ABSOLUTE v. RELATIVE THEORY

• The discussion now turns to space and time themselves, beyond things and events within them.

• The topic is very difficult and cannot be adequately treated in an elementary philosophy work.

• The first question is whether space and time exist independently of the things and events they contain.

• Traditionally, space is seen as a vast receptacle including the entire physical world; a similar idea applies to time, though time’s passing makes metaphor difficult.

• This traditional view is called the absolute theory of space and time.

• Language supports this view: we say things are “in space” and “in time”, unlike other properties (e.g., we don’t say all red things are in one big “Red”).

• The absolute theory is difficult to defend logically.

• When we try to conceive space apart from physical things or time apart from events, the concepts become vacuous or lose meaning.

• We can imagine empty space between things, but can we imagine space outside the entire physical universe?

• There is no empirical evidence for absolute space and time since we only perceive things in space and time, never space or time themselves.

• The doctrine that space and time cannot act as causes prevents using causal arguments to support absolute theory.

• Despite difficulties, the absolute theory has been widely accepted by philosophers and ordinary people.

• One major reason philosophers accepted it was its supposed necessity for classical physics (Newtonian laws of motion).

• This reason has now disappeared because modern physics, influenced by Einstein’s discoveries, is incompatible with absolute space and time.

• Philosophers cannot reasonably oppose scientists on this point.

• It is better to regard space and time as ways of looking at spatial and temporal properties and relations of things and events, not as independent entities.

• This is the relative theory of space and time (distinct from the scientific theory of Relativity, which includes more complex propositions).

• Our experience includes spatial properties like size, shape, and distance; geometry makes general statements about these.

• Talking about a vacuum does not mean space is a positive thing there; it means boundaries have a relation of distance without anything in between.

• The relative theory rejects absolute points; points are seen as abstract limits approached by division but never reached.

• The theory also rejects absolute motion.

• Motion is simply change of position relative to other objects, except where force is involved.

• For example, if I walk twenty miles, it is equally true that everything else has moved twenty miles relative to me as that I have moved twenty miles relative to everything else.

• The difference arises only if motion implies force; I feel tired because I have exerted force, but you, though stationary, have also changed your relative position but feel no fatigue.

BEARING ON PHILOSOPHY OF MODERN PHYSICS

• It is difficult to discuss the philosophical implications of modern physics fully without advanced qualifications in both philosophy and science.

• An important alleged implication is that time is inseparable from space.

• Bergson distinguishes between time of physics and time of living experience.

• The time of physics is measured in terms of space and thus already assimilated to space.

• The time of psychological life (experienced time) need not share the same properties as physical time.

• Time may be called the fourth dimension in the sense that:

  • To fix an event’s position completely in space and time, four independent pieces of information are needed.

  • For graphing, time can be treated like a spatial dimension (e.g., plotting depth vs. distance or depth vs. seasonal changes).

• However, time is not homogeneous with spatial dimensions:

  • Spatial dimensions are interchangeable with no intrinsic difference in their relations (length, breadth, height are arbitrary labels).

  • Time has an intrinsic difference as it represents the relation of before and after.

• Time is irreversible; unlike space, we cannot move backward in time.

• Philosophically, it is wrong to assimilate time to space, though scientifically they may be combined in a spatio-temporal system.

• Two unlike things may be combined in a system because they complement each other, which may be the case for space and time.

• Caution is needed in applying scientific statements directly to philosophy.

• Scientific statements (e.g., space is curved, the universe is four-dimensional, physical space is non-Euclidean) may be true only in a “Pickwickian” sense—a sense different from the literal meaning.

• It may be difficult to identify when expressions are used in a Pickwickian sense and what that sense is.

• It is safer to conclude that Euclid’s axioms and postulates probably do not apply perfectly to the physical world.

• This contributes to the modern distrust of the a priori, but it does not undermine the internal a priori necessity of pure geometry.

• We know a priori that if Euclid’s postulates were true, their conclusions would logically follow.

• We also know a priori that nothing exists that conforms to the premises but not the conclusions of Euclid.

• No a priori knowledge, inside or outside geometry, is both affirmative and categorical.

• A priori knowledge can be hypothetical and practical.

• By combining a priori hypothetical knowledge with empirical premises, we can derive affirmative categorical conclusions.

• We lack the empirical premise that the physical world is Euclidean but have the premise that it approximates Euclidean geometry closely except at very small distances or high velocities.

• Therefore, applied Euclidean geometry remains useful despite Einstein’s discoveries.