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Some Materialist Empiricists Are Either Libertarians or Hard Determinists B)

Question 269

Multiple Choice

Some materialist empiricists are either libertarians or hard determinists. But no empiricist is a hard determinist. So some materialists are libertarians.
-Which of the following is the best translation into M of this argument?


A) (x) [(MxEx) (LxDx) ](x) (ExDx) /(x) (MxLx) \begin{array} { l } ( \exists \mathrm { x } ) [ ( \mathrm { Mx } \cdot \mathrm { Ex } ) \cdot ( \mathrm { Lx } \vee \mathrm { Dx } ) ] \\\sim ( \forall \mathrm { x } ) ( \mathrm { Ex } \supset \mathrm { Dx } ) \quad \quad \quad \quad \quad / ( \exists \mathrm { x } ) ( \mathrm { Mx } \cdot \mathrm { Lx } ) \\\end{array}
B) (x) [(MxEx) (LxDx) ](x) (ExDx) /(x) (MxLx) \begin{array} { l } ( \exists \mathrm { x } ) [ ( \mathrm { Mx } \cdot \mathrm { Ex } ) \cdot ( \mathrm { Lx } \vee \mathrm { Dx } ) ] \\\sim ( \forall \mathrm { x } ) ( \mathrm { Ex } \supset \mathrm { Dx } ) \quad\quad \quad \quad \quad \quad / ( \exists \mathrm { x } ) ( \mathrm { Mx } \supset \mathrm { Lx } ) \\\end{array}
C) (x) [(MxEx) (LxDx) ](x) (ExDx) /(x) (MxLx) \begin{array} { l l } ( \exists \mathrm { x } ) [ ( \mathrm { Mx } \vee \mathrm { Ex } ) \cdot ( \mathrm { Lx } \vee \mathrm { Dx } ) ] & \\( \forall \mathrm { x } ) ( \mathrm { Ex } \supset \sim \mathrm { Dx } ) & / ( \exists \mathrm { x } ) ( \mathrm { Mx } \cdot \mathrm { Lx } ) \end{array}
D) (x) [(MxEx) (LxDx) ](x) (ExDx) /(x) (MxLx) \begin{array} { l } ( \exists \mathrm { x } ) [ ( \mathrm { Mx } \cdot \mathrm { Ex } ) \vee ( \mathrm { Lx } \cdot \mathrm { Dx } ) ] \\( \forall \mathrm { x } ) ( \mathrm { Ex } \supset \sim \mathrm { Dx } ) \quad / ( \exists \mathrm { x } ) ( \mathrm { Mx } \supset \mathrm { Lx } ) \\\end{array}
E) (x) [(MxEx) (LxDx) ](x) (ExDx) /(x) (MxLx) \begin{array} { l } ( \exists \mathrm { x } ) [ ( \mathrm { Mx } \cdot \mathrm { Ex } ) \cdot ( \mathrm { Lx } \vee \mathrm { Dx } ) ] \\( \forall \mathrm { x } ) ( \mathrm { Ex } \supset \sim \mathrm { Dx } ) \quad / ( \exists \mathrm { x } ) ( \mathrm { Mx } \cdot \mathrm { Lx } ) \\\end{array}

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