چالش‌های مبناییِ مشترک سه‌بعدگرایی و چهاربعدگرایی: تغییر و بقاء اشیاء مادی؛ یک راه حل فراسازگار

Abstract
The idea that ordinary material objects can change while remaining the same might seem obvious at first. However, some philosophers disagree and find it problematic. There is a serious debate in the literature concerning this problem: “persistence through change (or time)”. In this debate, two rival camps are introduced, each arguing that its interpretation is better than the other's. This discussion can be formulated within two different metaphysical frameworks: three and four-dimensionalism. This paper, in two parts, attempts to show that this metaphysical debate has no champion and that another solution must be sought. The first part addresses the problems with the arguments on both sides of the debate by showing that neither three-dimensionalism nor four-dimensionalism provides a convincing response to certain criticisms. In short, 3Dists fail to explain “Persistence of changing things,” whereas 4Dists are involved in describing how things really “change”. The second part also aims to show that there are more fundamental problems behind this debate that make both approaches problematic. We reveal this fundamental problem by posing a version of the Sorites Paradox. Finally, we show that by using a second-order version of LP (Logic of Paradox), a solution is at hand.
Keywords:The Problem of Change, Persistence through Change, Three-Dimensionalism, Four-Dimensionalism, Sorites Argument, Logic of Paradox
 

Introduction
We all intuitively accept that the material objects around us change, yet remain the same thing as before. For example, if we replace the battery of our watch, we believe that this watch is the very same watch that we received as a gift from a friend 10 years ago. There is also a widely accepted philosophical principle that states, "Two objects are identical if and only if they share all of their properties" (LLI). Here, there appears to be an inconsistency:
•    If things really change, then before and after the change they must be non-identical.
Therefore, if things are non-identical before and after the change, then in fact they have not changed at all.
Thus, the issue that initially appeared obvious is not simple at all. In confronting this issue, an extensive literature has emerged in contemporary metaphysics, which, with a slight lack of precision, may be formulated under the dispute between the three-dimensionalist and four-dimensionalist frameworks. This article is a sketch of that dispute, and an attempt to demonstrate the fundamental problems of both approaches.
Three-Dimensionalism and Four-Dimensionalism and the Problem of the Persistence of Material Objects
Three-dimensionalism and four-dimensionalism are two general metaphysical frameworks that present a general account of the way material objects exist through time; they also provide an interpretation of the real structure of the material object. Indeed, standard three-dimensionalism is the sum of A-theory and presentism in the ontology of time, while standard four-dimensionalism is the sum of B-theory and eternalism. Corresponding to these two metaphysical frameworks are two theories concerning the problem of the persistence of ordinary material objects through change (or time): endurantism, which holds that the object is a three-dimensional entity that is wholly present at every moment of time, that is, the persistence of the object requires that it endure through different times; and perdurantism, which states that the object is a four-dimensional entity, and its persistence through time is due to its temporal parts; in brief, the object perdures through time. If one asks what change means in the 3Dist and 4Dist frameworks, one may answer, for the former, change means that a three-dimensional object passes wholly from one moment to another, and in this transition some of its properties undergo alteration; whereas for the latter, the material object is like a worm extended throughout space-time, and change in it means that each of its temporal parts possesses different properties.
In the literature, there is an important turning point, namely David Lewis' argument from temporary intrinsics. Lewis argues that change is change in the intrinsic properties of an object, and that such a thing entails failure of three-dimensionalism (endurantism) and endorse of four-dimensionalism (perdurantism). How? If an apple was unripe in the spring and became ripe in the summer, and according to endurantism the three-dimensional object is wholly present at every moment, then the apple must be both unripe and ripe, and this is a contradiction. Therefore, Lewis concludes that the material object is a four-dimensional entity possessing temporal parts, one temporal part of which (in the spring) is unripe and another temporal part of which (in the summer) is ripe. In confronting this problem, there are several solutions, all of which have problems:
1.    Presentism + Endurantism → Failure in explaining the persistence of objects.
2.    Non-presentism + Endurantism → The fixity of properties relative to time.
3.    Perdurantism → Changing the subject: there is no such thing as change (in the sense of Alternation).
Although there are criticisms and responses to them in the literature between the two sides of the controversy, the problem with these two approaches is more fundamental. The problem actually lies in the inconsistency between the basic metaphysical and logical assumptions of both frameworks.
Sorites-Style Paradoxes, the 3D and 4D Dispute, and Paraconsistency
It appears that, from a meta-metaphysical perspective, it can be understood that both the standard 3Dist account and the standard 4Dist interpretation of the problem of change contain two incompatible assumptions: the acceptance of bivalent logic and the belief in the truth of LLI. Simultaneously accepting these two foundational assumptions commits us to accepting the undesirable consequences of Sorites-style paradoxes in the discussion of change. If a red object is exposed to sunlight and, over many years, gradually changes color until it ultimately becomes completely white, we must accept that the final object is still red. Why must we accept this? The answer is simple: because in standard logic it is assumed that identity has the properties of transitivity and substitutivity. This challenge has been presented in the literature through different versions of the Puzzle of the Ship of Theseus, and it has been shown that both three-dimensionalists and four-dimensionalists will provide unacceptable answers to this puzzle.
To solve this challenge, various approaches may be presented. This paper proposes that we should initially take a step back and say that change is fundamentally a gradual and inconsistent process. Then, in light of contemporary works in paraconsistent logic, we are able to introduce a second-order version of LP in such a way that, although LLI holds, identity exhibits non-standard (non-transitive) behavior, and for this reason the undesirable consequences of Sorites paradoxes in the discussion of change can be avoided.
Conclusion
The conclusion reached in this paper was formulated in two parts. First, in the dispute between three-dimensionalists and four-dimensionalists, there are serious criticisms and challenges against both sides of the dispute, such that neither side can be regarded as the winner of this controversy. Second, in addition to those criticisms, there is a more fundamental problem before them, and this problem becomes apparent through a meta-metaphysical study of the issue: the inconsistency between their two assumptions (the acceptance of standard logic and the acceptance of LLI), which leads us to accept the undesirable consequences of Sorites paradoxes. Finally, one solution was suggested, namely the acceptance of LP as the underlying logic of metaphysics.
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