The Theory of Space—like Time

  • F. Christensen


The Special and General Theories of Relativity have in this century inspired the belief that time is very much like space—or at least, much more like space than had hitherto been common-sensically believed. But this is a rather vague notion; what exactly is involved in the concept of space-like time? This paper marks a number of consequences of that theory of time, with special emphasis on the grammatical features required for its expression: it requires a language without tenses and other “adverbial” forms, replacing them with purely predicative expressions. It is shown rigorously how the common-sense idea that objects persist through time, and that events and objects pass into and out of existence, is replaced by the notion that all of the objects and events of history alike exist, in just the same sense, merely being spread across time.


Temporal Relation Temporal Part Prepositional Phrase Tense Logic Relational Predicate 
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  1. 1.
    Excerpts from and references to the relevant writings of these philosophers, and others with similar views, can be found in Problems of Space and Time, part IV, edited by J. J. C. Smart (Macmillan, New York, 1964) and in The Philosophy of Time, edited by R. M. Gale (Anchor Books, Garden City, N.Y., 1967).Google Scholar
  2. 2.
    Gale’s name ‘B-theory’, taken from McTaggart’s “B-series”, has gained some currency for this view of time. Unfortunately for my purposes, Gale directs his remarks primarily toward Grünbaurn’s notion that “nowness” is mind-dependent. Consequently, his characterization of the “B-theory” includes not on1y the view that “now” is perspectival, like “here”, but additionally this feature of minddependence, which is not part of the view as it is commonly held.Google Scholar
  3. 3.
    It is implicit in my way of saying this that I am using the term “predicate”, and its object-language correlates ‘property’ and ‘relation’, in a narrower way than is of ten done in pure syrnbo1ic logic, where any expression whatever that contains two free variables is apt to be called a dyadic predicate, and said to represent arelation — even, say, one of the form ‘Ox·Qy’. Hence, an open sentence such as ‘x is red at t’ could be said to express arelation between x and t, just as much as do ‘x is earlier than t’, ‘x is at t’, and the other phrases that I have listed here as paradigrns of relational predicates. But surely the former is very different in grammatical structure from the latter two; lumping both types under the same rubric obscures important distinctions between them. (Moreover, ‘x is red at t’ is commonly symbolized as ‘Rxt’, the same as wou1d be ‘x is at t’, in spite of the difference in structure that this obliterates.) It is the desire to stress these differences that leads me to ignore logicians’ usage in favor of terminology that seems much more natural to me: I find it highly strained to say, for example, that being red (or being red at) is arelation, which a thing bears to a time. Being red is a property, to be signified by a monadic predicate, and ‘at t’ is an adverbial phrase which modifies that monadic predicate.Google Scholar
  4. 4.
    The most common misunderstanding being to visualize objects as moving across space-time, rather than as being extended across space-time. The idea of (three-dimensional) objects that persist through time but also move constant1y from one time or event to another is a carry-over from certain ordinary ways of talking. I maintain that this “passage of time” notion cannot be taken literally even within the ordinary concept of time, and it most certain1y is out of place in the S-theory. See my paper “The Source of the River of Time”, Rario, Dec. 1976.Google Scholar
  5. 5.
    Some philosophers identifiab1e as S-theorists give the appearance — as do also some of their opponents — of not realizing that a four-dimensional wor1d of events carries a commitment to a four-dimensional wor1d of objects. But others are admirably clear in this regard, notably Quine, Williams and Smart. (See Smart, op. cit.)Google Scholar

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© Springer Science+Business Media New York 1978

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  • F. Christensen

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