>Comments after passages
>
>Dace wrote:
>>
>>. If
>> equations could exist in human brains, then what's to stop them from
>> existing on pieces of paper? In other words, you're still taking these
>> things at face value, which means you're conceding that they're eternal
and
>> ideal. We must never give an inch to Plato! Equations have no
>> self-existence. They do not exist on paper or in brains. They are
abstract
>> and exist only to the extent that we imagine them. You only *imagine*
that
>> the equation is written down on the piece of paper. In fact, when you
look
>> at the paper, what your eye sees is just bits of ink. It's the *mind*,
not
>> the eye, that "sees" the equation. In reality, the equation does not
exist
>> except in your mind.
>
>I suppose math teachers do not write equations on the board,
>or project them on screens etc. etc. Things written on paper
>are not
>eternal nor are things in brains. In a sense, however,
>equations are obviously not destroyed when a mathematician
>dies or a piece of paper with an equation on it is burned.
As soon as we except that an equation exists outside of our imagination, then we must take it for what it presents itself as, i.e. timeless, eternal, ideal, absolute, etc. In fact, the reason 2 + 2 = 4 is that the terms are defined such a way that the statement is correct. That's all it is. This equation has no self-existence. It is "true" only when someone is thinking of it. What has self-existence is the logic at the foundation of human mentality. It was because Einstein followed this logic scrupulously that he arrived at e = mc(sq). It's not the equations themselves that are intrinsically real. It's the topology of mentality (temporal, not spatial) that is real in-and-of-itself. Equations are abstract, but the process by which we arrive at correct ones is a self-existent mental form.
>This does not mean I cannot type 5 + 3 = 8. You can
>read that on your screen and recognise that it is true. It
>is not that your mind does something special independently
>of your eyes. YOU recognise it is true, and if you were
>blind you would not recognise it was true (unless there were
>some "translation" into braille or aural format.)
>
What is this "YOU"? Define!
>
> There is a difference between imagining you are seeing an
>equation written on a piece of paper and seeing an equation
>written down on a piece of paper.
Correct. The latter is simple imagination, whereas the former is imagination of imagination.
> Of course you put scare quotes around "imagine",
>"see","mind" so I suppose all this will be regarded as
>irrelevant. But unless you explain what special meaning you
>give to the terms in quotes I haven't got a clue as to what
>you are talking about.
The eye sees pixels. The mind imagines words.
> According to you equations exist only in minds. I have a
>few questions.
> 1) Take the equation x + y = 10. Is there a different
>equation in your mnd and my mind and everyone else's mind
>who reads this? Are there then equations or an equation we
>are talking about?
The meaning of "x + y = 10" is an image in our minds. We create this image through a shared logic, and it is therefore the same for all of us.
> 2) How do I know that the equation in your mind is the
>same as in mine?
>I cannot access your mind. Ditto everyone else who reads the
>equation.
We cannot access each other's minds (as far as I know), but each of our minds is an individuation of an enduring human mentality. In a sense, we already *are* in each other's minds.
> 3) Is the same equation in everyone's mind? And how are we
>to talk about the equation unless we assume this? But each
>"imagination" or "idea" corresponding to what was written
>down will be distinct as in each person's mind. How can this
>be unless there is something called the equation and these
>ideas are but instances or instantiations of the same
>equation in different minds. Of course this gets us back
>to something like Platonism.
Plato believed that ideas are transcendent; they are timeless. In fact, not only are they not eternally real, they're not even temporally real. They have no reality of their own. They exist only to the extent that we imagine them. You might conclude, then, that it's our imagination which is timeless and transcendent. No. It does not exist *beyond* time. It exists *across* time. It's a function of memory, not eternity.
> 4) If the mind sees the equation this seems to imply that
>the equation is something distinct from the mind just as
>when we see something it is not typically the eye except as
>reflected in some external medium such as a mirror. The
>implication of using "see" is that the equation itself is
>not within the mind.
>
When the mind perceives the equation, the equation exists in that mind. It
exists in your mind and then in my mind and nowhere in between. The same
visual cue (x + y = 10) that causes you to formulate the equation in your
mind also causes me to formulate this equation in my mind. That's because
we think the same way. We interpret the same visual cues the same way.
Ted