Teleology, broadly construed, is the study of design or purpose. Let us say that some object is teleological just in case it has an aim, function or purpose (what I will henceforth refer to as an object’s “telos”). For example, we may say that the telos of a hammer is to drive nails, and that the telos of the eyes is to perceive visual stimuli. Thus, both hammers and eyes may be described as teleological objects. Alternatively, we may say that an object is teleological just in case it displays design. In the case of artefacts, like hammers, the design is due to human ingenuity. In the case of biological systems, like the visual system, the design is due to evolution by natural selection. In sum, the telos of an object is the aim or purpose for which it is designed.
But how are we to formally represent the idea that some object has a telos? I wish to propose a Kripke-style modal semantics that has specific application to teleological objects. For example, let A be “X has eyes” and B be “X perceives visual stimuli”. To say that B is the telos of A means that, if all goes well (e.g., if the visual system is functioning as it ought), B follows from A. Of course, as in the case of blindness, having eyes is not always sufficient for perceiving visual stimuli; B does not always follow from A. In order to preserve the idea that B is the telos of A even in cases in which A is not sufficient for B, we must relativize the sufficiency claim. In keeping with our emphasis on design, we may say that A is prototypically sufficient for B, where the word “prototypical” is treated as a monadic modal operator. I will use □ to represent this operator. The claim that B is the telos of A may be formally represented as follows:
But how are we to formally represent the idea that some object has a telos? I wish to propose a Kripke-style modal semantics that has specific application to teleological objects. For example, let A be “X has eyes” and B be “X perceives visual stimuli”. To say that B is the telos of A means that, if all goes well (e.g., if the visual system is functioning as it ought), B follows from A. Of course, as in the case of blindness, having eyes is not always sufficient for perceiving visual stimuli; B does not always follow from A. In order to preserve the idea that B is the telos of A even in cases in which A is not sufficient for B, we must relativize the sufficiency claim. In keeping with our emphasis on design, we may say that A is prototypically sufficient for B, where the word “prototypical” is treated as a monadic modal operator. I will use □ to represent this operator. The claim that B is the telos of A may be formally represented as follows:
□(A → B) (literally: “prototypically, A is sufficient for B”)
The semantic elements here are in large part analogous to that of standard deontic logic. Roughly, let Γ be a world in which A: “X has eyes” gets ⊤, and let Δ be a world in which B: “X perceives visual stimuli” gets ⊤. We may represent the fact that B is the telos of A in terms of the two-place relation ΓAΔ (literally: “Γ aims at Δ”). I will refer to any world that is aimed at by another world as a “target world”. Target worlds are ones in which the relevant aim, function or goal is fulfilled. The □ and ◊ of standard modal logic becomes:
□P = in all target worlds, it is true that PSignificantly, the □ and ◊ of teleological logic satisfies Aristotle’s modal square of opposition; which is widely taken to be a minimal requirement for a modal logic.
◊P = in some target world, it is true that P
(1A) □P = It is prototypical that P
(1B) ~◊~P = It is not true, in some target world, that not P
(2A) □~P = It is prototypical that not P
(2B) ~◊P = It is not true, in some target world, that P
(3A) ~□~P = It is not prototypical that not P
(3B) ◊P = It is true, in some target world, that P
(4A) ~□P = It is not prototypical that P
(4B) ◊~P = It is true, in some target world, that not P
Each of the above A-B pairs are equivalent. (1) and (2) represent contraries (cannot both be true), and (3) and (4) are subcontraries (cannot both be false). (1) and (3), and (2)and (4), respectively, are subalternatives (the former implies the latter). (1) and (4), and (2) and (3), respectively, are contradictories (cannot have the same truth value). This represents a rough outline of what may be referred to as a teleological (modal) logic. I will have more to say about the axioms, motivations and applications of a teleological logic in future posts.
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