The most common and most likely answer to this crossword clue is the 7 letter word BOOLEAN
B
O
O
L
E
A
N
More clues leading to the result BOOLEAN
- I disapprove of that thin sort of logic
- Briefly guide into benefit of a certain logic
- Detailed book on network smuggling ecstasy - it could convey the truth
- One old lab developed a logical system of counting
- I disapprove of that list – revealing quality of some online searches
- Criticize unproductive style of algebra
- Without swearing, Scottish group admits error
Buddy explains!

The straight part
We know that "a logical system of counting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a logical system of counting = boolean.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does BOOLEAN mean?
BOOLEAN noun- A variable that can hold a single true/false (1/0) value.
- Of or pertaining to the work of George Boole.
- Pertaining to data items that can have “true” and “false” (or, equivalently, 1 and 0 respectively) as their only possible values and to operations on such values.