TPTP Axioms File: PHI002+0.ax


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% File     : PHI002+0 : TPTP v7.5.0. Released v7.4.0.
% Domain   : Philosophy
% Axioms   : Definitions for Spinoza's Ethics - the DAPI
% Version  : [Hor19] axioms.
% English  :

% Refs     : [Hor19] Horner (2019), A Computationally Assisted Reconstructi
%            [Hor20] Horner (2020), Email to Geoff Sutcliffe
% Source   : [Hor20]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :   10 (   0 unit)
%            Number of atoms       :   37 (   0 equality)
%            Maximal formula depth :    8 (   5 average)
%            Number of connectives :   27 (   0   ~;   2   |;  13   &)
%                                         (  10 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :   34 (   0 propositional; 1-2 arity)
%            Number of functors    :    0 (   0 constant; --- arity)
%            Number of variables   :   16 (   0 sgn;  16   !;   0   ?)
%            Maximal term depth    :    1 (   1 average)
% SPC      : FOF_SAT_RFO_SEQ

% Comments : 
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%----Definition I. Self-caused. By that which is self-caused, I mean that of
%----which the essence involves existence, or that of which the nature
%----conceivable as existent. Note that "or" in the "... or that of which the
%----nature ..." must be rendered as "&" to capture what Spinoza means.
fof(self_caused,axiom,(
    ! [X] :
      ( selfCaused(X)
    <=> ( essenceInvExistence(X)
        & natureConcOnlyByExistence(X) ) ) )).

%----Definition II. Finite after its kind. A thing finite after its kind, when
%----it can be limited by another thing of the same nature.
fof(finite_after_its_kind,axiom,(
    ! [X,Y] :
      ( finiteAfterItsKind(X)
    <=> ( canBeLimitedBy(X,Y)
        & sameKind(X,Y) ) ) )).

%----Definition III. Substance. By substance, I mean that which is in itself,
%----and is conceived through itself.
fof(substance,axiom,(
    ! [X] :
      ( substance(X)
    <=> ( inItself(X)
        & conceivedThruItself(X) ) ) )).

%----Definition IV. Attribute. By attribute, I mean that which the intellect
%----perceives as constituting the essence of substance.
fof(attribute,axiom,(
    ! [X] :
      ( attribute(X)
    <=> intPercAsConstEssSub(X) ) )).

%----Definition V. Mode. By mode, I mean the modifications of substance, or
%----that which exists in, and is conceived through, something other than
%----itself.
fof(mode,axiom,(
    ! [X,Y,Z] :
      ( mode(X)
    <=> ( ( modification(X,Y)
          & substance(Y) )
        | ( existsIn(X,Z)
          & conceivedThru(X,Z) ) ) ) )).

%----Definition VI. God. By God, I mean a being absolutely infinite.
fof(god,axiom,(
    ! [X] :
      ( god(X)
    <=> ( being(X)
        & absolutelyInfinite(X) ) ) )).

%----Definition VI. Absolutely infinite. ... that is, a substance consisting 
%----in infinite attributes, of which each expresses eternal and infinite 
%----essentiality. 
fof(absolutely_infinite,axiom,(
    ! [X,Y] :
      ( absolutelyInfinite(X)
    <=> ( substance(X)
        & constInInfAttributes(X)
        & ( attributeOf(Y,X)
         => ( expressesEternalEssentiality(Y)
            & expressesInfiniteEssentiality(Y) ) ) ) ) )).

%----Definition VII. Free. That thing is called free, which exists solely by 
%----the necessity of its own nature, and of which the action is determined 
%----by itself alone.
fof(free,axiom,(
    ! [X,Y] :
      ( free(X)
    <=> ( existsOnlyByNecessityOfOwnNature(X)
        & ( actionOf(Y,X)
         => determinedByItselfAlone(Y,X) ) ) ) )).

%----Definition VII. Necessary. ... that thing is necessary, or rather 
%----constrained, which is by something external to itself to a fixed and 
%----definite method of existence or action.
fof(necessary,axiom,(
    ! [X,Y] :
      ( necessary(X)
    <=> ( externalTo(Y,X)
        & determinedByFixedMethod(X,Y)
        & determinedByDefiniteMethod(X,Y)
        & ( isMethodAction(Y)
          | isMethodExistence(Y) ) ) ) )).

%----Definition VIII. Eternity. By eternity, I mean existence itself, in so 
%----far as it is conceived necessarily to follow solely from the definition 
%----of that which is eternal.
fof(eternity,axiom,(
    ! [X] :
      ( eternity(X)
    <=> existConcFollowFromDefEternal(X) ) )).

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