Review: Logic-A God Centered Approach (Poythress)

This isn’t a logic textbook, yet it isn’t quite a worldview approach to logic.  It is something of both, yet completely neither.  I still liked it, though.

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He begins with a theological “grounding” of logic, which amounts to a summary of his and Frame’s approach to worldview.  It’s good, but it lasts about 200 pages before you get into the “nuts and bolts” of logic.

He then gives a primer on deductive syllogisms, propositional logic, quantification, functions, sets, modal logic, and much else. I did enjoy the fact that he pointed out how pure systems like Russell’s and others are so formal as to have little content.  This is analogous to the desire for “pure being.”

64: Logic is an aspect of God’s mind.  It reveals God’s attributes.

89: Logic is God’s self-consistency

Key argument: Logic is personal, but it doesn’t depend on any one human person, since if all humans perished, logic would still be true. It is transcendent, displays his attributes, and is part of God’s speech (80).

This next part is important, as it provides another foundation for the rest of the book’s argument:

Axioms of Propositional Logic

Principle of Tautology: (p V p) ⊃ p 

You might need to learn this one.  Poythress’s work is unique in the sense that he puts every single axiom through a truth table.

Principle of Addition

⊃ (p V q)  “If it is dark, then (either it is raining or it is dark)”

The Principle of Permutation

(p V q) ⊃ (q V p)

If (either it is raining or it is dark), then (either it is dark or it is raining)

The Associative Principle

(p V (q V r)) ⊃ (q V (p V r))

If (either it is raining or (it is dark or it is cold)), then (either it is dark or (it is raining or it is cold))

The Principle of Summation

(q ⊃ r) ⊃ ((p V q) ⊃ (p V r))

If (it is dark implies it is cold), then (the assumption that (it is raining or it is dark) implies the conclusion that (it is raining or it is cold)).

While it might not seem like it, these are powerful tools and the reader is encouraged to work through a few of them in truth tables in the appendices.  The book has some severe drawbacks, in that it isn’t a logic textbook, and some important concepts are woefully underdeveloped (like modal logic).  But I did enjoy it and parts of it should be read.

Possible Worlds Semantics

Loux gives a great discussion on the topic of “possible worlds.”  This might seem irrelevant and arcane, but it is a powerful tool that helps us in discussions on the problem of evil, ontological argument, God’s foreknowledge, and human nature.  And it helps us understand Plantinga.

Modal notions: notions of necessity, possible, impossible, and contingent.

The empirical and nominalist traditions view modalities with suspicion (177).

  1. Leibnizian idea of possible worlds.
    1. To say that a proposition is true is to say that it is true in that possible world that is the actual world (181).
    2. Possible World (PW): the way the world might have been.
      1. De dicto: necessity or possibility applied to a proposition taken as a whole. A proposition has a certain property, the property of being necessarily true.
      2. De re: modal exemplification.  It is not talking about propositions, but about a property’s modal status (184).
      3. As propositions can be true or false in possible worlds, so can objects exist or fail to exist.
      4. To say that an object, x, has a property, P, necessarily or essentially is to
  2. Possible Worlds Nominalism
    1. David Lewis. Other possible worlds are “more things of that sort.”
      1. They are just further concrete objeccts.
      2. No causal relations tying objects from distinct worlds.  Hence, no transworld individuals.
      3. World-indexed property: a property a thing has just in case it has some other property in a particular possible world.
        1. Only world-bound individuals.
        2. It’s nonsensical to say, “That could have been me, had this happened” (as usual, nominalism goes against all prephilosophical notions).
  3. Possible Worlds Actualism: Alvin Plantinga
    1. A PW is part of the network of modal concepts and it can be understood only in terms of that network.
    2. We need concepts like de re and de dicto.
      1. Propositions are the subjects of de dicto modality.
    3. We must distinguish the existence of a property from its being exemplified.  We must distinguish the existence of a state of affairs from its obtaining (203).
      1. PWs are just states of affairs (SoA) of a certain kind.
      2. All SoA are necessary beings, so the PWs for them actually exist.  Not all of the PWs, however, obtain.
    4. A PW is a very comprehensive–maximally comprehensive SoA.
      1. One SoA may include or preclude another.
      2. PWs are SoA with a maximality property.
        1. The various PWs are abstract entities.
        2. It could have failed to obtain, but not failed to exist.
    5. Propositions have a property that no SoA does–that of being true of false (206).
      1. To say that a thing exists in a PW is not to say that it is physically contained or literally present in the world.  
      2. It is merely to make the counterfactual claim that had the world been actual, the thing would have existed.
    6. All of this is just another way of saying, “Things could have gone otherwise.”
    7. Leibnizian Essentialism: there are individual essences.
      1. A thing’s essence: the property such that the thing has it essentially and necessarily that nothing other than the thing has it.