The length of bits of wood

A thought occured to me while writing that Dhalgren review:

It should be allowed that:  if two men each believe they possess a true meter-rule, and each accordingly measures distances and arrives at different numbers, neither has any objective way to demonstrate to the other which of their measurement systems is ‘correct’. The most they can do is turn to a friend for corroboration with a third meter-rule.

Or: we judge length with a scale. How do we judge scales? Whatever system we employ is itself just another scale – we see how their scale ‘measures up’ to our scale – but when we do that, they can simply see this as our scale failing to measure up to theirs.

A related but different metaphor: how do we judge which of two sticks is longest when we cannot touch either of them? We can apply our scale to our vision of them, but the answer will vary with respect to where we stand relative to them.

However (and this is the thought I had): while we may not be able to tell objectively which stick is longer than the other, can we not tell when a stick has been extended? If our perspective remains the same during the change, the new stick will always look longer than the old stick!

The application to reviewing is clear: the issue of comparing one book to another may be distinct from the issue of comparing a book to its own potential. So, while we may not be able to say “book a is better than book b” (in an objective way rather than as a statement of taste), perhap we can say “book a would have been better if…”.

This is only possible if:

a) we are right to draw the analogy to Euclidean space, where an extension cannot make something appear smaller from any perspective; and

b) we are right in believing our perspective can remain stationary while the extension occurs; and

c) we are right in believing that we can effect this extension in our minds (ie we can ‘extend’ the stick, not merely create a new stick of a different and purportedly longer length).

This are, obviously, all contentious issues. In the third case, I think the assumption is justified. The A` we imagine has, or can be made to have, no characteristics other than those specified in the A and in our extension, which to me implies that the imagination is indeed of A being extended. Now, it can be objected that unless we create the whole of A` in our heads (eg write the entire new book), what we have is not A` at all but only, so to speak ~A`: a vision that might not reflect the actuality. This is true. However, it seems to me that the issue of how closely the vision meets the hypothetical reality is a plain ignorance problem, not a problem of perspective.*

What does b) mean? Well, if a stick is enlarged at the same time as we move to a new location, the stick may continue to appear the same length to us. BUT: if we bear in mind a second stick in a different location, we will see THAT stick change in length as we move! Thus, we should in theory be able use our view of other sticks to hold our perspective steady as the imagined extension occurs – or at least know when we have failed.

a) seems to me to mean the same as saying that polarity is universal – what we see as a unit of length is always seen as a unit of positive length from any perspective, even if how long it is to other units is not agreed on. Clearly, this is not always true – what I see as a positive, you may see as a negative. However, die-hard relativists should consider closely what a linear framework of this kind actually requires. It does not require objective agreements on magnitude. It does not require a unitary scale: if two scales both have a positive and negative axis, they can both be incorporated into this linear framework without us having to make any prejudicial decisions regarding their interaction or relative significance.

Can linear frameworks be agreed? First order frameworks, based on, eg, utility, clearly cannot be – but I see no reason to think that second-order frameworks (based on, eg, potential for utility) cannot be, at least between large groups of people. To take an example, both utility and freedom have been held up as positives, but there is no consensus on how these scales should be seen as interacting. But for a linear framework, we do not need this: we only need both to be recognised as, prima facie, positive. This seems far more achievable – while probably still not universal.

The practical issue, of course, is that pure extension is rare. In the political example, an extension of liberty often requires an decrease in utility and vice versa, and a linear framework cannot help us here.

As you can see, I’ve hardly worked out the consequences of this thought – but I think that nonetheless it’s an interesting (if very minor) step away from relativism, which allows a greater degree of agreement between people than a fully dimensional analysis. In practice, we can seek to find consensus on polarities, and when we are forced to assume them we can state these assumptions. The significance for book reviews I leave to the (imaginary) reader.

*Ok, this isn’t actually true.


Two other thoughts on those analogies: for the Wittgenstein one, does this mean that which stick is longer than the other can be measured objectively? This, I suppose, does not matter, as the length of the stick is not importance, only the distance measured. If we apply this to the discussion above, what is the implication?

For the Nietzsche: does the analogy of perspectives imply a distant, untouchable, object? If so, how does this interact with the dissolution of the noumenal/phenomenal distinction? Or is this only an artefact of the analogy?

Rambling now…


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