Is it possible to get a synoptic view of the ways in which a logic can, so to say, deviate from classical logic?

I think one can find rather easily a list ( though maybe incomplete) of non-classical logics.

But it seems more difficult to find a presentation of the field that exhibits in a systematic fashion under which respects a logic can be non classical.

The respects I can think of are the following :

(1) type of objects over which quantifiers range --> first order/ second order logic

(2) validity of "ex falso" or not --> paraconsistent logics

(3) use of modal operators, or not --> modal logics

(4) finite or infinite number of premises --> compactness ( not sure of this)

There is an attempt at such a presentation in Theodore Sider's book Logic For Philosophy, but I'd be much interested in other references.

Note : I'm not asking for an absolutely complete list of points of departure from clasical logic; I suppose it would be too long. Rather, what interests me is the systematicity of the presentation.

  • 2
    $\begingroup$ Fuzzy logics (where claims can be 'sorta true'. E.g. 'I am tall'), probabilistic logics (claims are not known to be true or false, but we do attach some kind of probability .. not to be confused with fuzzy logics; the fuzziness of 'I am tall' is not a matter of a lack of information, but rather with the vagueness of predicates/slipperyness of concepts), quantum logics (where claims can be both true and false at the same time), infinitary logics (not just number of statements, but also length of statements, and length of derivations) $\endgroup$
    – Bram28
    Nov 11, 2020 at 14:24
  • 1
    $\begingroup$ There are also 3-valued logics (true, false, and unknown). For a systematic taxonomy, maybe put three-valued logic into a class together with fuzzy logic. But again, I am not too sure how to classify probabilistic logics ... they strike me as more pof a modal logic... closer to a kind of epistemic logic. $\endgroup$
    – Bram28
    Nov 11, 2020 at 14:32

1 Answer 1


One attempt at classifying ways to alternate logic could be:

  • extending or restricting the language: This covers the transition to logics of higher order (introducing new types of variables and predicates) or, in the other direction, monadic logic (restricting the language to 1-place predicates), as well as e.g. modal logic (introducing additional modal operators). Of course, an extension of the language always comes with an extension of the semantics.
  • altering the range of semantic values: e.g. many-valued logics, fuzzy logics.
  • altering the semantics of the logical constants: e.g. intuitionistic logic and minimal logic, where $\neg$ does not adhere to the classical truth table semantics, as well as paraconsistent logic, where $\bot$ does not "mean" a proposition from which anything may be inferred.
  • $\begingroup$ The answer takes well into account the spirit of the question. Thanks! $\endgroup$ Nov 11, 2020 at 14:33

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .