What makes the material conditional material (also called the material implication)?

What does this logical connective have to do with matter?

Googling doesn't seem to help.

  • Reading Russel's Theory of Implication may help. In the end it is a notion of Russel in order to discriminate simple logic (with natural language in propositions) from proper logic (100% formalized) as far as I understand it, but material vs. formal is really historical, see e.g. here, where it is made clear (some kind of) that the truth value of material implications depend on the content and epistemological questions.
    – Philip Klöcking
    Jul 23, 2016 at 15:19
  • I need the answer for this question what is the material conditional? Mar 26, 2017 at 21:22
  • What is involved in confusing cause and effect Mar 26, 2017 at 21:27
  • I don't think "material" here has anything to do with materialism in the philosophical sense, the usage is more similar to that of the materiality of evidence or witnesses in legal terms, some notion of context-dependent relevance. Note that the truth of a given material implication also depends on the context in the sense of the "domain of discourse"--for ex. if the domain of discourse was a region where all cubes happened to be blue, then "for all X, cube(X)->blue(X)" would be true, but it wouldn't be true in all domains of discourse.
    – Hypnosifl
    Jun 27, 2020 at 21:31

1 Answer 1


The term "material implication" was coined by Russell, who made a distinction between formal and material implication.

Here's a quote from the Principia:

[W]herever [...] one particular proposition is deduced from another, material implication is involved, though as a rule the material implication may be regarded as a particular instance of some formal implication, obtained by giving some constant value to the variable or variables involved in the said formal implication.

So material implication concerns implication between particular propositions, whereas formal implication is supposed to be more general. It doesn't have much to do with matter as in physical stuff, it is material only in the sense of being a particular instance of something.

Nowadays the term "material conditional" just means the familiar conditional with its familiar truth conditions. I don't think that "formal conditional" or "formal implication" is still used though, but maybe others could elaborate.

Also note that there are other conditionals which are not material, like the subjunctive conditional (e.g. "If Oswald had not shot Kennedy, then someone else would have").

  • 3
    The contemporary descendent of the "formal conditional" is the "strict conditional" which was invented by C. I. Lewis in order to try to make the conditional in logic hew more closely to intuitions in natural language. note, however, that Lewis's strict conditional is modal in character, and there was no good semantic theory for modal logic in Russell or Lewis's time.
    – user5172
    Jul 23, 2016 at 15:28
  • See the post is there such a thing as "immaterial implication" for comments and the explanation of "formal implication". Jul 23, 2016 at 17:27
  • You didn't answer my question at all. My question was and still is "what does this logical connective have to do with matter?" I am well aware of the different kinds of conditionals. Just saying that Russell distinguished between two and called one material and the other one formal doesn't settle anything. Jul 24, 2016 at 17:25
  • 1
    @MichaelSmith The downvote is uncalled for. I did answer your question: there's nothing more to it. The name stuck since it was introduced by Russell, that's all. Nothing to do with matter whatsoever. You can also see this: philosophy.stackexchange.com/questions/22376/…
    – E...
    Jul 24, 2016 at 17:27
  • @EliranH I don't really think it reasonable to believe that such an intelligent person as Bertrand Russell would give something a particular name without bothering about what this name would mean naturally. You're essentially saying that he named the two conditionals, and the only thing he bothered to do was make those names different. According to this logic, he could have called one formal and the other one banana-flavored. There has to be some reason he chose material (with its noun form matter) over something else. Jul 24, 2016 at 17:34

You must log in to answer this question.

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