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I don’t understand the following things from Bertrand Russell's The Problems of Philosophy, page 49-52:

  1. What is meant by “we can only know what is required in order to secure the correspondence.” (green high light). Also, when I say “x can only” that means there are boundaries. What exactly are these boundaries, fleshed out?

  2. “we can know the properties of the relations required to preserve the correspondence with sense-data” — What does "properties of the relations" mean?

  3. What point is being made about time-order seeming to have and really having the same order. He seems to say that orders stay the same. But, for example, lightning and thunder, really happen simultaneously, however, we perceive one after the other. Isn’t that a change in order?

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The key-concept is acquaintance :

We shall say that we have acquaintance with anything of which we are directly aware, without the intermediary of any process of inference or any knowledge of truths. (Russell , The Problems of Philosophy (1912)).

Physical distance, like any other scientific concepts, is not an immediate sense-data.

We do not perceive distance; we infer it through a process: measuring it.

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Here are the paragraphs in question from Russell's The Problems of Philosophy, original pages 49-53 from Wikisource with highlighted portions relevant to the questions:

Assuming that there is physical space, and that it does thus correspond to private spaces, what can we know about it? We can know only what is required in order to secure the correspondence. That is to say, we can know nothing of what it is like in itself, but we can know the sort of arrangement of physical objects which results from their spatial relations. We can know, for example, that the earth and moon and sun are in one straight line during an eclipse, though we cannot know what a physical straight line is in itself, as we know the look of a straight line in our visual space. Thus we come to know much more about the relations of distances in physical space than about the distances themselves; we may know that one distance is greater than another, or that it is along the same straight line as the other, but we cannot have that immediate acquaintance with physical distances that we have with distances in our private spaces, or with colours or sounds or other sense-data. We can know all those things about physical space which a man born blind might know through other people about the space of sight; but the kind of things which a man born blind could never know about the space of sight we also cannot know about physical space. We can know the relations required to preserve the correspondence with sense-data, but we cannot know the nature of the terms between which the relations hold.

With regard to time, our feeling of duration or of the lapse of time is notoriously an unsafe guide as to the time that has elapsed by the clock. Times when we are bored or suffering pain pass slowly, times when we are agreeably occupied pass quickly, and times when we are sleeping pass almost as if they did not exist. Thus, in so far as time is constituted by duration, there is the same necessity for distinguishing a public and a private time as there was in the case of space. But in so far as time consists in an order of before and after, there is no need to make such a distinction; the time-order which events seem to have is, so far as we can see, the same as the time-order which they do have. At any rate no reason can be given for supposing that the two orders are not the same. The same is usually true of space: if a regiment of men are marching along a road, the shape of the regiment will look different from different points of view, but the men will appear arranged in the same order from all points of view. Hence we regard the order as true also in physical space, whereas the shape is only supposed to correspond to the physical space so far as is required for the preservation of the order.

In saying that the time-order which events seem to have is the same as the time-order which they really have, it is necessary to guard against a possible misunderstanding. It must not be supposed that the various states of different physical objects have the same time-order as the sense-data which constitute the perceptions of those objects. Considered as physical objects, the thunder and lightning are simultaneous; that is to say, the lightning is simultaneous with the disturbance of the air in the place where the disturbance begins, namely, where the lightning is. But the sense-datum which we call hearing the thunder does not take place until the disturbance of the air has travelled as far as to where we are.

Let's consider the questions:

  1. What is meant by “we can only know what is required in order to secure the correspondence.” (green high light). Also, when I say “x can only” that means there are boundaries. What exactly are these boundaries, fleshed out?

We are like people born blind with respect to physical space. What we know is our private spaces. There is an assumed correspondence between our private spaces and physical space because we assume "there is physical space".

  1. “we can know the properties of the relations required to preserve the correspondence with sense-data” — What does "properties of the relations" mean?

The "sense-data" is our private space. If there is a physical space that corresponds to our private space, and we assume there is, all we can know about that physical space are how it corresponds with sense-data, that is, what the properties are of the relationship of physical space with our private space of sense-data.

  1. What point is being made about time-order seeming to have and really having the same order. He seems to say that orders stay the same. But, for example, lightning and thunder, really happen simultaneously, however, we perceive one after the other. Isn’t that a change in order?

The thunder and lightning are events that happen simultaneously but the "sense-data" of seeing the lightning and hearing the thunder are different events from the events of lightning striking and the disturbance of the air that starts the thunder. The ordering of these different pairs of events may not be the same.


Reference

Russell, B, The problems of philosophy, Wikisource edition https://en.wikisource.org/wiki/The_Problems_of_Philosophy/Chapter_3

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we can only know what is required in order to secure the correspondence.

means we can only know what we perceive, we can only see an object the way we perceive it, we cannot necessarily know nothing what it is like in itself.

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we can know the properties of the relations required to preserve the correspondence with sense-data

Meaning here we can know what some things we "see" or "feel" through our sense-data, but we cannot grasp what the true form of them are, and cannot fathom to explain something as such to a person without such ability, such as a blind man born without vision, we cannot explain to him what something looks like for he cannot fathom it.

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what point is being made about time-order seeming to have and really having the same order.

The meaning behind "time-order" here is that while things may happen simultaneously, for example the lightning and thunder example here, is to say that there can be a difference between our sense-data of events and the physical science data behind them, When a lightning causes disturbance in the air around it, it instantaneously created a sounds, but when you are further away you experience the aforementioned sounds later, which is to say that "the order of events has changed" in your own sense data, such is indeed true, but in physical science data, it has not because it always starts from the same thing but we simply perceive it later depending on where we are.

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Re. question 1, the preceding assumption is relevant since it makes clear the question is about the relation of map to territory, (private space to physical space).

"Assuming that there is physical space, and that it does thus correspond to private spaces, what can we know about it? We can know only what is required in order to secure the correspondence."

So I will complete the answer with a quote from Gregory Bateson:

What gets onto the map, in fact, is difference, be it a difference in altitude, a difference in vegetation, a difference in population structure, difference in surface, or whatever. Differences are the things that get onto a map.

A difference is a very peculiar and obscure concept. It is certainly not a thing or an event. This piece of paper is different than the wood of this lectern. There are many differences between them - of colour, texture, shape, etc... Of this infinitude, we select a very limited number which become information. In fact, what we mean by information - the elementary unit of information - is a difference which makes a difference. - (Steps to an Ecology of Mind, pp.457-459).

source: web archive

The differences are what is required to secure the correspondence.

Re. question 2: "What does 'properties of relations' mean?" Properties like altitude, a difference in vegetation, etc.

Re. question 3: "Lightning and thunder, really happen simultaneously, but we perceive one after the other. Isn’t that a change in order?"

Presumably Russell is saying that in the private space lightning and thunder is known to happen simultaneously, as they actually do in physical space.

Hence "the time-order which events seem to have is, so far as we can see, the same as the time-order which they do have."

He also says "it must not be supposed that the various [phenomena] have the same time-order as the sense-data which constitute the perceptions of those [phenomena]."

So you hear lightning and thunder separately, you are aware they happen simultaneously, and in physical space they do happen simultaneously.

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