A Brief Introduction to Roedl’s ‘Categories of the Temporal’

Rodl’s mission in Categories of the Temporal can be summarized as the attempt to show the following: deductive or inferential logic is possible only by its being supervenient, or structurally dependent, on temporal or transcendental logic. This is so because although it is the case that deductive logic aims at Truth which is timeless it is also the case that inference and deduction (i.e. judgments) occur in time. Thus, in order to grasp, assert, and comprehend Truth, philosophy must be able to give an account of how temporal thought is able to access the eternal. This can be formulated as the question: ‘how is it possible for the finite intellect to know the infinite?’

Before we can join Rodl on his journey, it is first necessary to make some preliminary conceptual preparations.  We first must understand why Truth is timeless and what it means for thought that it is temporal.  Analyzing the expression ‘Truth is timeless’ we discover by definition that a true thought will be one whose truth value does not change as time passes since ‘timeless’ and ‘changeable’ cannot be predicated of the same concept as their meanings are mutually exclusive, contradictory, or otherwise conceptually incompatible.  There is no x such that it is both timeless and changing.  Rodl describes it this way: a true thought is one of which it is not possible to assert that it was true before but is now no longer, or that it was not but now is true.  Mathematical statements seem to satisfy this condition. For it is not possible to say that ‘7 + 5 = 12’ was true in the past but is not true now, nor that such truth perishes as the present moment passes into the future. That is to say, there is no point anywhere in time at which ‘7 + 5 = 12’ is not true. One cannot take back a truth once it has been established nor can one fix his gaze upon a falsehood and hope to, by eye or by camera, catch a glimpse of its sudden or gradual metamorphosis into a species of verity.

Now, in examining mathematical laws as candidates for membership in the fraternity of the timeless and the true, we might notice that we have been implicitly relying on logical principles to use as rules by which are able to carry out our examination. Finding ourselves unable to think the truths of mathematics as merely temporal, we discover that those principles of logic which mediate our presentation of mathematical necessity must themselves be true and timelessly so. That is, we presuppose only on pain of pragmatic failure that mathematics and logic guide us on our journey to think what is true. We presuppose on strictly pragmatic grounds that the rules of general logic and mathematics are the right criteria on which to base our assessment of the meaning of the proposition ‘Truth is timeless”. But by pragmatic here we do not simply refer to the ease-of-use of these principles over and above others – as if we are choosing between a pair of power tools – but rather by pragmatic we mean necessitated by the very act of thinking in general. That is, we assume that Truth is thinkable and thinkable by us. It is possible to deny that the rules of mathematics and general logic (e.g. modus ponens, the principle of sufficient reason, the law of non-contradiction, the identity of indiscernibles, etc.) are the proper rubric by which to assess the nature of Truth, but in doing so, one forecloses on the possibility of remaining intelligible and thus critically evaluable.  In other words, we begin with the purely axiomatic presupposition that thought is possible and that my writing this and your reading this are both manifestations of thinking taking place and thoughts occurring in time.  One is invited to leave the principles of logic and arithmetic by the wayside and engage in whatever activity he so pleases; but whatever he is doing thereafter, he will not be thinking. It is entirely consistent of course, to believe that thought occurs in tandem with any number of different processes that are themselves not instances of thinking, neurons firing, for example, electrons spinning, or space-time expanding.  However, to claim that these processes are or could be preclusive of the possibility that thought takes place beside, beneath, between or because of them is to claim something literally beyond belief.  Since it is the business of both science and philosophy to adjudicate precisely what is within the purview of the believable and what is outside of it, we take it on faith that both science and philosophy have devised for themselves a real subject matter. Accepting this, we discover that logical principles as well as mathematical principles participate equally in the category of the timeless. If one asserts that ‘A = A’ was true on Monday but now, on Friday, Friday which is so far away, ‘A = A’ has broken off its relationship to Truth, we must dogmatically commit ourselves to the view that it is no longer possible for us to enter into dialogue with whosoever believes that in stating this proposition he has stated something which is able to rouse the scientist or philosopher out of bed, i.e., something meaningful.  Being eternal, it is of the essence of Truth to be dogmatic.  And a temporary Truth would be no truth at all. Thus, in order to seek Truth we must first presuppose that it exists.

We have hereby designated the nature of those with whom we are in dialogue. They are the philosopher and the scientist, for these two are the figures whom refuse to cede ground to any who would reject the timelessness of truth, and the truthfulness of logic and mathematics. An interlocutor who is unable or unwilling to accept these assertions as axiomatic is therefore, regardless of what he takes himself to be, neither a scientist nor a philosopher. We, the finite and temporal, who have chosen to spend our days in pursuit of the timeless, do not have time to spare in consideration of the ravings of the truth-denier once we have shown that his position can only be pronounced but never actually proposed. Thus, making a wager on Truth’s timelessness and its logico-mathematical character, we ask ourselves what the nature of reality must be in order for us to be able to think truth in this way.

At this point we might decide to examine the nature of the temporal, or those things that are not timeless. Something that exists in time must be able to change as time passes even if the form of its changing is only its persistence through time or its remaining in a particular state.  A mountain, a galaxy, a population of pine trees or a person may persist in time and remain in a particular state while all the while it still being true of them that they are subject to change, that is that they are changeable.  Thus we notice an interesting fact about temporal beings: in describing them, I find that I give an incomplete description of their being if I only use the present tense as a logical copula, that is, as a verb joining them to a predicate.  This, we recall, was not the case when I tried to ascribe truth to something timeless, such as the statements ‘7 + 5 = 12’ and ‘A = A’.  There, the present tense was sufficient. But when I assert of something temporal, say a moose, that it is molting, I soon discover that though it is now, on Friday, true of the moose that it is molting, it may not have been the case that it was molting on Monday. That is, the truth value of my statement depends on my being able to differentiate what is happening at a time from the time at which it is happening. That is, when judging a temporal object, I know that what is predicated of it in the present may or may not pertain to it in the past or in the future.  This is troubling, because our starting assumption was that truth was timeless; how then can the truth value of my statement change depending on whether or not it is said on Monday or Friday?  If it is true now that ‘the moose is molting’, how is it the case that this statement if uttered on Monday would have been false?  If I am not yet willing to give up my conviction that truth is timeless I must look for a way to salvage the timelessness of the truth represented in the statement ‘the moose is molting’ without falling into the absurd position of having to insist that it is always true of the moose that it is molting.  I realize that had it been Monday when I made a judgment about this moose, I could have accessed the same truth represented by the proposition ‘the moose is molting’ when uttered on Friday by my having said on the prior Monday that ‘the moose will be molting.’  It is also possible for me to access the same timeless truth tomorrow, on Saturday, by saying of the very same moose that it was molting yesterday.  Rodl puts it like this: “We think situational thoughts by means of the time at which we think them…[and] the thoughts we thus think are [thereby still] timelessly true.” [Categories of the Temporal, pg. 65]

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One response to “A Brief Introduction to Roedl’s ‘Categories of the Temporal’

  • Adrian

    Interesting post. Two quick points I would like to make.

    (1) I would disagree that logic aims at truth. Indeed, I would say that logic aims only at the goal of establishing a linguistic-relative, conditional truth where a standard, textbook, classical-logic argument is taken to be valid if and only if it is impossible for the premises to be true while the conclusion is false. This is not the same as aiming for truth; this is ensuring that should truth occur, this truth does not lead to falsity.

    (2) You write: “For it is not possible to say that ‘7 + 5 = 12′ was true in the past but is not true now, nor that such truth perishes as the present moment passes into the future. That is to say, there is no point anywhere in time at which ‘7 + 5 = 12′ is not true.”

    You may be interested in a counter-example from Graham Priest where it is indeed mathematically coherent to assert that a number is both equal to some other and is not equal to that same other number. See his paper on Inconsistent Arithmetic here: http://www.math.helsinki.fi/logic/LC2003/presentations/priest.pdf

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