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Ayer sees the statements of geometry as

    { 1 } - synthetic (and hence empirical).
    { 2 } - analytic (and hence true by convention).
    { 3 } - either analytic or synthetic, depending on how they're understood.

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1 is wrong. Please try again.

Ayer sees the statements of geometry as

We can take a statement of geometry (like "Parallel lines never meet") two ways:

PURE GEOMETRY is concerned with whether the statement follows from the axioms of the system in question (e.g., the Euclidean axioms). Pure geometry is part of mathematics -- and hence analytic.

APPLIED GEOMETRY is concerned with the properties of physical space. Applied geometry is part of physics -- and hence synthetic (and empirical).

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2 is wrong. Please try again.

Ayer sees the statements of geometry as

    { 1 } - synthetic (and hence empirical).
    { 2 } - analytic (and hence true by convention).
    { 3 } - either analytic or synthetic, depending on how they're understood.

We can take a statement of geometry (like "Parallel lines never meet") two ways:

PURE GEOMETRY is concerned with whether the statement follows from the axioms of the system in question (e.g., the Euclidean axioms). Pure geometry is part of mathematics -- and hence analytic.

APPLIED GEOMETRY is concerned with the properties of physical space. Applied geometry is part of physics -- and hence synthetic (and empirical).

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3 is correct!

Ayer sees the statements of geometry as

    { 1 } - synthetic (and hence empirical).
    { 2 } - analytic (and hence true by convention).
    { 3 } - either analytic or synthetic, depending on how they're understood.

We can take a statement of geometry (like "Parallel lines never meet") two ways:

PURE GEOMETRY is concerned with whether the statement follows from the axioms of the system in question (e.g., the Euclidean axioms). Pure geometry is part of mathematics -- and hence analytic.

APPLIED GEOMETRY is concerned with the properties of physical space. Applied geometry is part of physics -- and hence synthetic (and empirical).

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