Two-dimensional semantics
The two-dimensional semantics is a semantic approach, the importance of linguistic utterances possible worlds to analyze time. Accordingly, the intention of utterances made in the actual world can be viewed in two different ways in other possible worlds.
Two-dimensional semantics of indexical expressions
Suppose a person P utters the sentence “It is dark here” in the actual world. In the actual world, this sentence refers to the place where P is and it is true when it is dark there. The following two readings are now available for the semantics of this sentence in other possible worlds:
1. One can assume that the sentence in every possible world relates to the place where it is uttered in the respective world. Its truth value now depends on where P is in the world under consideration. This so-called primary intention picks up the context of the use of the indexical expression "here" from the respective world under consideration. Because it is considered whether the proposition indicated by the utterance of the sentence is true in the world there, it is also referred to as a verificationist intention.
2. One can assume that the sentence relates to the place where it is uttered in the actual world. Its truth value in another possible world depends on whether it is dark there in the place where P is in the actual world. This secondary intention takes the context of the use of the indexical expression from the actual world and, proceeding from this, considers the meaning in other possible worlds. Since the counterfactual worlds are viewed as subordinate to the actual world, one also speaks of subjunctive intention.
With the help of two-dimensional semantics, David Kaplan analyzes indexical expressions and demonstrative pronouns . These would have a general character and a context-dependent content. The character is the way in which the expression in question works, i.e. how it picks out what is designated. The content is what is designated by the individual occurrence of the expression. Two-dimensionality now occurs in that, in the case of the verificationistic intention, the character of the expression in question is considered (in the above example the function of the word "here" to denote the place where it is uttered) and the content in every possible way World is redefined by this character. In the case of the subjunctive intention, however, the content of the expression in question is considered (in the above example the place where P uses “here” in the actual world) and considered across possible worlds.
Two-dimensional semantics and a posteriori necessity
The two-dimensional semantics can also be used for the analysis of necessities a posteriori. When considering the statement “Water is H 2 O”, the following picture emerges.
“Water is H 2 O” is necessarily true considering the subjunctive intention of this statement. We have found out in the actual world that water and H 2 O are identical and, with regard to other possible worlds, we only speak of the fact that a substance there is water if it has the empirical formula H 2 O (and vice versa). Even if, in a counterfactual world, a substance with a molecular formula other than H 2 O were to play exactly the role that water plays in the actual world, it would not be called water.
When considering the verificationist intention, the statement “water is H 2 O” is not necessarily true. Because it is quite possible that in another possible world it turns out that water is a substance with a different structural formula than H 2 O. Suppose that in a possible world that is otherwise identical to the current one, a substance with the structural formula "XYZ" played the role that H 2 O plays in our world. There chemists would have found that the phrase "water is XYZ" is true and the phrase "water is H 2 O" is false.
It should be noted that only in the case of the subjunctive intention “water” is a rigid designator (identifier), that is to say it is the same in all possible worlds. In his consideration of necessities a posteriori, Saul Kripke assumes that certain designators are rigid, because these identifiers can be clearly traced back to the object identified by a causal act of baptism, and that statements of identity with these designators have the modal-logical status of necessity. Kripke assumes that rigid designators have no intention, but only extension mediated by the act of baptism and tradition, and that there are therefore no properties or functions that make something called something with a proper name.
Two-dimensional semantics and philosophy of mind
David Chalmers uses two-dimensional semantics to develop an argument against his form of physicalism, which is classified as Type B materialism . The Type B materialist argues that there is an epistemic gap between psychic phenomena and the physical world, but that the psychic is ontologically traceable back to the physical. So we are not able to say everything about the mind with physical vocabulary, but it is based on a material substance. The Type B materialist therefore at least represents that the spiritual supervises over the material . On the other hand, he does not argue that this relationship can be explained without recourse to categories of qualitative experience . Hence the first two premises of the argument are:
(1) In a world that is physically identical to the actual world, beings that are physically identical to us and that have no qualitative states or that differ from our qualitative states (" zombies ") are impossible.
The type B materialist must assume this because he represents the supervenience relationship characterized above, which implies that differences in qualitative states are only possible if the physical supervenience basis is different.
(2) In a physically identical world to the current one, zombies are imaginable.
This is what the Type B materialist must assume because he does not believe that we can grasp qualitative states by referring to physical states alone. So we can imagine physical similarity and phenomenological dissimilarity of a world.
From (2) results
(3) There is a possible world in which physical similarity and dissimilarity of qualitative experience exist.
This is the case because the type B materialist who does not consider the possibility of grasping qualitative phenomena from physical phenomena to be given can only understand the relationship between the material and the psychological as a necessity a posteriori . The two-dimensional semantics, however, show that necessities can be verified a posteriori as wrong. From (3) follows
(4) There is a possible world that fulfills physical similarity and dissimilarity in qualitative experience.
We have seen above that a world can verify a statement but cannot fulfill it in cases where something other than in our world plays the role of what is designated in the statement, so that this other is verified there as what is designated. In the above example, XYZ plays the role which H 2 O plays in our world and the inhabitants of that world find out that water is XYZ. In order for this to be the case in this case, it would have to be possible to find something that plays the role of the qualitative states in our world in that world, but is different from them. However, this would contradict the materialistic minimum requirement of the type B materialist, which consists in the fact that qualitative phenomena can only differ if physical things differ.
However, (4) and (1) are in direct contradiction to one another. Therefore it arises
(5) Type B materialism is wrong.
Possible ways out could be strong necessities or panpsychism , according to Chalmers . Strong necessities exist a posteriori, but cannot be verified in any possible world. But Chalmers is skeptical whether such necessities can be sensibly constructed. Panpsychism starts with the transition from (3) to (4) and postulates that physically identical worlds could be different in terms of intrinsic properties of matter. These intrinsic properties would be proto-phenomenal and constituted qualitative sensation. This theory would then no longer be classically materialistic, but would be a form of monism in which the physical aspects of substance would not include its spiritual aspects. Thus something else could play the role of our qualitative properties in another world without this world having to be physically different from the actual world.