Two-dimensionalism is an approach to

semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comp ...

in analytic philosophy. It is a theory of how to determine the

sense and reference In the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the ...

of a

word A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no conse ...

and the

truth-value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Computing In some progra ...

of a sentence. It is intended to resolve the puzzle: How is it possible to discover empirically that a

necessary truth Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement whic ...

true True most commonly refers to truth, the state of being in congruence with fact or reality. True may also refer to: Places * True, West Virginia, an unincorporated community in the United States * True, Wisconsin, a town in the United States * ...

? Two-dimensionalism provides an analysis of the semantics of words and sentences that makes sense of this possibility. The theory was first developed by

Robert Stalnaker Robert Culp Stalnaker (born 1940) is an American philosopher who is Laurance S. Rockefeller Professor Emeritus of Philosophy at the Massachusetts Institute of Technology. He is a Fellow of the American Academy of Arts and Sciences and a Correspo ...

, but it has been advocated by numerous philosophers since, including

David Chalmers David John Chalmers (; born 20 April 1966) is an Australian philosopher and cognitive scientist specializing in the areas of philosophy of mind and philosophy of language. He is a professor of philosophy and neural science at New York Univers ...

Two-dimensional semantic analysis

Any given sentence, for example, the words, :"Water is H₂O" is taken to express two distinct

proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

s, often referred to as a ''primary intension'' and a ''secondary intension'', which together compose its meaning. The primary intension of a word or sentence is its

sense A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of stimuli. (For example, in the human body, the brain which is part of the central nervous system re ...

, i.e., is the idea or method by which we find its referent. The primary intension of "water" might be a description, such as ''watery stuff''. The thing picked out by the primary intension of "water" could have been otherwise. For example, on some other world where the inhabitants take "water" to mean ''watery stuff'', but, where the chemical make-up of watery stuff is not H₂O, it is not the case that water is H₂O for that world. The ''secondary intension'' of "water" is whatever thing "water" happens to pick out in ''this'' world, whatever that world happens to be. So, if we assign "water" the primary intension ''watery stuff'', then the secondary intension of "water" is H₂O, since H₂O is ''watery stuff'' in this world. The secondary intension of "water" in our world is H₂O, which is H₂O in every world because unlike ''watery stuff'' it is impossible for H₂O to be other than H₂O. When considered according to its secondary intension, "Water is H₂O" is true in every world.

Impact

If two-dimensionalism is workable it solves some very important problems in the philosophy of language.

Saul Kripke Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American philosopher and logician in the analytic tradition. He was a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and em ...

has argued that "Water is H₂O" is an example of a necessary truth which is true '' a posteriori'', since we had to discover that water was H₂O, but given that it is true (which it is) it cannot be false. It would be absurd to claim that something that is water is not H₂O, for these are known to be ''identical''. However, this contention that one and the same proposition can be both a posteriori and necessary is considered absurd by some philosophers (as is Kripke's paired claim that the same proposition can be both

a priori ("from the earlier") and ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. knowledge is independent from current ...

and contingent). For example, Robert Stalnaker's account of knowledge represents knowledge as a relation on

possible world A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their me ...

s, which entails that it is impossible for a proposition to fail to be a priori given that it is necessary. This can be proven as follows: If a proposition ''P'' is necessary it is true in all possible worlds. If ''P'' is true at all possible worlds and what we know are sets of possible worlds, then it is not possible ''not'' to know that ''P'', for ''P'' is the case at all possible worlds in the set of worlds that we know. So if ''P'' is necessary then we know it necessarily, and ''ipso facto'' we know it a priori.Stalnaker, Robert. "Propositions." ''Issues in the Philosophy of Language''. Yale UP, 1976. Under two-dimensionalism, the problem disappears. The primary intension of "Water is H₂O" is the ''a posteriori'' component, since it is contingent that the referent of "water" is H₂O, while the secondary intension is the ''necessary'' component of the sentence, since it is necessary that the stuff we in fact call water is H₂O. Neither intension gives us both a necessary and an ''a posteriori'' component. But one gets the false impression that the sentence expresses a ''necessary a posteriori'' proposition because this single sentence expresses two propositions, one ''a posteriori'' and one ''necessary''.

In the philosophy of mind

Two-dimensional semantics has been used by David Chalmers to counter objections to the various arguments against materialism in the philosophy of mind. Specifically, Chalmers deploys two-dimensional semantics to "bridge the (gap between) epistemic and modal domains" in arguing from knowability or epistemic conceivability to what is necessary or possible (modalities). The reason Chalmers employs two-dimensional semantics is to avoid objections to conceivability implying possibility. For instance, it's claimed that we can conceive of water not having been , but it's not possible that water isn't . Chalmers replies that it ''is'' 1-possible that water wasn't because we can imagine another substance XYZ with watery properties, but it's not 2-possible. Hence, objections to conceivability implying possibility are unfounded when these words are used more carefully. Chalmers then advances the following "two-dimensional argument against materialism". Define P as all physical truths about the universe and Q as a truth about phenomenal experience, such as that someone is conscious. Let "1-possible" refer to possibility relative to primary intension and "2-possible" relative to secondary intension.

# P&~Q is conceivable
zombies A zombie (Haitian French: , ht, zonbi) is a mythological undead corporeal revenant created through the reanimation of a corpse. Zombies are most commonly found in horror and fantasy genre works. The term comes from Haitian folklore, in wh ...
are conceivable] # If P&~Q is conceivable, then P&~Q is 1-possible # If P&~Q is 1-possible, then P&~Q is 2-possible or Neutral monism, Russellian monism is true. # If P&~Q is 2-possible, materialism is false. # Materialism is false or Russellian monism is true.

Criticism

Scott Soames Scott Soames (; born 1945) is an American philosopher. He is a professor of philosophy at the University of Southern California (since 2004), and before that at Princeton University. He specializes in the philosophy of language and the history o ...

is a notable opponent of two-dimensionalism, which he sees as an attempt to revive Russelian–

Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic ph ...

an descriptivism and to overturn what he sees as a "revolution" in semantics begun by Kripke and others. Soames argues that two-dimensionalism stems from a misreading of passages in Kripke (1980) as well as Kaplan (1989).