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It is not that common sense should have any more authority in psychology than it does in physics
or astronomy.
But this part of common sense has so much power and precision in
predicting, controlling, and explaining everyday behavior, compared to any alternative ever entertained, that the odds are high that it will be incorporated in some
form into our best scientific theories.

About the part in red, I take it as something like:

common sense should not have any authority in physics, astronomy, or (even) psychology.

Is my interpretation correct?

Plus, about the 'should', how do you interpret it?

1. Used to express obligation or duty: You should send her a note.
2. Used to express probability or expectation: They should arrive at noon.
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Comments  
The complete sentence, IMO, should be:

It is not expected that common sense should have any

Should is in a "that"-related subordinate sentence.
This is formal BrE usage.

Should is required here in the subordinate sentence by the expectation/importance assigned to that thing, its contents (see Swan, should).
Marius HancuThe complete sentence, IMO, should be:

It is not expected that common sense should have any

Should is in a "that"-related subordinate sentence.
This is formal BrE usage.

Should is required here in the subordinate sentence by the expectation/importance assigned to that thing, its contents (see Swan, should).

For your information, here is the original text:

In our daily lives we all predict and explain other people’s behavior from what we think they know and what we think they want. Beliefs and desires are the explanatory tools of our own intuitive psychology, and intuitive psychology is still the most useful and complete science of behavior there is. To predict the vast majority of human acts - going to the refrigerator, getting on the bus, reaching into one's wallet - you don't need to crank through a mathematical model, run a computer simulation of a neural network, or hire a professional psychologist; you can just ask your grandmother.
It is not that common sense should have any more authority in psychology than it does in physics
or astronomy. But this part of common sense has so much power and precision in predicting, controlling, and explaining everyday behavior, compared to any alternative ever entertained, that the odds are high that it will be incorporated in some form into our best scientific theories.

Contextually, I don't think it's ellipsis of 'It is not expected that...' as you suggest.

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Sorry, I don't have time for more discussion here.

But it could be

It is felt that she should ....

(expressing personal opinions also requires should, which Swans describes in the same chapter)
Taka In our daily lives we all predict and explain other people’s behavior from what we think they know and what we think they want. Beliefs and desires are the explanatory tools of our own intuitive psychology, and intuitive psychology is still the most useful and complete science of behavior there is. To predict the vast majority of human acts - going to the refrigerator, getting on the bus, reaching into one's wallet - you don't need to crank through a mathematical model, run a computer simulation of a neural network, or hire a professional psychologist; you can just ask your grandmother.
It is not that common sense should have any more authority in psychology than it does in physics or astronomy. But this part of common sense has so much power and precision in predicting, controlling, and explaining everyday behavior, compared to any alternative ever entertained, that the odds are high that it will be incorporated in some form into our best scientific theories.


My interpretation:

We are not saying that common sense should have any more authority in psychology than it does in physics or astronomy

This does not imply that common sense should have any more authority in psychology than it does in physics or astronomy

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I agree with Anonymous. It doesn't say that common sense should not have ANY influence, that that it should not have MORE in psychology than it goes in those other sciences.
This is what I said:
It is not expected that common sense (1st posting)
We don't feel/We're not of the opinion that common sense
(2nd posting)

This is what anonymous said:
We are not saying that common sense
This does not imply that common sense

I think the meaning is very similar for all four.

Marius HancuThis is what I said:
It is not expected that common sense (1st posting)
We don't feel/We're not of the opinion that common sense
(2nd posting)

This is what anonymous said:
We are not saying that common sense
This does not imply that common sense

I think the meaning is very similar for all four.

They look similar, but actually they are different, and the difference makes the meaning of the 'should' quite different.

According to GG's and Mr. Anonymous's interpretation, the 'should' implies obligation, which is quite different from your understanding of it.

I'd take their interpretation.
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