How is the nature of logical principles commonly defined in contemporary philosophy?

Question

In contemporary philosophy, how exactly is the nature of logical principles defined? For example, the way I've commonly seen logical principles construed are as true propositions which described the most general laws of reality. The previous definition does seem very intuitive to me; if we understand logical principles as being concerned with truth, and if we accept a correspondence theory of truth, then logical principles simply describe fundamental laws regarding various states of affairs occurring in reality. (e.g. If state of affairs S₁ obtains and state of affairs S₂ obtains, then state of affairs S₃ must also obtain given logical law L).

However, I've mostly heard the previous view expressed among laypersons. I'm interested to know how most philosophers would think about the nature of logical principles.

Answer 1

Your question is a deep one about the very nature of logic. If logical truths are true, what exactly are they true of? And how do we know? There are many possible answers to these questions, and no general agreement among philosophers. Since the literature is pretty huge, I can only briefly summarise the main positions.

1. Simple logical realism would have it that there are logical rules that hold universally and eternally. They may be thought of modally as necessary truths or relations, because they hold everywhere and could not be otherwise. This runs into the difficulty that logicians disagree about many things. Does "All A's are B's" entail "Some A's are B's"? Aristotle says yes; Frege says no. Does "Everything is an F" entail "Something is an F"? Frege says yes; some free logics say no. Are higher order logics really logic? Quine says no. Does the law of excluded middle hold universally? Constructivists say no. Is the principle of explosion correct? Relevance logicians and paraconsistent logicians say no. Some logicians reject quantified modal logic; some reject all modal logic. There are lots of different logics, and on this position one would seem to be committed to saying that all but one are wrong.

2. Another approach bases logic on a priori knowledge, rather than necessity, and holds that logical rules are what allow us to proceed from true premises to a true conclusion without possibility of error, and without additional information. This is open to the same objection as previously. It places a great deal of weight on the power of human intuition, which history has shown to be remarkably fallible. A variation of this emphasises conceptual necessity or analyticity.

3. Some accounts emphasise the concept of formality, since logic appears to be topic-neutral, and we may typically check whether arguments are invalid by systematically substituting terms to see whether the implication continues to hold. This position depends upon there being a way to distinguish between terms that are logical constants (and, or, not, if, etc.) and those that are not. Some believe there is a principled way of distinguishing the logical constants, while others just use a 'laundry list'. Others again reject the idea that logic is essentially formal and maintain that there is a kind of 'material validity' that is logical but not formal.

4. Another approach places prime weight on the concept of proof. Logic involves being able to prove or derive things, so logic can be thought of as what can be proved. This position is consistent with the possibility of there being many logics, since each might have its own proof system. Advocates of this approach like to state the rules of implication in a way that exhibits their harmony and stability and other desirable formal properties. Doing so helps to explain or justify the logic with reference only to its syntactical features. It is open to the objection that formal systems without an intepretation are just games with strings of symbols, and it is the semantics that drives the syntax, not the other way round.

5. A more specialised version of the previous position emphasises computation rather than proof. Logicians may disagree about what is provable, but it is harder to disagree about what constitutes a computation. Computation is fundamentally grounded in what is physically possible. Advocates of this approach place great store by the Curry-Howard correspondence which relates proof and computation.

6. Another important position gives prime place to model theory. This attempts to set up a formal theory of meaning, usually involving some set-theoretical apparatus, and holds that logical truths are true in all structures in the language. In practice this might be explicated as true under all interpretations, or true in all possible worlds, or true in all permutations of the domain. Soundness and completeness proofs exhibit the connection between this approach and number 4 by showing that what is provable is always true, and what is always true is provable respectively. This approach is very common, though its detractors say that the formal theories of meaning are just themselves another kind of syntax, and so the soundness and completeness proofs are question-begging.

7. Another approach is more naturalistic and maintains that logic is continuous with scientific theories, in that it describes relationships, but in a more abstract way that is independent of subject matter. It allows that logic is revisable in the light of empirical discoveries. It holds that, like scientific theories, logic represents our best account of consequential relationships and is justified by surviving our best attempts to subject it to criticism. It is difficult at first to think of logic as empirical, because we do not test logical truths by experiment, but the idea behind this is that logic as a whole (and perhaps mathematics as well) is justified by the contribution it makes to our scientific knowledge.

8. There are some who maintain a version of logical relativism, conventionalism, or even nihilism. Deeply pessimistic given the success and usefulness of logic.

Answer 2

I don't believe that there is wide agreement among contemporary philosophers on the answer to your question. The layperson's position you describe above sounds like logical realism. Logical realism states that there are facts of logic, and these facts are completely independent of us (our minds and our language). If humans had never existed, the law of non-contradiction, excluded middle, identity, De Morgan's theorems, etc. would still be true. Logic is not relative to us humans and our pragmatic purposes; there is "one true logic", and it is so because it describes in the most general way the subject matter of logic in the same way that a scientific realist might say there is "one true theory of everything", because it describes its subject matter (the physical world) in the most general way.

One problem about logical realism is trying to say exactly what logic's subject matter is. Particle physics is about fundamental particles, biology is about living organisms. Logic, as conceived by the realist is about propositions, facts, states of affairs, or some other very general feature of the world. These are controversial entities that are difficult to make sense of in a materialist ontology, so that if materialism is probably true, logical realism is probably false. How compelling this objection is depends on how compelling one finds materialism in the first place.

A second difficulty with logical realism is an epistemological one. Knowledge of logic doesn't seem to be like any other kind of knowledge about the world. Most knowledge about the external world is got at through experience, through theorizing, predicting, testing, and revising our theories. How does knowledge about logic, the most general principles of reality come so easy, while scientific knowledge about the same world comes so tough? Logical realists owe us an epistemological theory that explains this. (This paper sounds like it might discuss this objection, but it's behind a paywall so I cannot say for sure.)

An alternative to logical realism is anti-realism. Anti-realists conceive of the world like an amorphous blob, without any knowable structure. We carve up the amorphous blob-world filtered through our cognitive faculties, using our conceptual schemes and theories. This process of carving up the world is relative to our interests and so there isn't one true way of going about it. What gives logic the "feel" of universality and generality is that it's about the very tools we're using to do the carving. It's about our logical vocabulary; the words "all", "some", "not", "and", "or", "if-then, if-and-only-if", "is-identical-with", etc., are the subject matter of logic, and certain sentences are tautologies and certain arguments are valid because of how we define our logical vocabulary. But the logical vocabulary does not carve the world at its joints, and logic is found in our words, not in the extra-linguistic world. I believe anti-realists also usually endorse the idea that logic is revisable. If a definition (a truth table, for example, in the case of a connective) of some logical term is more appropriate or convenient for some purpose, then we should adopt it instead of the "classical" definition; there is no "one true logic".

This question asks for resources on the realist vs. anti-realist debate for logic. Check out the answer and comments if you want resources to read further!

Answer 3

In my philosophy program (fifteen years ago) I learned to distinguish symbolic logic (a symbolic, or formal language) from philosophy, which relies on meanings derived from natural languages.

I don't think that it's very useful to conflate these two fields of study.

Assertions claimed in natural language differ in their properties from logical "propositions" which are purely symbolic statements. Propositions have no relationship to observable phenomena or dynamic processes! Their meanings are irrelevant to preserving the truths which are given a priori. Philosophy isn't like that.

Although some natural statements (which refer to consensual definitions or operational measures) may be acclaimed as extremely coherent ("A bachelor is an unmarried man"; "If John is taller than Frank and Frank is taller than Jim then John is taller than Jim"), this principle doesn't apply to inductive inferences (that is, science) about unobservable phenomena. (Kant, A Critique of Pure Reason; Popper, Objective Knowledge: an Evolutionary Approach)

"if we accept a correspondence theory of truth"

Don't postmodern (contemporary) theorists reject this theory as untenable?

The objection that may well have been the most effective in causing discontent with the correspondence theory is based on an epistemological concern. In a nutshell, the objection is that a correspondence theory of truth must inevitably lead into skepticism about the external world, because the required correspondence between our thoughts and reality is not ascertainable.

Marian David, Stanford Encyclopedia of Philosophy

"the most general laws of reality"

Umm, physics? I don't know of any philosophy which defines the laws of reality. If jammed into a metaphysical framework I'd vote for a pluralistic approach.