Wednesday, November 17, 2010

Where Are You, When You’re Not Inside Time?

Different philosophers have assigned different explanations to what it means to be outside of time. Any of these is very difficult to understand, and even more difficult to imagine. In any case, the idea of not being in time is non-intuitive or even counter-intuitive. Immanuel Kant wrote

It is a common expression, used chiefly in pious language, to speak of a person who is dying as going out of time into eternity.

This statement requires us, in turn, to consider the definition of “eternity” — often conceived as endless time. But this common notion of eternity quickly collapses: if you’re leaving time altogether, then you’re not in endless time, you’re in no time at all.

This expression would in fact say nothing if eternity is understood here to mean a time proceeding to infinity; for then the person would indeed never get outside time but would always progress only from one time into another. Thus what must be meant is an end of all time along with the person’s uninterrupted duration; but this duration (considering its existence as a magnitude) must be meant as a magnitude wholly incomparable with time (duratio noumenon), of which we are obviously able to form no concept (except a merely negative one).

Yet another puzzle arises: if the person’s existence “endures” the fact that he left time, how do we define “endure” — which is itself a temporal concept? We want to say that the person continues to exist after leaving time - but “continue” is a chronological notion! How can we say that the person still exists, when “still” makes no sense without reference to time?

Here we have to do (or are playing) merely with ideas created by reason itself, whose objects (if they have any) lie wholly beyond our field of vision; although they are transcendent for speculative cognition, they are not to be taken as empty, but with a practical intent they are made available to us by law-giving reason itself.

Kant reminds us here that in contemplating existence outside of time, we are at the very limit, or perhaps past the limit, of what human reason can grasp. His famous distinction between pure reason and practical reason comes into play here. On the level of pure reason, we can know little or nothing about the process of leaving time, or about exactly what it even means to leave time or be outside of time. On the level of practical reason, however, Kant informs us that we have license to follow the evidence and form hypotheses about this topic, because such working hypotheses are necessary for practical (which Kant often means moral or ethical) decisions.

A slightly different topic is, rather than an individual person leaving time, the notion that time itself ends. Again we are faced with puzzling imaginations of what this might mean. Grappling with this question in an eschatological context, Kant writes that the end of time would mean

that henceforth there shall be no alteration; for if there were still alteration in the world, then time would also exist, because alteration can take place only in time and is not thinkable without presupposing it.

Outside of time, there can be no change, for example, I cannot stand now and sit then, because there is no “now” and no “then” — presumably, I would always be both standing and sitting. Our difficulty, or inability, to even imagine or conceptually frame such things results, Kant would argue, from the fact that our minds are structured around time, or that time is the structure which our minds use to form concepts. If a man were born blind and had never seen colors, it would be difficult for him to imagine blue or green. Our minds must always structure concepts within the framework of time, and so it is difficult for us to create concepts in any other way, or to create any other kind of concept.

Now here is represented an end of all things as objects of sense - of which we cannot form any concept at all, because we will inevitably entangle ourselves in contradictions as soon as we try to take a single step beyond the sensible world into the intelligible.

Kant writes that is perhaps for the purposes of practical hypotheses that the concept of eternity (in the sense of an infinite span of time) is used; clearly, being in eternity and being outside of time are two very different things. Eternity is, however, perhaps somewhat easier to imagine, and forms a ready concept which works as well as “being outside of time” for practical purposes. This may be somewhat like our habit of sloppily blurring the distinction between weight and mass in the butcher shop: I might get a pound of pork, or a half kilogram of pork. A rude violation of physics, but for practical purposes an equivalent measure.

Wednesday, November 3, 2010

Varieties of Logic

Logic comes in many varieties. Modern logicians have learned to vary the axioms, the definitions, postulates, etc., to create many different formal systems. The same is true of geometry, as we know that there are many types of non-Euclidean geometry generated in this same way - for geometry simply is logic clothed in multidimensional shapes.

There are more sophisticated and subtle ways of forming new logics. Hieronymous Pardus (often called “Pardo”) developed an interesting logic. He came from Spain and did some work in Paris between 1481 and 1502. John Longeway describes Pardo’s logic as

defending a wholistic account of the meaning of propositions rather than building up their meanings out of the independently established meanings of their parts.

Traditionally, we consider a proposition like “the chair has four legs” as having a meaning which is assembled by adding the meanings of individual words like “chair” and “four” and “legs” — but Pardo challenges us to grasp the entire proposition as a unit, as atomic, as simple not complex. Offering, however, a slightly different interpretation of Pardo, Professor Nuchelmans at the University of Leiden put it this way:

the signification of the whole complex was commonly held to be of a compositional nature and to be determined by the signification of its parts. As Pardo put it, only incomplex expressions have been given conventional meanings in a primary and immediate way; a propositional complex, such as Homo est animal, on the other hand, has been destined to signify its meaning only in a mediate, consequential and secondary manner, since its signification can be derived from the significations of the incomplex parts.

Let’s let Pardo speak for himself, then. He wrote:

For the truth of a proposition in which there is distribution is recognized by means of a conjunctive descent; and that of a proposition in which there is a term suppositing determinately is recognized by means of disjunctive descent; and of a term suppositing merely confusedly, by means of the disjunct or conjunct descent. For what else is it for a term to be distributed, but for it to be taken for its significata conjunctively, and for a term to supposit determinately, but for it to be taken for its significata disjunctively, and for a term to supposit merely confusedly, but for it to be taken for its significata disjunctly or conjunctly? Therefore, to explicate the way of taking the term (acceptionem explicare) is to descend. Thus, if descent is negated, nothing reliable remains for the cognition of the truth of a proposition on the basis of supposition.

These are murky waters: the reader is advised to re-read the above paragraphs several times slowly. In any case, there is sufficient evidence to show that Pardo was a powerful and creative thinker, capable of executing sophisticated and intricate maneuvers in the subtle landscape of systematic logic.

Sadly, this era of technical sophistication in logic and mathematics faded away: Longeway writes:

I found the excitement at an end when the Renaissance began.

Popular historians have often painted the Renaissance as a time a great intellectual activity. In reality, the natural and mathematical sciences both languished, and philosophy was reduced to trite slogans, during this era. Investigating logical theory during the Renaissance leaves Longeway with the suspicion

that there is little pioneering work to do. What bothered me was the lack of any real semantic theory in these thinkers. Nuchelmans does what he can by them, but despite every effort at respect, in the end he points out “the general neglect” in Renaissance thought “of those fundamental problems to which late-scholastic philosophers gave pride of place.”

Despite the intellectually vacuous Renaissance which constitutes the gap between them, Medieval and modern symbolic logic share a sophisticated subtlety, and have much to say to each other.

Accident and Essence

In philosophy, essence is the attribute or set of attributes that make an object or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity. Essence is contrasted with accident: a property that the object or substance has contingently, without which the substance can still retain its identity. Emile Brehier writes:

The sharp distinction between essential and accidental attributes make possible a clear statement of the problem of universals. For universals, whose reality was the subject of speculation, are nothing but the genera and species - for example, “animal” and “man” — which are essential attributes of an individual like Socrates.

This notion was first clearly stated by Aristotle, although it was doubtless present earlier, and it was refined to its most precise and modern form during the Middle Ages. Aristotle dealt with this topic in several of his books, including one called Categories:

the Categories, the study of attributes, cannot refer to things (since res non praedicatur) but only to words as signifiers of things. Hence the solution, imbued with the spirit of Aristotle, of the problem of universals: genus and species exist only by virtue of predicates essential to the individual. “Individuals, species, and genus are one and the same reality (eadem res), and universals are not, as is sometimes stated, something different from universals.”

By the phrase res non praedicatur, we note that things are not predicates, and predicates are not things. If we say that “the car is old,” then “old” is a predicate, and therefore there is no thing which is “oldness” - “old” only exists in old things, but it does not exist by itself.

genus is to species and species is to the individual as matter is to form.

The debates about universals and nominalism become more interesting in special cases, like identity: why am I still me, even though everything about me might change? Also interesting are spiritual cases: how can bread and wine be transformed into body and blood? Such questions are located in a territory which is shared by philosophy and religion. Thinkers who deal with these questions see themselves as both philosophical and religious: Berengar of Tours, for example, agreed

that the Eucharist was a sacrament in the sense in which the word is used by Augustine: a sacred sign that takes us beyond the sensible appearance to an intelligible reality.

The sacraments have been repeatedly analyzed by philosophers, with many different understandings and interpretations of what their true nature is: in any case, they are not merely symbolic in the usual sense. As with physics at the micro and macro levels - subatomic and astro - our intellect with regard to reality

is like our senses in comparison with intelligence or one sense in comparison with another, that is, unable to understand but forced to believe what it does not understand. It would hardly be possible to state in more radical manner the fundamental discontinuity of the mind.

Can we really understand what it means for time to slow down, as general relativity shows? We encounter the limits of human reason in such situations, and our language has developed certain mechanisms for talking about those situations. We risk falling into error if we either take our language in such situations to function as it does in other more normal cases, or if we confuse the ability to talk about these cases with the ability to understand them.

Foundational Principles in Logic

William of Ockham, writing in the early 1300’s, developed a grand logical system, part of the Scholastic foundation laid in the Middle Ages for the later development of modern mathematics, physics, and chemistry. Like all logical systems, Ockham begins with a few relatively simple principles.

John Corcoran, at the State University of New York, writes that one of Ockham’s starting points is an

nominalistic ontology, a key principle of which is that a general term such as ‘animal’ denotes not a universal but rather each and every individual of which the term is truly predicable.

By pointing out that Ockham’s thought is “nominalistic,” we contrast Ockham with, for example, Plato, who thought that universals were independently existing objects. Plato thought that “blue” or “blueness” existed independently of any or all blue objects. Ockham, by contrast, writes that “blue” is merely a property or characteristic of blue objects, and has no being aside from actual blue objects. Ockham has a “lean ontology,” meaning that he believes that fewer things exist than Plato, who has a “rich ontology” - “ontology” being the study of what exists and what does not.

Building upon this first principle, Ockham talks about “supposition”:

According to Ockham’s terminology, a general term supposits for the individuals, if any, of which it is truly predicable.

So, for example, we can correctly substitute “a man” for the proper names John, Robert, and William in any sentences such as: “John eats pizza. Robert rides a bicycle. William reads a book.” This fact emphasizes Ockham’s nominalistic view that general or universal terms (like “man” or “blue”) are linguistic concepts - i.e., it’s all about the words - and not metaphysical concepts - i.e., not about actually existing things called “blueness” or “manhood” - and so the essence of the matter is revealed in the substitution in sentences, which keeps the center of the discussion of universals at the linguistic level, not the ontological level.