.
He also goes over Hume's skepticism regarding the unity of consciousness and the soul's identity in some detail, concluding with an interesting point reminiscent of the Argument from Reason: "It may be noted, however, that Hume's ultimate scepticism concerning the self is, paradoxically enough, based on the reflexive character of thought, on selfconsciousness."
The final chapter goes over the argument's role in the development of Idealism. Mijuskovic argues that Kant's claim that space is merely an appearance is not based -- or at least is not solely based -- on his antinomies but also on the Simplicity Argument (indeed, it was Kant who referred to this argument as Rationalism's "Achilles").
In what ultimately may be traced back to "Platonic," "Aristotelian," "Neoplatonic," or "Cartesian" sources, the principle that both thoughts and minds are unextended seems to lead philosophically to a conclusion which states that whatever "appears in" or "belongs to" the mind also must be thereby necessarily unextended. For in whatever fashion we contrast or distinguish thoughts and minds (and term the former the attributes or accidents and the latter the substances, or if we identify the two) the important consideration revolves around the recognition of the essentially unextended nature of thoughts and minds. And if both thoughts and minds are incorporeal, and the immaterial is identified with the unextended ... then it follows that everything which is cognitively apprehended by the mind must likewise by essentially unextended. And indeed, even the common man -- who may be tempted to say figuratively that a thought is deep in meaning or that his cares weigh him down -- would find it literally meaningless to speak of an idea two feet deep or a pound in weight.
He concludes by pointing to some possible influences of this argument on 20th century philosophy, such as Husserlian phenomenology, and its relevance for combating certain reductivist philosophies, such as Behaviorism and Materialism. Overall it's an interesting book and a valuable contribution to the history of ideas.