While the nature of God is incomprehensible to us in its totality, many great philosophers have concurred that certain aspects of God are accessible either to our reason or to our imagination. Whenever we say that God is good, we cannot claim a total befuddlement in the understanding of goodness, at least in its limited sense. Otherwise, we would confess ourselves incapable of distinguishing good from evil, which very few people would be happy to admit. Now, goodness is not a “finite” concept, like in “good works,” where it is an application, rather than the concept itself. Yet, being infinite, we can still grasp it, and even distinguish its infinite quality from the finite quality of evil, for instance, as I do elsewhere.
On the other hand, the distinction of the definite from the indefinite is another story. In this case, I totally agree that we cannot understand the indefinite at all, except that it is not well-defined. (Let us not confuse the indefinite in general with such a term as “the indefinite article,” where the word ‘indefinite’ is used in a very definite limited sense, which is clearly defined.)
This goes well with my argument about the necessity of clear definitions; the absence thereof makes most of our concepts incomprehensible not by reason of their reaching beyond our perceptive capacity, but because of their inherent fatal flaw. It is with this clarification in mind, that the famous idea of Dèscartes, regarding God as infinite rather than indefinite, starts making more sense than if we had chosen to view these concepts of the indefinite and the infinite on the, so-to-speak, equipollent level, which, I insist, would be wrong.
By the same token, the mathematical concepts of plus or minus infinity should be comprehensible, as long as we empower them with being definite through the magic of clear definitions. We can even comprehend the oneness of plus infinity with minus infinity, if we define the straight line as a perfect circle in infinity. What we definitely cannot have is the indefinite character of a flawed definition.
In view of everything said above, I have a strong disagreement with Hobbes in the following passage from his Leviathan (I-3):
“What we imagine is finite. There is no idea or conception of anything we call infinite. No man can have in his mind an image of infinite magnitude nor conceive an infinite swiftness, infinite time, infinite force, or an infinite power. When we say anything is infinite, we mean only that we are not able to conceive the ends and bounds of the thing named, having no conception of the thing, but of our own inability. And, therefore, the name of God is used not to make us conceive Him (for He is incomprehensible and unconceivable), but that we may honor Him. Also because what we conceive has been perceived first by sense, a man can have no thought representing anything not subject to sense. No man can conceive anything, but must conceive it in some place, endued with some magnitude, and which may be divided into parts; nor that anything is all in one place and all in another place at the same time; nor that two or more things can be in the same place at once: for none of these things can be incident to sense, but are absurd speeches taken upon credit without any meaning, from deceived philosophers and deceiving Schoolmen.”
I can hardly call myself a “deceived philosopher,” and even less so a “deceiving Schoolman,” in suggesting that it is our power of abstract thinking which allows us to comprehend the infinite. Otherwise, what exactly does “abstract thinking” signify, if anything at all? Even the simple abstraction of “cat” presupposes certain infinity, insofar as no matter how many “cats” we can visualize, multiplied and raised to a great power, the “number” of cats in abstracto will always be far greater, leading us to the core mathematical significance of the concept of infinity.
Indeed, our thinking capacity is well equipped with abstract reasoning, and also irrational leaps of insight, to grasp certain infinite concepts, and has a self-protecting mechanism as well, to guard our mind against a host of “viruses,” which can all be described as a group by the excellent term the indefinites. As long as we are capable of distinguishing between the infinite and the indefinite, our conception of infinity is safe and sound, and, therefore, we must always keep the necessity of such distinction at the top of our list of mental priorities.
The bottom line of my philosophical disagreement with Hobbes is that, all his religiosity notwithstanding, he presents himself here as a materialistic thinker in the sense that ‘matter is an objective reality perceived by our five senses,’ and thus denies us the ability of ‘idealistic’ perception. The value of practical idealism is crucial to our ability to comprehend the absolute (which, in this case, is synonymous with the infinite), as in the Absolute, unlimited, infinite authority of God, thwarting, among other things, our understanding of the basic philosophical ideas of good and evil and effectively destroying the very foundations of ethics and philosophy as such.
On the other hand, the distinction of the definite from the indefinite is another story. In this case, I totally agree that we cannot understand the indefinite at all, except that it is not well-defined. (Let us not confuse the indefinite in general with such a term as “the indefinite article,” where the word ‘indefinite’ is used in a very definite limited sense, which is clearly defined.)
This goes well with my argument about the necessity of clear definitions; the absence thereof makes most of our concepts incomprehensible not by reason of their reaching beyond our perceptive capacity, but because of their inherent fatal flaw. It is with this clarification in mind, that the famous idea of Dèscartes, regarding God as infinite rather than indefinite, starts making more sense than if we had chosen to view these concepts of the indefinite and the infinite on the, so-to-speak, equipollent level, which, I insist, would be wrong.
By the same token, the mathematical concepts of plus or minus infinity should be comprehensible, as long as we empower them with being definite through the magic of clear definitions. We can even comprehend the oneness of plus infinity with minus infinity, if we define the straight line as a perfect circle in infinity. What we definitely cannot have is the indefinite character of a flawed definition.
In view of everything said above, I have a strong disagreement with Hobbes in the following passage from his Leviathan (I-3):
“What we imagine is finite. There is no idea or conception of anything we call infinite. No man can have in his mind an image of infinite magnitude nor conceive an infinite swiftness, infinite time, infinite force, or an infinite power. When we say anything is infinite, we mean only that we are not able to conceive the ends and bounds of the thing named, having no conception of the thing, but of our own inability. And, therefore, the name of God is used not to make us conceive Him (for He is incomprehensible and unconceivable), but that we may honor Him. Also because what we conceive has been perceived first by sense, a man can have no thought representing anything not subject to sense. No man can conceive anything, but must conceive it in some place, endued with some magnitude, and which may be divided into parts; nor that anything is all in one place and all in another place at the same time; nor that two or more things can be in the same place at once: for none of these things can be incident to sense, but are absurd speeches taken upon credit without any meaning, from deceived philosophers and deceiving Schoolmen.”
I can hardly call myself a “deceived philosopher,” and even less so a “deceiving Schoolman,” in suggesting that it is our power of abstract thinking which allows us to comprehend the infinite. Otherwise, what exactly does “abstract thinking” signify, if anything at all? Even the simple abstraction of “cat” presupposes certain infinity, insofar as no matter how many “cats” we can visualize, multiplied and raised to a great power, the “number” of cats in abstracto will always be far greater, leading us to the core mathematical significance of the concept of infinity.
Indeed, our thinking capacity is well equipped with abstract reasoning, and also irrational leaps of insight, to grasp certain infinite concepts, and has a self-protecting mechanism as well, to guard our mind against a host of “viruses,” which can all be described as a group by the excellent term the indefinites. As long as we are capable of distinguishing between the infinite and the indefinite, our conception of infinity is safe and sound, and, therefore, we must always keep the necessity of such distinction at the top of our list of mental priorities.
The bottom line of my philosophical disagreement with Hobbes is that, all his religiosity notwithstanding, he presents himself here as a materialistic thinker in the sense that ‘matter is an objective reality perceived by our five senses,’ and thus denies us the ability of ‘idealistic’ perception. The value of practical idealism is crucial to our ability to comprehend the absolute (which, in this case, is synonymous with the infinite), as in the Absolute, unlimited, infinite authority of God, thwarting, among other things, our understanding of the basic philosophical ideas of good and evil and effectively destroying the very foundations of ethics and philosophy as such.
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