Usage of “this” and “that” in logical and mathematical argumentation

I know that the use of those – [is “those” here correct since it is referring to something I already mentioned?] – words commonly depend upon the (physical) distance to the referring object.

But how do I proceed if there is no physical object to which I am referring?
In particular, in a chain of arguments and conclusions.

For instance:

“… assertion A holds.

-This/That means …

-By this/that we can see…

-With this/that observation

-We can apply this to…”

and so on.

Since I have no feeling for the difference, and expect the rule mentioned in the beginning, I am not sure of the proper use.

My thoughts are:

-If we refer to something previously mentioned, based on the rule, I would be inclined to use “this” since, as it is already mentioned, we “posses” the argument already, thus providing a kind of closeness.

-If we refer to something that will be mentioned subsequently, then as opposed to the argument above I would use “that” since, as it is not yet mentioned, it is still far away, figuratively.


This is quite a difficult question to answer without more specific examples but in general you can use either term.
“This” is usually used when you have just mentioned what this is, ie the line prior.
However both are interchangeable.
“From this, we learn….”
“From that, we learn….”
both could be used for the same terms.
So if you are to use the term “das ist” it can be both “this is” or “that is”.
Unfortunately, it is a case of learning what sounds right and wrong.

Source : Link , Question Author : mr.gaussian , Answer Author : Sean O’Donoghue

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