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Not so. This "theory" is composed of a number of specific theorems not open to individual interpretation. But the "meaning" of this theory certainly is an individual's prerogative. — jgill
As I said, I believe a theorem is literally the terms that state it. Therefore any and all theories or theorems are open to individual interpretation. Each of us understands them according to one's own experience of learning and practicing. You can state that one must understand the words in a specific way (provide definitions), but then the words of the definitions need definitions, etc., ad infinitum. And we do not avoid the reality of individual interpretation.
But nevertheless, it is real independently of your or my mind or anyone's mind. As Augustine says:
Intelligible objects must be independent of particular minds because they are common to all who think. In coming to grasp them, an individual mind does not alter them in any way, it cannot convert them into its exclusive possessions or transform them into parts of itself. Moreover, the mind discovers them rather than forming or constructing them, and its grasp of them can be more or less adequate. — Wayfarer
I do not accept this argument, because what is common to all who think is that they have ideas, but we all have different ideas. So I think it is wrong to say that we all grasp the same thing, we clearly have different ideas. My discussions on this forum with a number of mathematicians has indicated very clearly to me that we do not even understand basic concepts of arithmetic like "+" and "=" in the very same way as each other. And since there is a multiplicity of number systems we do not even understand symbols like "2" in the very same way.
So I've come to what I believe is a more realistic view, that each mind constructs its own understanding which is unique and particular to the person, dependent on each individual's learning process. This is why standardized education is so important in our societies, to create the degree of sameness in our thinking patterns, which is required for us to properly understand each other, and have standard "concepts". I, for instance, cannot understand 180proof's use of the English language, because the thinking patterns which are supposed to be represented by the words are unintelligible to me.
Which is similar to the kind of Platonism that Frege advocated. The problem for empiricists and materialists is that such 'objects' are non-physical but real, so they can't accept that. In actual fact the fundamental elements of reason itself - ideas, in the true sense - are themselves intellectual in nature, not physical. Our experience and judgement always contains elements of both the sensory and the intellectual, but empiricism will only admit the reality of the sensory and will insist that the intelligible must be dependent on or produced from that (which is then explained with reference to evolutionary theory). But this is a backwards way of looking at it (as explained by Maritain.) — Wayfarer
I definitely agree that the fundamental elements of reasoning are non-physical. But I disagree on the character of these non-physical features, and their position in reality. I believe that the fundamental feature, which is at its base non-physical, is the act of thinking. I also believe in a fundamental difference, a categorical separation between an act, and an object. An act is a change over a temporal duration, while an object is what stays the same over temporal duration.
And this is why the non-physical, which has active existence within the human being, ought not be represented as an object. The active, non-physical element (soul, if you like) uses physical objects as signs or symbols for recognition, but is itself not physical yet still active. Think of this as an activity without an object engaged in the activity, because it is a completely non-physical activity. It does have a physical effect though, it creates the signs and symbols.
Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. — Bertrand Russell, The Problems of Philosophy - The World of Universals
I believe this is exactly what is the case. No two men think the very same thing, nor does one man ever think the very same thing twice. Aristotle made this point in the part of "On The Soul" which we were discussing in the other thread. So Russell's conclusion here is the opposite of what it should be. What leads him to assert an "object" of thought, instead of simply an activity called "thought", is the idea that two different men think the very same thing when thinking whiteness. We do not though, my images of whiteness which I employ when thinking whiteness, are different from yours.
In reality, the "object" of thought is the word, "white". That's what stays the same, as an object, the symbol. And when I hold that object, or a mental representation of it, within my mind, asking what is the meaning of "white", i.e. what is whiteness, I produce images or descriptions, which are not the same as the ones you would produce when asking yourself what is whiteness.
So, for example, no two people can really disagree about fundamental physical laws, like the laws of motion; it's not a matter of opinion how they will determine the outcome of motion. In fact, that is the very meaning of 'objectivity'. But in many areas of science, for example atomic physics and evolutionary theory, there is enormous scope for disagreement about what the theories mean. — Wayfarer
I conclude you have not encountered me discussing fundamental laws of motion on this forum, clear evidence that two people can disagree on such laws. Take Newton's first law of motion for example. People claim it's a brute fact which cannot be otherwise. But I argue that Newton actually stated that the truth of his first law requires the will of God. This is because it is a statement about what has been, in the past, and it assumes the premise that what has been in the past, will continue to be so, into the future, necessarily, if not caused to change. In reality though, the nature of free will demonstrates that we cannot take the continuity of physical existence, from past to future, for granted. When reality is understood in this way, we see Newton's first law in a completely different way. A cause, "God's will" is required for the continuity of existence which we call "inertia". And many theologians and mystics assume that God must recreate the material world anew, at each passing moment of time, so Newton's first law of motion requires the will of God to be true.