Philosophy Now Forum

Can you, and if so, how, do you translate "should" in propositional logic?

Damags wrote: ↑Mon Oct 01, 2018 5:40 am Can you, and if so, how, do you translate "should" in propositional logic?

In propositional logic you cannot do that. Propositional logic is the logic of sentential connectives, I.e. we are only concerned with connectives such as 'and', 'or', 'not', 'if...then' and 'if and only if'. Propositional logic itself is part of First Order Logic.
For you to express "should" in logic, you will have to go to an extension of classical First Order Logic called modal logic and specifically to a specific branch of modal logic called deontic logic. You can read a bit more about this here: https://en.m.wikipedia.org/wiki/Deontic_logic
I hope this helps.

Damags wrote: ↑Mon Oct 01, 2018 5:40 am Can you, and if so, how, do you translate "should" in propositional logic?

Propositional logic is pointless and deontic logic is even more pointless.

All they do is to substitute symbols for words, and what is the point of that??

If propositional logic were to have a point it would generate some original and interesting theorems that could not be generated in any other way. But it doesn't, hence it is pointless.

A_Seagull wrote: ↑Mon Oct 01, 2018 9:28 pm

Damags wrote: ↑Mon Oct 01, 2018 5:40 am Can you, and if so, how, do you translate "should" in propositional logic?

Propositional logic is pointless and deontic logic is even more pointless.

All they do is to substitute symbols for words, and what is the point of that??

If propositional logic were to have a point it would generate some original and interesting theorems that could not be generated in any other way. But it doesn't, hence it is pointless.

You are wrong. Propositional logic is extremely important in the field of computer science and mathematics. From a web resource the following can be read:

Prof. Jussi Rintanen wrote:The classical propositional logic is the most basic and most widely used logic. It is a notation for Boolean
functions, together with several powerful proof and reasoning methods.
The use of the propositional logic has dramatically increased since the development of powerful search algorithms
and implementation methods since the later 1990ies. Today the logic enjoys extensive use in several areas
of computer science, especially in Computer-Aided Verification and Artificial Intelligence. Its uses in AI include
planning, problem-solving, intelligent control, and diagnosis.
The reason why logics are used is their ability to precisely express data and information, in particular when the
information is partial or incomplete, and some of the implicit consequences of the information must be inferred
to make them explicit.
The propositional logic, as the first known NP-complete problem [Coo71], is used for representing many types
of co-NP-complete and NP-complete combinatorial search problems. Such problems are prevalent in artificial
intelligence as a part of decision-making, problem-solving, planning, and other hard problems.
For many applications equally or even more natural choices would be various more expressive logics, including
the predicate logic or various modal logics. These logics, however, lack the kind of efficient and scalable
algorithms that are available for the classical propositional logic. The existence of high performance algorithms
for reasoning with propositional logic is the main reason for its wide use in computer science.
Reference: https://mycourses.aalto.fi/pluginfile.p ... -logic.pdf

There are a lot of resources on the web which explains the importance of propositional logic nowadays.

Averroes wrote: ↑Wed Oct 03, 2018 10:28 am

A_Seagull wrote: ↑Mon Oct 01, 2018 9:28 pm

Damags wrote: ↑Mon Oct 01, 2018 5:40 am Can you, and if so, how, do you translate "should" in propositional logic?

Propositional logic is pointless and deontic logic is even more pointless.

All they do is to substitute symbols for words, and what is the point of that??

If propositional logic were to have a point it would generate some original and interesting theorems that could not be generated in any other way. But it doesn't, hence it is pointless.

You are wrong. Propositional logic is extremely important in the field of computer science and mathematics. From a web resource the following can be read:

Prof. Jussi Rintanen wrote:The classical propositional logic is the most basic and most widely used logic. It is a notation for Boolean
functions, together with several powerful proof and reasoning methods.
The use of the propositional logic has dramatically increased since the development of powerful search algorithms
and implementation methods since the later 1990ies. Today the logic enjoys extensive use in several areas
of computer science, especially in Computer-Aided Verification and Artificial Intelligence. Its uses in AI include
planning, problem-solving, intelligent control, and diagnosis.
The reason why logics are used is their ability to precisely express data and information, in particular when the
information is partial or incomplete, and some of the implicit consequences of the information must be inferred
to make them explicit.
The propositional logic, as the first known NP-complete problem [Coo71], is used for representing many types
of co-NP-complete and NP-complete combinatorial search problems. Such problems are prevalent in artificial
intelligence as a part of decision-making, problem-solving, planning, and other hard problems.
For many applications equally or even more natural choices would be various more expressive logics, including
the predicate logic or various modal logics. These logics, however, lack the kind of efficient and scalable
algorithms that are available for the classical propositional logic. The existence of high performance algorithms
for reasoning with propositional logic is the main reason for its wide use in computer science.
Reference: https://mycourses.aalto.fi/pluginfile.p ... -logic.pdf

There are a lot of resources on the web which explains the importance of propositional logic nowadays.

Translating words into symbols is important for computing of expert systems or of translating words into instructions.

When I said propositional logic was pointless, I was referring to the field of philosophy.

Great, thanks, the closest I could come up with was If p or q, then q. But then again, that has nothing to do with the contingency associated with "should."

What is propositional logic?

"Should" is the first, second, third person plural and singular conditional mood of the word "shall".

What language do you wish to translate "should" in a proposionally logical context?

In order to answer your question, it would be very helpful if I knew something about propositional logic.