What is your answer?

William James's neutral monism (which Russell finds attactive) claims that

    { 1 } - only matter ultimately exists; so-called mental events are chemical processes in your brain.
    { 2 } - the ultimate components of the world are neither mental nor physical, but a kind of "neutral" thing that can be arranged to form either.
    { 3 } - the only thing that exists is the Absolute -- an all-encompassing entity that we are all part of.
    { 4 } - only mental ideas ultimately exist; so-called material objects are complexes of sensations.

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1 is wrong. Please try again.

William James's neutral monism (which Russell finds attactive) claims that

This is materialism.

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2 is correct!

William James's neutral monism (which Russell finds attactive) claims that

    { 1 } - only matter ultimately exists; so-called mental events are chemical processes in your brain.
    { 2 } - the ultimate components of the world are neither mental nor physical, but a kind of "neutral" thing that can be arranged to form either.
    { 3 } - the only thing that exists is the Absolute -- an all-encompassing entity that we are all part of.
    { 4 } - only mental ideas ultimately exist; so-called material objects are complexes of sensations.

Russell gives this simplified example. Suppose that we all look at a chair. When I speak about a "chair," I'm talking about the set of somewhat similar appearances of the chair that we all have. When I talk about "myself," I'm talking about a somewhat different set of appearances -- those that I have of the chair and of other things (including my internal state). In both cases, what ultimately exists is a set of appearances (or sense-data).

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3 is wrong. Please try again.

William James's neutral monism (which Russell finds attactive) claims that

    { 1 } - only matter ultimately exists; so-called mental events are chemical processes in your brain.
    { 2 } - the ultimate components of the world are neither mental nor physical, but a kind of "neutral" thing that can be arranged to form either.
    { 3 } - the only thing that exists is the Absolute -- an all-encompassing entity that we are all part of.
    { 4 } - only mental ideas ultimately exist; so-called material objects are complexes of sensations.

This is Hegelian Absolute Idealism -- which Russell and James both opposed.

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4 is wrong. Please try again.

William James's neutral monism (which Russell finds attactive) claims that

    { 1 } - only matter ultimately exists; so-called mental events are chemical processes in your brain.
    { 2 } - the ultimate components of the world are neither mental nor physical, but a kind of "neutral" thing that can be arranged to form either.
    { 3 } - the only thing that exists is the Absolute -- an all-encompassing entity that we are all part of.
    { 4 } - only mental ideas ultimately exist; so-called material objects are complexes of sensations.

This is idealism.

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the end