Does the Infinite Exist?: the Distortion of Language and Self

Does the Infinite exist apart from our thinking it? or is it bound to our cognition? This is similar to other questions in philosophy, such as, whether numbers exist in objective reality or are they simply “in the head” as entities created by human cognition. In this post, I will present two arguments for and against the existence of the Infinite. These arguments will dovetail into one another. The first argument will be an ontological argument. Ontological arguments attempt to prove a position by the meaning of the term alone. In this case the meaning of the Infinite will be used to show that the entity corresponding to the term must exist independent of our minds. The second argument will be a reductio ad absurdum. It will begin with the claim that the Infinite exists—the conclusion of the first argument—and show that this position leads to absurd, untenable results. In the end, I will briefly elucidate the consequences of accepting either position.

The term the Infinite means that which is unbounded.[1] We can think about this concept and understand its meaning. Yet, in thinking about the Infinite, if we suppose that it is confined to our cognition alone—i.e. it does not exist independent of us—then we are not thinking about that which is completely unbounded. After all, an entity which is bound to our cognition is not completely unbounded. Since the Infinite means that which is completely unbounded, the entity we refer to in using the term the Infinite must exist independent of our thinking it.[2] In other words, what we mean by the term the Infinite requires that something actually exist independent of us in order to satisfy the meaning of the term. Therefore, the Infinite exists independent of us.

The Infinite exists and is wholly unbounded. To be wholly unbounded, the Infinite must encompass all that we encounter in experience, viz. the whole cosmos. The Infinite contains all abstract objects and concrete objects, including human agents.[3] However, these entities have distinct properties that demarcate them from one another. For example, human agents have the distinct property of subjectivity—i.e. they are aware of themselves as freely acting subjects with an independent identity separate from other agents and entities.[4] If these various entities truly can be demarcated from one another, and if the Infinite, by definition, must contain them since it is unbounded and encompasses all things, then either the Infinite is not unbounded since it has divisions in itself setting forth various boundaries between various types of entities and human agents, or these various entities and human agents are mere illusions arising from human cognition. It cannot be the case that the Infinite has divisions within itself, since it would not be truly unbounded. Therefore, the entities we encounter in experience, including ourselves as distinct subjects, are merely illusions. The Infinite requires that all reality is one, unbounded whole and since it must exist (see the Ontological argument above) we as human agents cannot have an independent existence over and against each other or other things. It therefore follows that there is no such thing as individual personalities—i.e. your sense of being an independent personality is an illusion—or separate entities, all reality is one; it is all the Infinite.

If these arguments are both sounds and cogent, respectively, what they show is that inherent difficulties result from taking either position. If we conclude that the Infinite actually exists, it follows that we as human agents—as independent personalities which are thinking about the Infinite—do not exist as individuals. All things are metaphysically one. If, on the other hand, we conclude that the Infinite does not exist, then we must conclude that our language is not a reliable guide to reality; for the term the Infinite seems to require a corresponding object independent of us. If our language is unreliable the next natural conclusion would be an epistemic skepticism about what we can know by means of our language. We may suppose that we can deny the existence of the Infinite and rethink the way our language works; in particular, that our language doesn’t have to reliably refer to things in reality, by its terms, in order to grant us knowledge. A language detached from referential relations in this manner may engender greater difficulties than just biting the bullet and maintaining the existence of the Infinite, though. So, we either don’t exist as individuals or, if we do exist, our language is an unreliable guide to reality leadings us into a type of skepticism.[5]

As for my part, I would refer the reader to my previous blog post entitled “The Infinite.” I suggested there that any attempt to speak about the Infinite annihilates our understanding of it. For if the Infinite is truly unbounded, it cannot be encapsulated in a definition or, more broadly, in our language through description. And perhaps this blog has further demonstrated that point. When we attempt to encapsulate such a grandiose entity into our language it distorts it—almost as if it is trying to break free of our concepts, being too large for them, and in the process completely bends the usual boundaries of our linguistic concepts. Further, in the attempt to encapsulate the Infinite it began to bend and warp our sense of self or our sense that we can reliably know the world through our language. In short, whatever the Infinite is, the attempt to encapsulate it in human thinking and language leads to the inevitable distortion of the same. Perhaps Wittgenstein’s wisdom comes radiating through even more brilliantly, “whereof one cannot speak, thereof one must be silent.” Tractatus Logico-Philosophicus.

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[1] See my previous post entitled “the Infinite” for further clarification on this premise.

[2] Kant’s criticism that “exist” is not a true predicate may seem appropriate here. However, when it is observed that the Infinite cannot be bounded in any sense, including bounded to modal contingency, then it seems appropriate to say that the Infinite must “necessarily exist.” Important, necessary existence is a true predicate.

[3] If the Infinite did not encompass all entities then it would have a boundary, viz. a boundary separating it from these entities.

[4] We all have this experience. I experience myself as Judson Burton with certain memories, habits, desires, interests, etc. And I recognize that my identity in all of this is separate from the identity of my wife, Angela. She is an independent person apart from me.
[5] As with all philosophical arguments, these conclusions can be resisted. In a later post, I will take up a response to these arguments to ward of potential skepticism and maintain our common sense notion of the self.

The Infinite

The infinite cannot, by definition, be defined. Our common sense notion of “the infinite,” after all, is that which is unbounded.[1] Paradoxically, this notion is a definition that seeks to contain or encapsulate that which by definition cannot be encapsulated. Oddly, we understand what we are talking about when we use the term, “the infinite.” Yet, in speaking of it, or in defining it, we annihilate our understanding of it by attempting to encapsulate it. Perhaps the best we can do when speaking about the infinite is follow Austrian philosopher Ludwig Wittgenstein’s lead, “whereof one cannot speak, thereof one must be silent.”  Tractatus Logico-Philosophicus.[2]

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[1] It is important to note that the term “the infinite,” uses the definite article, “the” since only one thing could possibly be totally and completely unbounded. If two things were unbounded they would be totally inclusive of each other thereby being the same entity.

[2] I appreciate the recent conversations I’ve had with a close friend which has brought Wittgenstein and a few of his teachings to my awareness.

The Value of an Intelligence in Mormon Thought

Nearly all Western Judeo-Christian religions affirm the value of men and women. The devotees of these faiths oft claim that God is our creator and we are, accordingly, of immeasurable worth. For most of these religions, the value of a particular human being is derived from God. God created all things ex nihilo (i.e. out of nothing) and it is through His creative act that we are constituted in our present form. Whatever value we have is derivative upon God’s prior creative act. God is the author of all things, including our worth as human agents. [1]

But what of a religion that denies creation ex nihilo and the concept that God is the ground of all being? In such a belief system could human souls have value free of God’s complete creative act? Interestingly, Mormons are confronted with such questions. Upon one construal of the teachings of Joseph Smith, Mormonism maintain that human souls are eternal intelligences. [2] As philosopher Sterling McMurrin put it:

“The Mormon concept of man is distinguished from the classical Christian doctrine primarily in its denial that man is essentially and totally a creature of God. This follows from the fundamental thesis of Mormon metaphysics that all primary being is original and uncreated. In contrast to the view of traditional Christianity, both Catholic and Protestant, Mormonism describes all reality in its constituent elements as ultimately uncreated and imperishable. The most important facet of this denial of origins, with radical meaning for the Mormon religion as well as for the theology, is the doctrine that the human self in its essential being is given and uncreated. . . . Whatever is essential to at least the elementary being of the individual person in his full particularity, therefore, existing in the most ultimate and mysterious sense, is uncreated, underived, and unbegun.” The Theological Foundations of the Mormon Religion (Salt Lake City, UT: Signature Books, 2000), 50.

This novel teaching about man leads to the conclusion that we are coeternal with God. As the Prophet Joseph Smith maintained:

“We say that God Himself is a self-existing being. . . . Who told you that man did not exist in like manner upon the same principles? Man does exist upon the same principles. . . . The mind or the intelligence which man possesses is co-equal [co-eternal] with God himself. . . . The intelligence of spirits had no beginning, neither will it have an end. . . . The first principles of man are self-existent with God.” History of the Church of Jesus Christ of Latter-day Saints, Period I, ed. B.H. Roberts (2^nd ed.; Salt Lake City, Deseret News, 1950), VI, 310 – 12.

But, if we are co-eternal with God, what accounts for our value as human agents? God's creative act cannot provide a full explanation since we are not totally his creatures. [3] Therefore, it is apparent that Mormonism must provide an alternate account explaining the value of human agents. Further, in presenting an account, Mormonism cannot reference abstract laws independent of man. Such laws would be timeless, immaterial principles. Importantly, if Joseph's teachings are correct, "there is no such thing as immaterial matter." D&C 131: 7 – 8. [4] A materialistic, monist account, which does not draw upon abstract, immaterial laws, must be offered. Fortunately, a concept used in modern Analytic philosophy known as "supervenience" may provide the necessary tool to render an explanation of how an eternal, self-existent human agent can have value free of God's creative act.

Supervenience is the notion that there cannot be an A-difference without a B-difference. In other words, B-properties supervene on A-properties if two situations identical as to their A-properties are identical as to their B-properties. For a concrete example, imagine a painting, say the Mona Lisa. The painting, as an object, is the B-property. Those physical constituents that make it up, i.e. its atoms and complex molecules which form the canvas and paints, are the A-properties. What supervenience maintains is that if two objects have identical arrangements of A-properties--in this case an identical arrangement of atoms--then the two objects will also be identical as to their B-properties--i.e. they will both be the same painting; the Mona Lisa.

But how is this principle relevant to our inquiry? By recognizing that even if two objects are identical as to their A-properties--the arrangement of their fundamental physical constituents--thereby being identical as to their B-properties--in this case being the same painting, they can still, nevertheless, vary as to their value. This concept may appear complex, but it is quite simple.

Let us say we have the original Mona Lisa sitting in front of us--which was painted under the care of Leonardo da Vinci. Sitting next to it is a particle for particle duplicate. The duplicate was created in a lab by a scientist which scanned the original for its physical composition and made an exact atom for atom copy. They are, accordingly, indistinguishable as to their B-properties, being identical paintings. However, it is clearly the case that the original Mona Lisa is exponentially more valuable than its duplicate. The duplicate may, importantly, still be valuable. Even if the duplicate has a copy, its value is still not of the same degree nor depth as the original. The original is connected up with history in a way that the duplicate is not. As philosopher David Chalmers has pointed out, value is a "context-dependent" property which does not merely supervene, in a local sense, upon the underlying physical A-properties alone. The Conscious Mind: In Search of a Fundamental Theory (New York, NY: Oxford University Press, 1996), 34.

With this principle in hand we can begin to construct a picture as to why human agents are of worth free of God's creative act. To do so, let us take up another thought experiment which runs in parallel to the one above: in this thought experiment, instead of paintings and scientists we will use persons and God. Imagine Jane, an eternal, unbegun intelligence, whom God has decided to make a physically identical (A-property) copy of. Since Mormon thought maintains that our bodies, spirits and the whole of reality is matter, God could arrange the physical properties in such a manner as to create Jane's duplicate. Let us say God decides to do this. he perfectly arranges all the physical constituents to create a particle for particle duplicate of Jane. Duplicate Jane will look the same, speak the same and, likely, will have the same memories. Supposing God could do this, would Jane's duplicate have the same value as Jane? If our reasoning from above holds here, we would say she clearly does not. Importantly, duplicate Jane will still have value since she has been created into a conscious human agent by God. God's creative act accounts for part of our value as well. However, duplicate Jane's value would not be of the same kind, type, nor depth as Jane. Jane is eternal, without beginning. She has been through an eternal history of experiences and has been refined through the corridors of time to arrive at her current station as Jane. Duplicate Jane was brought into being at a later point. She is like the copied Mona Lisa, in a sense. She does not have the same historical context nor the actual-real experiences that Jane has. In fact, none of her experiences are her own. They are the real Jane's experiences. Duplicate Jane's memories are, in this sense, merely an illusion. Lacking the authenticity of Jane, duplicate Jane cannot have the same value.

God cannot, in Mormon thought, make a particle for particle duplicate of us with the same value. [5] Any creation to mimick us would not be eternal, for it would have a beginning whereas we are without beginning. In a real sense, the difference between an eternal being's value and a created being's value is the same difference as between the value of God as a necessary, uncreated being, in traditional Christian thought and the value of human agents as contingent created beings. Mormonism turns the whole picture on its head. We are all eternal. In Mormon thought it is our uncreated nature, therefore, which spans the eternity and accounts for our inherent value. We are the being that God, however powerful, cannot actually replicate. For any duplicate would have a beginning and we are without beginning. In a paradoxical turn, in traditional Christianity the value of souls derives from God's creative act; in Mormonism, the value of souls derives from the fact that God cannot actually create us.

If this understanding of the human agent is correct, then when we look into the face of the other, we are looking down a corridor of time that has no end; and when they look back at us, they are also looking down a similar corridor—almost like two mirrors facing one another. It is perhaps for this reason that the salvation of every soul is so important in Mormonism. After all, Mormonism teaches that we had to take upon ourselves a body since certain knowledge can only be obtained from actual experience. Without the actual experience, the acquisition of that knowledge is not possible. When one agent acquires the knowledge it seems that divine agents can then share than knowledge amongst themselves. This accounts for the fact that Christ was able to “tap-into” our experience in the atonement to learn of our pains. Without our prior experience, there would have been nothing to tap into. It is this type of full knowledge of the other that exemplifies the community of the Gods, in Mormon theology. To borrow a phrase from philosopher Cornelius Plantinga, Jr. “Each member [of the Godhead] is a person, a distinct person, but scarcely an individual or separate or independent person. For the divine life there is no isolation, no insulation, no secretiveness, no fear of being transparent to another. Hence there may be penetrating, inside knowledge of the other as other, but as co-other, loved other, fellow Father, Son, and Spirit are “members one of another” to a superlative and exemplary degree.” “Social Trinity and Tritheism,” in Trinity, Incarnation, and Atonement: Philosophical and Theological Essays, ed. Ronald Feenstra and Cornelius Plantinga Jr. (Notre Dame, Ind.: University of Notre Dame Press, 1989), 28. In Mormonism, this “inside knowledge of the other” is not limited to three; it is multiplied by an innumerable host of human souls who will become divine and share in the divine life in the same way that our Father, his Son Jesus Christ, and the Holy Spirit do.

To sum up, in Mormonism our value as human agents cannot be wholly derivative upon God’s creative act since we are not totally God’s creatures. Instead our value is inherent to the types of beings we are: eternal, everlasting and unbegun. No being, however powerful, can replicate us. We are, as the Mona Lisa, works of art with a history that cannot be duplicated. To look into the face of another is to look into the corridors of limitless time. Importantly, since our value and experiences cannot be duplicated, and since certain knowledge in Mormon thought can only arise from experience, the community of Gods cannot gain access to the stores of our knowledge without us. The salvation of every human agent is therefore of the utmost priority. When even one agent is lost, a potential divine relationship, of “penetrating inside knowledge of the other” is compromised; for only the fully divine have completely opened up the stores of their being to the other. In short, Mormonism provides a powerful image of how we as human agents have value. The image it presents, to my reckoning, is of deeper beauty than traditional Judeo-Christian theologies.

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[1] Some Christian theologies claim that the concept of who we are has existed in the mind of God for all eternity. God determined which agents from those he foreknew in his mind to create. In these traditions, our value may be inherent in the concept of our personhood which God has had within the stores of his mind for time immemorial. However, even in these systems our value is still derivative upon God, since it required a conscious deity to maintain the concept of our being. Without that deity we would not be. See, e.g. the teachings of Luis de Molina, the 16^th Century Jesuit.

[2] The other primary construal of Joseph’s teachings maintains that the spiritual element/intelligence that God made our souls from is eternal. Our particular identity and conscious events are, however, a creation of God. Bruce R. McConkie, among others, maintained this interpretation of Joseph Smith’s teachings. My analysis may not be as relevant to this interpretation. The main thrust of my argument is therefore is geared towards the construal of Joseph’s teachings that views our particular conscious events, our personhood, as eternal—without beginning nor end. For a detailed elaboration on these different interpretations, see Ostler, Blake T., The Idea of Preexistence in Mormon Thought, in Line Upon Line, ed. Gary James Bergera (Salt Lake City: Signature Books, 1989), 127 – 144. For an online edition of the same, see http://www.dialoguejournal.com/wp-content/uploads/sbi/articles/Dialogue_V15N01_61.pdf

[3] God's creative act may provide a partial explanation of our value. Yet, since we are eternal, God is not totally responsible for our existence, and therefore our value, as such. Accordingly, a more holistic account must be provided.
[4] As Truman Madsen noted, the phrase, “there is no such thing as immaterial matter,” is a mere tautology. It is like saying, “there is no such thing as inhuman humans.” It is an obvious logical truth. However, according to Madsen, the correct construal of Joseph’s revelation is “there is no such thing as immaterial [substance].” This would eliminate the substance dualism familiar to traditional Christian religions. If Madsen's construal is correct, which it appears to be, then Joseph taught that all reality is material; there are no entities residing outside of space-time. The physical plane is the whole of reality. See Madsen, Truman G. "The Meaning of Christ – the Truth, The Way, The Life: An Analysis of B.H. Robert's Unpublished Masterwork," BYU Studies 15.3 (1975), 264.
[5] In Mormon thought it is doubtful whether God could even create a conscious duplicate of Jane. However, for purposes of this blog, this way of framing the issue is illustrative. 

Scientific Explanation, Philosophical/Theological "Reasons" and Abstract Entities

A basic, yet crucial, distinction in philosophical explanations concerns the difference between abstract and concrete entities. An abstract entity is not located in space-time and does not stand in causal relations to other entities (e.g. numbers and propositions). A concrete entity is located in space-time and does stand in causal relations to other entities (e.g. rocks, rivers, mountains and stars). Philosophers frequently reference both types of entities when providing explanations for various phenomena. Typically, abstract entities are taken up to explain why concrete entities are the way they are.

For example, Plato invoked forms, abstract entities which explain why things are the way they are, how they are meaningful to us, and how we can recognize disparate instances of them.  A chair, as the theory goes, is meaningful by its participating—this is not a causal relationship as forms qua abstract entities don’t enter into causal relations—in the form of chairness. That form is what we intuit when we look at a chair. It provides an explanation of how the particular chair is meaningful and how we can recognize objects that are completely dissimilar as chairs. Further, in an elaborate myth of how the world was created, Plato posited a demiurge that modeled concrete, physical objects after the intelligible forms. Christians, who appropriated Neo-Platonism would later claim that the forms reside in the mind of God and that God used these intelligible principles to model the world. This schema leads to the beautiful conclusion that whenever you have an experience of meaning—which is during every conscious moment—it is because your consciousness is subtly enveloped in the mind of God in such a way that entities are illuminated for you. Each conscious experience is made possible by being wrapped up into the mind of God—the ground of all Being.

Currently, however, there is a trend amongst the scientifically minded and among philosophers that wish to model philosophical explanations after scientific ones, to completely discredit the existence of abstract entities. Foremost amongst philosophers in this regard is David Armstrong. In arguing for the nonexistence of abstract entities, Armstrong invoked Ockham’s Razor—a primary tool in distinguishing between parsimonious scientific theories and those which are over-encumbered with unneeded explanans (i.e. things which explain). In short, Ockham’s Razor is the requirement that “entities are not to be multiplied without necessity.” Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy (London: Routledge, 1914), 107. Drawing upon this time honored principle, Armstrong levels the following argument against abstract entities:

(1) Abstract entities, unlike concrete entities, do not exist in space-time.

(2) If objects do not exist in space-time they are not causally related to other objects.

(C1) So, even if abstract entities exist, they would make no causal difference to concrete entities. (By modus ponens with the implicit premise that concrete entities are in space and time and thus are causally related).

(C2) Abstract entities, even if they exist, provide no causal explanation for concrete entities.

(C3) Thus, there is no reason to suppose the existence of abstract entities.

See Armstrong, D.M., Nominalism and Realism: Universals and Scientific Realism, vol. 1 (Cambridge: Cambridge University Press, 1978), 130.

This argument, demonstrating no “reason” for the existence of abstract entities, is intended to take us to the conclusion that without a reason for the existence of some entity, we ought not believe that it exists—i.e. we have the epistemic duty to withhold belief. Armstrong’s argument may appear detached from any practical concerns of daily life. However, if his argument succeeds, much of traditional philosophy and western religious theology will have been undermined. Further, the reason that I selected Armstrong’s argument is because it is representative of many attitudes of the scientifically inducted. I have oft heard individuals claim that since science does not need to invoke abstract entities, including God, to explain concrete/physical phenomena, then there is no reason to believe in those things. Armstrong captures with precision these sentiments.

However, Armstrong’s conclusion rests on a questionable inference. C2 speaks of “causal explanations.” Thereafter, Armstrong’s argument abruptly turns to “reasons;” “there is no reason to suppose the existence of abstract entities.” In other words, Armstrong seems to be claiming that causal explanations are the only types of explanations that provide reasons for believing one way or the other. This is unsurprising since scientific theorizing rests, more often than not, upon plotting out the causal connections underlying phenomena as a way of reductively explaining them. Yet, causal explanations are not the only type of explanation which provides “reasons” for believing. The principles in geometry and statistics are used heavily in various scientific fields as bases of scientific explanations. These appropriated principles are often, importantly, not causal. In fact, much of the scientific reasoning underlying all of scientific theorizing (e.g. verificationist and falsificationist schemes) is not causal in nature. Causality is not the only type of explanation which provides reasons for believing things. And even though the scientist qua scientist is urged, more often than not, to ignore non-causal explanations for purposes of the scientific process, we ought not, as the scientifically minded Positivists frequently quipped, mistake our scientific models for reality.

Reality is broader and various forms of explanations, not just causal explanations provided by concrete entities, provide a roadmap in understanding it. The wisest of philosophers and theologians have for centuries recognized this principle. Their struggle to find a rational explanation for reality as such has repeatedly led these sages to posit abstract entities. Does this mean that abstract entities (e.g. numbers, forms and certain notions God) must exist? Well, if the ancients are correct, abstract entities oft provide the very best explanation, and at time the only explanation, for various concrete phenomena. In these extreme instances it appears that they must exist. This philosophical argument has not, importantly, proven that abstract entities do conclusively exist. What is has attempted to demonstrate is that the prevailing attitude which snubs abstract entities as sound principles for explanation, since science doesn’t need to rely on them, rests upon faulty reasoning. Barring stronger arguments from scientific materialists, we should not be ashamed to invoke non-causal, philosophical/theological explanations for the world around us—assuming of course that the explanations we invoke are grounded upon sound reasons.