General Determinism

Outline

Thesis of General Determinism

Every event is “determined by” antecedent conditions and laws of nature, i.e. every event is a logical consequence of prior conditions and scientific laws.

The term event can be taken in broad or narrow senses:
- all events, both physical and mental
- only physical events
- only basic physical variables such as time, location, velocity, acceleration, wavelength, frequency, time period, wave speed and amplitude

Determinism is a generalization from deterministic theories of physics such as:

Classical Mechanics
Newton’s Theory of Gravitation
Theory of Electromagnetism
Classical Thermodynamics
Einstein’s Special Theory of Relativity
Relativistic Mechanics
Einstein’s General Theory of Relativity (Theory of Gravitation)

Laws of nature and earlier events determine later events through the magic of differential equations.

View Magic of Differential Equations

How Determinism Works: Newton’s Theory of Gravitation

Suppose a plastic tube is 10 inches in diameter and 554 feet in length, the height of the Washington Monument. The tube is located at sea level, positioned vertically, and all the air inside extracted, making a vacuum. A marble is dropped down the tube.
That the marble takes 5.86 seconds to hit bottom at a speed of 129 mph is a logical consequence of two scientific laws and a handful of initial conditions.
- Scientific Laws
  - Newton’s Law of Universal Gravitation
  - Newton’s Equation of Motion
- Initial Conditions
  - Mass of Earth
  - Radius of Earth
  - Height of the tube
  - Initial vertical speed of marble
  - The fact that the only force on the marble is the gravitational force exerted by Earth
  - The fact that the condition of the tube remains the same throughout the experiment.

Scientific Laws
- Law of Universal Gravitation: For any pair of physical bodies there’s a force on each, toward the other, with magnitude Gm₁m₂/r²
  - where G = 6.67384 10^-11 (the gravitational constant), m₁ and m₂ are the masses of the bodies, and r is the distance between them
  - Abbreviated F = Gm₁m₂/r²
- Equation of Motion: The acceleration a physical body undergoes equals the net force on the body divided by its mass
  - Acceleration is how fast or slow the velocity of a body changes
  - Abbreviated A = F/M

Initial Conditions
- Mass of Earth
  - m_earth = 5.9736 x 10²⁴ kilograms
- Radius of Earth
  - r_earth = 6.3781 x 10⁶ meters
- Height of the tube
  - d =169 meters
- Initial vertical speed of marble
  - v = 0 kilometers / second
- The only force on the marble is the gravitational force exerted by Earth, per F = Gm₁m₂/r²
- The condition of the tube remains the same throughout the experiment.

Derivation
- F = Gm₁m₂/r²
- F = m A
- Therefore, m₁ A = Gm₁m₂/r²
- Therefore, A = Gm₂/r²
- Therefore, g = G m_earth/ r_earth²
  - where g = the gravitational acceleration of an object near sea level
- g = 9.823 = G m_earth/ r_earth² = 6.6743 x 10^-11 x 5.9736 x 10²⁴ / (6.3781 x 10⁶)²
- d = g t² / 2
  - Follows using the mathematics of differential equations
  - Mathematica command
    - d ==y[t]/.DSolve[y”[t]== g&&y[0]==0&&y'[0]==0,y,t]
- t = √((2 d)/g)
  - Follows from d = g t² / 2
- t = 5.8660 seconds = √((2 x 169)/ 9.823 )
- v = g t
  - Follows using the mathematics of differential equations
  - Mathematica command
    - v = y[t]/.DSolve[{y'[t] == g ,y[0] == 0},y, t]
- v = 57.62 meters / second= 9.823 x 5.8660 (128.9 mph)

Thus, that the marble takes 5.86 seconds to hit bottom at a speed of 129 mph follows from Newton’s Law of Gravitation, his Equation of Motion, and the initial conditions.

Pierre Laplace, from A Philosophical Essay on Probabilities, 1814

“We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in a single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. The perfection that the human mind has been able to give to astronomy affords a feeble outline of such an intelligence. Discoveries in mechanics and geometry, coupled with those of universal gravitation, have brought the mind within reach of comprehending in the same analytic formula the past and future state of the system of the world. All the mind’s efforts in search for truth tend to approximate to the intelligence we have just imagined although it will forever remain infinitely remote from such an intelligence.”

Determinism is like Falling Dominoes

Assume it’s a law of nature that if a domino falls then the next domino falls.
- This is the Law of Dominoes
Then the falling of Domino #1000 follows logically from
- The Law of Dominoes
- Prior events, e.g. the falling of Domino #25.

Formulations of Determinism

Leucippus, fifth century B.C
- “nothing occurs at random, but all things for a reason and by necessity.”
Pierre Laplace, 1814
- “We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in a single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes.”
C.S. Peirce, early 20th
- “The state of things existing at any time, together with certain immutable laws, completely determine the state of things at every other time.”
C.J. Ducasse, mid 20th
- “On the basis of knowledge of (a) the state of the world at any given time and (b) the laws according to which its state at any time is related to its states at other times, it would be possible to infer what the state of the world was, or will be, at any earlier or later time.
Alvin Goldman 1970, 172
- Every event e is such that a proposition asserting that e occurs (at t) is deducible from some conjunction of (true) propositions describing laws of nature and events prior to t (but not deducible from propositions describing prior events alone).
Bernard Berofsky 1971
- (x)[x is an R-sentence → (Ey)(Ez)(y is a state-description-sentence & z is a law-sentence & (y & z) → x)]. An R-sentence is true, contingent, singular, and temporal.
Nicholas Denyer, 1981
- For every stage of the universe there are truths about that stage which, together with some law or conjunction of laws, entail a complete description of every later stage of the universe.
Peter van Inwagen 1983, 65
- For every instant of time, there is a proposition that expresses the state of the world at that instant; If p and q are any propositions that express the state of the world at some instants, then the conjunction of p with the laws of nature entails q
John Earman 1985, 13
- Letting W stand for the collection of all physically possible worlds, that is, possible worlds which satisfy the natural laws obtaining in the actual world, we can define the Laplacian variety of determinism as follows. The world W e W is Laplacian deterministic just in case for any W’ e W, if W and W’ agree at any time, then they agree for all times. By assumption, the world-at-a-given-time is an invariantly meaningful notion and agreement of worlds at a time means agreement at that time on all relevant physical properties.
plato.stanford.edu/entries/determinism-causal/
- Causal determinism is, roughly speaking, the idea that every event is necessitated by antecedent events and conditions together with the laws of nature. The idea is ancient, but first became subject to clarification and mathematical analysis in the eighteenth century.
britannica.com/topic/free-will-and-moral-responsibility
- Determinism is the view that, given the state of the universe (the complete physical properties of all its parts) at a certain time and the laws of nature operative in the universe at that time, the state of the universe at any subsequent time is completely determined. No subsequent state of the universe can be other than what it is.
merriam-webster.com/dictionary/determinism
- a theory or doctrine that acts of the will, occurrences in nature, or social or psychological phenomena are causally determined by preceding events or natural laws
ahdictionary.com/word/search.html?q=determinism
- The philosophical doctrine that every state of affairs, including every human event, act, and decision, is the inevitable consequence of antecedent states of affairs.

Addendum

Let the dominoes represent the states of the universe at time t₁, time t₂, and so on.
- Fallen dominoes are in the past
- Standing dominoes are in the future
- A falling domino is in the present
  - We’ll assume only one domino falls at a time.
Assume it’s a law of nature that if a domino falls then the next domino falls.
- This is the Law of Dominoes
Take any domino in the future, maybe the domino at t₁₀₀. That it falls at t₁₀₀ is a logical consequence of the Law of Dominoes and the fact that any past domino has fallen, say the domino at t₁₀.
- That is, the state of the universe at t₁₀₀ is determined by the Law of Dominoes and the state of the universe at t₁₀.