4D Forms as a Solution to the Problem of Forms and Particulars Joe MacMaster, St. Francis Xavier University Introduction Arguably Plato’s most significant contribution to the world of philosophy is his theory of the forms. These forms are mysterious things which can only be grasped by the intellect as opposed to any sense perception (Timaeus, 28a). Though mysterious, and the basis of much questioning and philosophical discussion, the forms pervade every aspect of our existence. In Phaedo Socrates teaches that after death the philosopher’s soul goes on to the world of the forms (63e-64a). In the Republic Plato uses the Divided Line analogy to explain how the forms are both beyond, and more real than this world (509d-511c). In Timaeus we are introduced to the Receptacle of all Becoming (48e - 49a). In this paper I will argue that for the theory of forms to work, the forms themselves must be four-dimensional objects that intersect our three-dimensional world. My initial reasoning for why this must be the case was to solve the problem presented in Parmenides that if forms can be expressed in different unconnected locations at once, then a form is separate from itself, or that a form is not One. Forms being either separate from themselves, or not One, is contrary to the theory of the forms that Plato seems to posit throughout his works. The 4D form model allows for a form to exist independently, undivided from itself, while also being able to intersect all points of the 3D world without compromising its nature. This theory faces several challenges. A) It is unclear whether this argument works just as an analogy or if it actually how the forms relate to particulars. If it is just a helpful analogy, where exactly does it break down, and what exactly does it explain? B) If the forms actually are 4D objects, what’s to say that two different 4D objects couldn’t appear exactly the same to us as they intersected the 3D world. It seems like the forms must be extremely different from the things we see in the material world for this to be the case either by analogy or literally. In this paper I will argue that the 4D form theory in not just an analogy, but that the forms are in fact 4D objects. I will break this argument into four parts: (1) The necessity of forms as having more than three dimensions. (2) Why this theory must work literally and not just as an analogy. (3) How the forms retain their essence while intersecting this world. (4) Our understanding of the forms is limited
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