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Kant says that dogmatic idealism is unavoidable if

    { 1 } - the existence of external things in space is doubtful and indemonstrable, and that the only certain empirical proposition is 'I am.'
    { 2 } - unavoidable if one holds that space is a property of things in themselves
    { 3 } - he can assert the empirical reality of both space and things-in-themselves.
    { 4 } - one holds that space is a property of things in themselves

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1 is wrong. Please try again.

Kant says that dogmatic idealism is unavoidable if

Problematic (Cartesian) idealism for Kant <=> the existence of external things in space is doubtful and indemonstrable, and that the only certain empirical proposition is 'I am.'

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2 is wrong. Please try again.

Kant says that dogmatic idealism is unavoidable if

    { 1 } - the existence of external things in space is doubtful and indemonstrable, and that the only certain empirical proposition is 'I am.'
    { 2 } - unavoidable if one holds that space is a property of things in themselves
    { 3 } - he can assert the empirical reality of both space and things-in-themselves.
    { 4 } - one holds that space is a property of things in themselves

Dogmatic (Berkelian) idealism for Kant <=> unavoidable if one holds that space is a property of things in themselves

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3 is wrong. Please try again.

Kant says that dogmatic idealism is unavoidable if

    { 1 } - the existence of external things in space is doubtful and indemonstrable, and that the only certain empirical proposition is 'I am.'
    { 2 } - unavoidable if one holds that space is a property of things in themselves
    { 3 } - he can assert the empirical reality of both space and things-in-themselves.
    { 4 } - one holds that space is a property of things in themselves

Since Kant does not hold that space is a property of things in themselves <=> he can assert the empirical reality of both space and things-in-themselves.

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4 is correct!

Kant says that dogmatic idealism is unavoidable if

    { 1 } - the existence of external things in space is doubtful and indemonstrable, and that the only certain empirical proposition is 'I am.'
    { 2 } - unavoidable if one holds that space is a property of things in themselves
    { 3 } - he can assert the empirical reality of both space and things-in-themselves.
    { 4 } - one holds that space is a property of things in themselves

Kant says that dogmatic idealism is unavoidable if <=> one holds that space is a property of things in themselves

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