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The phrase "abilities of deduction" is correct and usable in written English.
It can be used when discussing someone's skills or talents in reasoning or drawing conclusions based on available information.
Example: "Her abilities of deduction allowed her to solve the mystery that had baffled everyone else."
Alternatives: "deductive skills" or "powers of deduction".
Exact(1)
In addition, Monk has a brother whose abilities of deduction are even more amazing than his, yet much more geographically limited due to his own personal problems, somewhat in the style of Mycroft Holmes (who is more adept than Sherlock but also notoriously lazy).
Similar(59)
That rising temperature gradually boosts our energy level and alertness which in turn "enhances our executive functioning, our ability to concentrate, and our powers of deduction".
The other half of Holmes' utter genius (apart from actually being a genius) is his ability to pick up details, and then transpose fact into conjecture, using the science of deduction.
Let me begin by psychology of deduction.
The process of deduction goes roughly like this.
Realizing that he should be male took years of deduction.
Includes effect of deduction giveback.
The argument is a piece of deduction.
This valid syllogism Peirce accepted as representative of deduction.
Now let's test your powers of deduction.
This is also a major cause of deduction.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com