There is an evident tension within Wittgenstein’s Tractatus. This tension can be summed up as follows: how much does logic reflect the world/reality and how much –if at all — can logical propositions represent states-of-affairs? Ultimately, this tension boils down to the tension between saying and showing. Wittgenstein claims that what can be shown, cannot be said. The following paper intends to explore this tension, in the hopes of resolving it. The method of resolution will entail an exegesis of the ability of mathematics to not only accurately represent reality/the world (and, specifically, logical form), but also the ability that mathematics gives to human beings to alter and shape [their] reality/world. (5.63) §1 will explicate the above-mentioned tension; §2 will attempt to bridge the gap between saying and showing, through providing explicit examples of mathematics saying things about that which is shown. While it will not be concluded that all merely showable things can be said, it will be concluded that “what can be shown cannot be said” is a largely false proposal; this is because there are many things which mathematics can say, which are directly mappable onto showable things. Most jarringly, I will show that what Wittgenstein says is explicitly unsayable –i.e., logical form — is indeed sayable through mathematical propositions. In §3, in light of the conclusions drawn from §2, I will analyze the following inter-related claims: “The limits of my language mean the limits of my world,” (5.6) “Logic fills the world: the limits of the world are also its limits.” (5.61) The primary point of §3 is realizing that, once it has been established that what can be shown can also be said, many of the core propositions contained in the Tractatus must be radically altered. The Tractatus implies that logic and language respectively are limited. In light of the observations made in §2, §3 will challenge the existence of such limits. Drawing from both mathematical examples and examples from modern physics, this section will conclude that if there are limits to logic and the world, it isn’t clear at all just how limited they are; in light of this lack of clarity, from a mathematical, physical, and probabilistic standpoint, it is quite plausible to believe that there are not any limits to logic and language, thus making the/our world limitless –thereby altering the notion that “the contemplation of the world sub specie aeterni is its contemplation as a limited whole,” (6.45) as sub specie aeterni as the contemplation of the world as an unlimited whole –which I will utilize Spinoza’s Ethics to illustrate; given our ability to speak about the unlimited nature of the/our world –which, I will draw from my own work on Spinoza/Heidegger to further explicate — I will argue that the contemplation of the world as sub specie aterni is not an unspeakable and mystical feeling, but one that is at the very core of our Being –our Being in its “average everydayness” as Heidegger puts it. Finally, in § 4, I wish to highlight why this is important –namely, that what is most important to us (i.e., being present/the feeling of eternity, ethics, aesthetics, meaning and other things commonly associated with mysticism) is not mystical and rare, but is proximal; it only seems rare due to our embeddedness in our everyday lives –i.e., we take these things for granted. Once we are able to grasp this, and cease our unnecessary blindness regarding these matters, we become more capable of virtue –as, insofar as we are blind to these matters, we have less power over our own ability to think and act towards our teleological ends, which is the pre-cursor to virtue.
§1: The Tension between Saying and Showing
One of the core conclusions of Wittgenstein’s Tractatus is that all logical propositions are tautologies. (6.1) Tautologies are propositions that are true no matter what — for instance, “I am eating, or I am not eating” is a tautology. Tautologies, according to Wittgenstein, are “senseless.” In light of this, par Wittgenstein, all of the propositions of logic are senseless — meaning, that their truth-conditions are the same in all cases. In light of this, Wittgenstein believes that all of the propositions of logic essentially say nothing — as they do not represent any situation/state-of-affairs in reality/the world. (4.461–4.462; 6.11) Nor can they represent logical form, or the form of atomic propositions. According to Wittgenstein, “Mathematics is a logical method,” (6.2) and “mathematics is a method of logic.” (6.234) Through syllogism, this must mean that all of the propositions of mathematics are also senseless.
Yet, there is a paradoxical hint of skepticism towards the senselessness of logic in the Tractatus. “Logic is not a theory but a reflexion of the world.” (6.13) And this hint of skepticism is quite consistent with many of the propositions in the Tractatus. Namely, it is consistent with the notion that logic (or, “logical space”, as Wittgenstein often calls it), language and the world are all metaphysical concepts which run parallel to one another. There are several ways in which this ontology is made clear in the Tractatus. A salient example here is Wittgenstein’s views surrounding pictures. Pictures are essentially anything that can represent facts/states-of-affairs. (2.1) Let’s say, for instance, that as I leave the café I am currently sitting in, I encounter a horse. Now, this encountering of a horse is a true fact –it is something that has actually occurred. Now, if I go home and either draw a picture of this horse, write about this horse, or maybe even speak about this horse to my girlfriend, all of these are examples of Wittgensteinian pictures. Now, according to the Tractatus, such pictures of this horse necessarily share something in common with the actual horse that I encountered outside of the café. Namely, the picture of the horse and the actual horse share a logical form –the logical form of language mirrors the logical form of the world. (2.18) How to determine the accuracy of a picture regarding how much it mirrors reality is quite simple: “In order to discover whether the picture is true or false we must compare it with reality.” (2.223) This observation is synonymous to a core ontological claim of Spinoza’ Ethics, wherein thought and extension are considered one and the same. (E2P7)
4.462 represents Wittgenstein’s worries about the ability of logic to say things — i.e. The ability for logic to represent states-of-affairs/true facts regarding reality. Logic cannot represent states-of-affairs, logic cannot represent logical form, and the logic of facts cannot be represented, according to Wittgenstein. (4.0312) By contrast, 6.13 affirms that logic is a transcendental reflection of the world — this can be understood as saying that the logical form of the world is something that is shown. Hence, what is being said here, is that despite the fact that there is a logical form to the world, it is only shown, and it cannot be said. The logical form of the world is, so to speak, ineffable.
There is tension in the ability of logic to represent the world. The idea Wittgenstein lets on, is that logical propositions cannot represent the world, but rather that the logical form of the world is something that shows itself. It is clear, however, that Wittgenstein believes that logic is a crucial component of the world — i.e., Logic is what set’s the world’s limits and coherence. (5.61) Facts exist in logical space –there are no facts that exist within the “illogical” because all possibility resides in that which can be thought (3.02), and thoughts are necessarily logical. (5.4731) The ontological grounding for the possibility of all states-of-affairs rests in their logical form — which consists of the internal logical properties of objects, which determines their ability to relate and combine with other objects. (4.124) Therefore, the propositions of mathematics and logic cannot say anything of substance about states-of-affairs, nor the logical form of the world and propositions. Such is the basis of the following claim: “What can be shown cannot be said.” (4.1212) Par Wittgenstein, what mathematics and logic are trying to talk about are phenomena that shows itself –i.e., “unspeakable” phenomena. In light of this, the proposition of mathematics and logic say nothing. (6.11)
§2 Mathematics Representing States-of-Affairs and Logical Form as Being-Spoken-Of:
How true is the claim made in 4.1212, however? It seems fairly obvious that we can talk about things that show themselves. And it is quite often the case that such talk entails the usage of mathematics as our mode of expression. For instance, modern science cannot operate without the help of mathematics and its propositions. When one is doing physics for example, — i.e., attempting to understand the nature of reality — one is not necessarily conducting experiments — though, of course, this is one part of how science is done. Quite often, instead, one is doing math, which as Wittgenstein rightly points out, is not the same as doing experiments; (6.233I) the former is a logical activity, while the latter is an empirical activity.
Indeed, there are many cases wherein phenomena show themselves, but our only way of accurately grasping what this showing is, is through mathematics. Which is to say, our grasp of certain states-of-affairs is largely dependent upon mathematics. This, right off the bat, negates Wittgenstein’s proposal that logic cannot represent any state-of-affairs. (4.0312)
To give an example of mathematics’ ability to represent states-of-affairs we can look at an example that Wittgenstein himself borrows from David Hume. This is the example of the sun rising every day. “That the sun will rise to-morrow, is a hypothesis; and that means that we do not know whether it will rise.” (6.36311) At the core of Wittgenstein’s skepticism is his skepticism regarding the authority of the “laws of nature.” “At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena.” (6.371) The content of his skepticism, is rooted in the purported ability of the laws of nature to be causal laws — ones which are necessary, rather than contingent. Causality –at least with reference to induction and empirical observations — , for Wittgenstein, is merely a pragmatic illusion that has little basis in logic –there is no logical necessity to the supposition that the sun will rise tomorrow, on such a view. (5.1362)
However, is it not the case that mathematics can represent that the sun will rise tomorrow and why it will continue to rise every day? Yes, it can. As Karl Popper pointed out, scientific observations –the sun rising, being one such observation — are not purely based on inductive inferences –as Wittgenstein assumes it does. Science does not operate like Epicurean epistemology, wherein what is commonly observed is what is true and therein causally true; rather, the logic of scientific proposals are deductive in their nature. True conclusions drawn by scientists cannot be drawn without a proper mathematical analysis of a given set of phenomena –that is the purpose which meta-analyses serve. Thus, there is something truthful in the notion that the sun rising every day is merely a hypothesis –that is, insofar as we are only coming to this conclusion simply because we see it continue to rise every morning. (6.36311) However, the corollary to this statement, which states “that means that we do not know whether it will rise,” is false. The hypothesis that the sun will rise is one that, on the one hand, has been proven through countless repeatable experiments to be true –which is Popper’s criteria for our ability to know the truth or falsity of a scientific proposition. Such insights on deduction, are in fact something which we can even draw directly from Hume’s skepticism of induction. As Russell noted,
Hume’s skepticism rests entirely upon his rejection of the principle of induction. The principle of induction, as applied to causation, says that, if A has been found very often accompanied or followed by B, then it is probable that on the next occasion on which A is observed, it will be accompanied or followed by B. If the principle is to be adequate, a sufficient number of instances must make the probability not far short of certainty. If this principle, or any other from which it can be deduced, is true, then the casual inferences which Hume rejects are valid, not indeed as giving certainty, but as giving a sufficient probability for practical purposes. If this principle is not true, every attempt to arrive at general scientific laws from particular observations is fallacious, and Hume’s skepticism is inescapable for an empiricist. The principle itself cannot, of course, without circularity, be inferred from observed uniformities, since it is required to justify any such inference. It must, therefore, be, or be deduced from, an independent principle not based on experience. To this extent, Hume has proved that pure empiricism is not a sufficient basis for science.
What, then, is a sufficient basis for science? Experience alone is not –this is quite a fair point to make. Rather, it is when experiential observations that are notably recurrent are understood logically and/or mathematically, that we can say we have a sufficient basis for science. That is, when logical necessity underpins our observations and the propositions associated with them, the truth-conditions of said propositions become justified — not just in a practical sense, but in a sense of certainty.
Such a claim, however, might be perceived as a slight on science. After all, if experiential observations are logically/mathematically vetted, doesn’t this make them tautological and therefore not scientific? The addition of mathematics and logic in the structure of scientific propositions doesn’t entail tautologies. How might this be? It is often believed that all science is capable of doing is failing to disprove things, rather than establishing proven facts. In light of this, we might be satisfied by merely citing what the evolutionary biologist Richard Dawkins calls a “scientific theorum.” Namely, the fact that scientific facts are “supported by massive quantities of evidence, accepted by all informed observers, undisputed facts in the ordinary sense of the word.” For the more “pedantic” amongst us, this might not suffice; after all, “it is undeniably possible that our measuring instruments, and the sense organs with which we read them, are the victims of a massive confidence trick.” But “given the evidence now available, for evolution to be anything other than a fact would require a similar confidence trick by the creator, something few theists would wish to credit.” Science isn’t as much of a contextually contingent paradigm as Thomas Kuhn theorized that it was: just like evolution by natural selection, the existence of DNA and micro-biological organisms are not merely speculatory hypotheses; it would be quite a spectacle –the odds of which occurring are extremely improbable (creator confidence trick-level improbable) — if the existence of DNA and micro-biological life were somehow disproven by a paradigm shift. When we speak of the immense weight of the evidence of these scientific discoveries, we are not merely speaking about empirical observations; rather, we are speaking about complicated statistical analyses (i.e., mathematical/logical propositions) of endless observations, that prove where the weight of the evidence rests. When these statistical analyses (which are predicated on logical laws) conclude that things like evolution by natural selection, DNA and micro-biological organisms exist, that is where the notion of “evidence” and epistemic justification bottoms out –there is no further analysis possible on such matters. How can this be? Wittgenstein has a helpful answer: “It is clear that the laws of logic cannot themselves obey further logical laws.” (6.123) Thus, when the sun rises every day, we know it will tomorrow, because statistically speaking, it has been proven to do so –this is even to the point to where we now have a good idea of when the sun will no longer rise every day–or, more accurately, scientists know that in a few million years, the Earth will stop rotating and the sun will eventually explode. These are empirical observations, surely, but they are grounded in mathematical propositions –which, if Wittgenstein is right regarding their tautological nature, are true in all cases. This doesn’t mean that such propositions say nothing: rather, it is that they are saying what is shown. In such instances, the propositions which are being made are causal in nature –as, if they were merely correlations, they would not be true in all cases.
Hence, something which is shown can be said. Wittgenstein might object to this rebuttal with the following: “Mathematical propositions express no thoughts.,” and therefore, mathematics cannot say anything. (6.21) Wittgenstein’s justification for saying that mathematical propositions express no thoughts, is because his conception of what thoughts are consists of propositions, which, in his mind, are by their very nature purely linguistic. (3.5–4.002) Mathematics does not operate through the mode of propositions, but instead, operates through equations. (6.2)
But does this really mean that mathematical propositions cannot express thoughts? Are thoughts essentially linguistic and propositional? There are, indeed, some ways one can utilize propositions from the Tractatus itself to show that thoughts are not merely linguistic. For instance, “The logical picture of the facts is the thought.” (3) Now, as has been stated in §1, a picture is any representation of reality, regardless of what it is. (2.12) A literal drawing of a horse is a picture of a horse. The word “horse” is a picture of a horse.” So too with any mathematical representation of a horse –let’s say, for instance, that the horse was running and we measured its speed (having written down “the horse is going x MPH” is a picture of the horse that is represented mathematically through numbers). How, then, could mathematical propositions — which, in essence, are very often logical pictures of facts — not be thoughts?
To give another example, Wittgenstein himself in his Remarks on Logical Form changes his tone regarding the ability of mathematics — and thereby, logic — to represent states-of-affairs. In this paper, Wittgenstein draws the following system of co-ordinates:
Now, it is quite fair to say that “‘[6–9, 3–8]’ represents ‘P’” is a mathematical proposition. Why might this be fair to state? In order to qualify this, we must ask “what is the definition of a proposition?” The Tractatus can help clarify this: “In the proposition the thought is expressed perceptibly through the senses.” (3.1) It has already been established that mathematical provisions convey thoughts. And it is clear here, that this system of co-ordinates expresses a thought (which represents a state-of-affairs) — namely, that “P” resides at a certain place in space — perceptibly through the senses — i.e. On the co-ordinate plane itself. In this case, [6–9, 3–8] as representing P is a proposition. In light of this, the notion of what a mathematical proposition constitutes is expanded beyond mere equations — which Wittgenstein in the Tractatus narrows mathematical propositions down to. (6.2) “The system of co-ordinates here is part of the mode of expression; it is part of the projection by which the reality is projected into our symbolism.”
Again, in his Remarks on Logical Form, Wittgenstein makes an even more radical claim about the utility of mathematics in its ability to say things. Specifically, he believes that mathematics is crucial in our ability to talk about that which in the Tractatus is deemed completely unspeakable: the form of atomic propositions (i.e. logical form). In the Tractatus, Wittgenstein asserts that logical form is something that is only shown [in language] but it is not something that can be expressed by language. (4.121) However in his Remarks on Logical Form, Wittgenstein heavily implies that logical form is indeed something that can be expressed; namely, through numbers: “The occurrence of numbers in the forms of atomic propositions is, in my opinion, not merely a feature of a special symbolism, but an essential and, consequently, unavoidable feature of the representation.” (166) Indeed, Wittgenstein goes beyond merely implying that logical form can be expressed: in fact, he gives explicit examples of logical form. Specifically, he talks about the mutual exclusivity of atomic propositions. (168) Such mutual exclusivity is a matter difference of degree between atomic propositions — which is a property that is internal to these propositions. For example, take the following proposition: “x is in the chair.” Let’s say that x is “Daniel.” “Daniel is in the chair” is a perfectly logical and coherent proposition. Another statement: “y is in the chair.” Let’s say that y is “Bob.” Again, “Bob is in the chair” is a totally logical and coherent proposition. There is a commonality between these two propositions: namely, their symbolic representation, “( ) is in the chair,” or “( )PT.”[i] As Wittgenstein notes, “ ‘( )PT’ leaves room for only one entity –in the same sense, in fact, in which we say that there is room for one person in a chair.” (169) In the first case, only Daniel is capable of being in the chair, and in the second, only Bob; there is no place for both Daniel and Bob to be in the same chair –this is an observation regarding the quantitive ability of variables to fit or not to fit into specific propositions. If this chair, instead, was a couch, perhaps the statement might change to the following: “( , )PT,” there in allowing x and y to fit into the same place at the same time –while, any added variable (say, “z”) would not fit.
Hence, XPT and YPT in the chair scenario are mutually exclusive, as ( )PT is a proposition that only leaves room for one variable. They are, so to speak, “colliding.” This is an observation regarding the logical form of a proposition (propositions, which routinely express states-of-affairs)–namely, that part of the logical form of propositions entails the quality of propositions having “degrees” of mutual exclusivity; the numerical necessity of only one variable being able to “fit” is an explicit facet of the logical form of “( )PT.”
§ 3: What is Shown, Can Be Said: Sub Specie Aeterni as our Average Everyday Being
§2 illuminated the power of mathematics to represent states-of-affairs, and therefore, logic’s ability to represent states-of-affairs. Likewise, §2 showcased the ability of mathematics –and therefore, also the ability of logic — to represent logical form; which is to say, mathematics and logic can say things about logical form. Hence, the idea that “what can be shown cannot be said,” (4.1212) is a largely false notion. So too with the notion that logic and mathematics say nothing.
In light of these observations, I would like to shift our attention over to another core claim of the Tractatus. Namely, two inter-related claims: “The limits of my language mean the limits of my world,” (5.6) and “Logic fills the world: the limits of the world are also its limits.” (5.61) The Tractatus makes it quite clear that the/our world is limited. Not only in 5.6 and 5.61 but elsewhere as well: for instance, Wittgenstein states that there is a limited number of possible propositions. (4.51) Wittgenstein’s theory of numbers is a form of finitism, inasmuch as it only accounts for finite numbers, rendering such a theory limited. (6.02) Even empirical reality itself is limited, according to Wittgenstein. (5.5561) The limited nature of the world, logic, language, and reality –and our supposed inability to speak about these things in any clear manner — leads Wittgenstein to conclude that, it isn’t so much that these concepts don’t exist (indeed, along with ethics and aesthetics, they are arguably the most important concepts) but rather that these concepts belong in the realm of mysticism –i.e., in the realm of the merely showable, not the expressible. As Russell points out, a huge justification for Wittgenstein’s propositions regarding mysticism and its ineffability is the supposed inexpressibility of logical form. (pp. 18)
In Russell’s introduction to the Tractatus, he shares the following thoughts on the inexpressibility of “shown” things as being mystical: “It may be that this defense is adequate, but, for my part, I confess that it leaves me with a certain sense of intellectual discomfort.” (pp. 18) In light of the observations made in §2 –that things which are shown, can be spoken about (including logical form), and that the propositions of logic can represent states-of-affairs) I share such sentiments with Russell. However, there is a salient point that Russell brings up in his introduction that bolsters Wittgenstein’s ideas surrounding mysticism, which has yet to be mentioned in this paper. That is the problem of generality. For Wittgenstein, the world as a [limited] whole –the [limited]totality of all facts — is something that can only be conceived of mystically: “The contemplation of the world sub specie aeterni is its contemplation as a limited whole. The feeling of the world as a limited whole is the mystical feeling.” (6.45)
It seems like a quite fair point to believe that we cannot speak about the totality of facts in the world. “The world” as a general notion, seems on the surface to be far too broad for the human mind to grasp. For instance, try formulating a sentence that can really explicate all of the possible facts in the world or the world as a general concept; such a task would be, to put it mildly, beleaguering. Yet, in terms of “speaking,” Wittgenstein limits himself here to ordinary language and in doing so, takes the supposed limited nature of reality for granted. As Russell points out,
These difficulties suggest to my mind some such possibility as this: that every language has, as Mr. Wittgenstein says, a structure concerning which, in the language, nothing can be said, but that there may be another language dealing with the structure of the first language, and having itself a new structure, and that to this hierarchy of languages there may be no limit.
And now that we’ve established in §2 that mathematical propositions can say things about states-of-affairs and logical form –i.e., mathematics can serve as this other “language dealing with the structure of the first language.” Mathematics as a language that can deal with the structure of other languages throws the notion that the world –insofar as it is and is shown — and our ability to talk it are limited into question.
Why might this be? Mathematics, as a mode of logic that can express states-of-affairs and logical form, does not exclusively deal with finite notions. Rather, it also deals with infinite notions –“infinity”, being a notion which the Tractatus is clearly skeptical of. In both pure logic and in mathematics, infinity is a notion that is commonplace –nor is this commonality merely theoretical, speculative or abstract (as we will see, it is a necessary notion in the development of pragmatic tools, such as computing and other technology and it is a necessary notion in the ability of modern physics to understand the nature of reality.)
There are various reasons to believe that the concept of “infinity” is a salient and very real property of reality. Many of these reasons can be derived from modern physics. And within the context of the Tractatus, it should not be moot point to argue from the purview of science. Scientists are quite modest with their ontological proposals –they are quite willing to be proven otherwise and do not hedge all of their bets on making everything “appear as though everything were explained”, despite Wittgenstein’s evident disbelief in such modesty. (6.371–6.372) Indeed, even with the salience of “infinity” in modern physics, physicists will routinely admit that “our minds may not be able to easily comprehend infinites.” Nonetheless, “that doesn’t tell us infinites don’t exist.”
With regard to pure logic, we need only look to the infinite regress. Given that the infinite regress depends upon causality, we need only look back at our observations made in §2 regarding Wittgenstein’s example of the sun rising every day to nullify his skepticism regarding causality, so as to make this point. It is widely believed in modern physics that the process by which the universe came about is much more akin to an infinite regress than to a cosmological argument that negates the possibility of an infinite regress by the inculcation of a “first cause.” Next, to cite Heisenberg’s Uncertainty Principle, particles can –in principle — carry an infinite amount of energy, due to their ability to pop in and out of “existence,” so to speak –in light of this, it is now a task of modern physics to define the total energy in the universe in a way that will accommodate an infinite spatial extent. Finally, from the standpoint of modern physics, there are very good reasons to believe that the universe –if not universes — is infinite. At the very least, we know that the universe is rapidly expanding (indeed, expanding at the threshold of being faster than the speed of light, the speed of which physicists believe will only increase) and is not static, hence, its limits are not clear. It might even be that if we have a spatially finite universe, we might have a temporally infinite universe –one which expands and contracts ad infinitum. One thing that should be mentioned in light of the findings of modern physics is to avoid the assumption that because the universe is not static, that it had a beginning. We are only able to see this supposed “beginning” –i.e. the big bang — because of the place and time for which we exist in the universe; due to the expanding nature of the universe, there will be a time where the big bang and all of the evidence for its existence is no longer observable from our purview. Finally, it is widely speculated that there was “nothing” –which, from a Parmenidean standpoint of non-contradiction, amounts to “something” — before the big-bang. This “nothing” according to the theoretical physicist Lawrence Krauss, was something that was potentially “infinitesimally small; “to quote Krauss, “based on everything we know about the universe, is the possibility that the future, perhaps the infinite future, is one in which nothingness will once again reign.” This doesn’t mean that the universe had a beginning or will have an end. Rather, it means that the universe is in an infinite flux in its spatial size. Denoting limits on the world is preliminary and due to the mounting evidence from physicists, is growing more and more implausible.
With regard to mathematics, as Russell points out, the system in the Tractatus is only capable of dealing with finite numbers. (17) I, however, am not as confident as Russell was, that Wittgenstein’s system can survive with the inclusion of infinite numbers. For, under the logical system of the Tractatus, the world and logic are necessarily limited; mathematics with the inclusion of infinite numbers, is necessarily unlimited. What does “infinity” mean? It is that which represents what is boundless/endless. Things like infinite numbers, infinite sets, and infinity with respect to geometrical concepts in Euclidian space. To give such a geometrical example, “I believe that I perceive something drawn very fine in a segment of a series, a characteristic design, which only needs the addition of “and so on”, in order to reach to infinity.” (§229 Philosophical Investigations) Why should we care that mathematics can establish that the notion of “infinity” is a valid notion in this context? It is because mathematics –including its use of the notion of infinity — is an integral tool to our Being-in-the-world. In other words, our pragmatic orientation towards the/our world (and even our merely our wish to understand the world) as such would be far less efficient without the profound power of mathematics to accurately represent reality. Physics, for instance, requires calculus to operate, and calculus requires the concept of infinity to operate. And our understanding of physics is largely responsible for our immense ability as a species to make advances in technology.
However, even in light of such mathematical, physical, and logical observations on the existence of infinity –and thereby, the limitless of the/our world — we needn’t become logicians, physicists, or mathematicians to recognize such limitlessness. Our experience in-the-world/of-our-world has a limitless nature to it. Wittgenstein vaguely alludes to this in the Tractatus with one of his propositions that describes the “mystical”: “If by eternity is understood not endless temporal duration but timelessness, then he lives eternally who lives in the present.” (6.4311) The idea here is that the limited nature of the world is something that is given to us in our phenomenology –i.e., our qualitative experience of things. Now, Wittgenstein is quite vague regarding what he refers to as “mystical.” Indeed, it is fair to say that how he defines the “mystical” is contradictory –e.g., saying the mystical is ineffable, whilst going on to talk about what it is. But, it is, I believe, fair to think that his notion of timelessness and living eternally, are ones that can be understood in accordance with his notion of the “mystical.”
The term “mystical” connotes rarity; mystical experiences are not ordinary ones. Rather, mystical experiences are exceptional, profound and infrequent. Indeed, Wittgenstein makes it quite clear that what composes the mystical is what is most important. The salience in our lives of ethics, aesthetics, and being present, among other things, are needless to state. One such rare experience Wittgenstein cites is the “feeling of a world as a limited whole,” or, “the contemplation of the world sub specie aeterni.” (6.45) But it is not the case that the contemplation of the world sub specie aeterni is the contemplation of the world as a limited whole, given the above remarks regarding infinity, its existence and its salience with respect to representing, manipulating, and maneuvering in reality –which is to say, the world isn’t a limited whole, but rather, it is almost certainly unlimited. Hence, whatever contemplating the world as a limited whole might amount to, we needn’t worry ourselves about it, because it is a contemplation with reference to nothing; if this is truly what constitutes mysticism, then mysticism itself is nonsense. For, what is the point of contemplating something that does not exist? Even if the contemplation of that which does not exist feels profound, that does not make it profound in-itself.
In agreement with and in anticipation of modern takes on infinity, Spinoza noted regarding the contemplation of the world under a species of eternity: “Insofar as our mind knows itself and the body under a species of eternity, it necessarily has knowledge of God, [i.e., Being-itself, which is infinite and eternal] and knows that it is in God and is conceived through God.” (E5P30) Hence, insofar as we contemplate the world sub specie aeterni, we contemplate it in terms of its infinite, eternal, and elusive essence — which is not the same as contemplating it in terms of its totality/the totality of all possible facts, as doing so is quite impossible (a fact which Spinoza himself in the consistent system of the Ethics readily admits, as, a species of eternity is not the same thing as eternity as such (E2P40Schol1)) — , not in terms of it being a limited whole. Knowledge under a species of eternity is not the same things as “an attempt to conceive the world as a whole by means of thought,” as Russell theorized. (305 — McGuinness) Rather, it is a phenomenological occurrence, wherein we contemplate the world and our experience the world in terms of the Being of things –as, the world in terms of its infinite essence, is the world in terms of Being in-general (“God” for Spinoza, is synonymous with the word “Being” for someone like Heidegger –that is, Being is the grounding for the possibility of things and their intelligibility.)
Such contemplation is something that we can speak about in a clear manner, as we will see shortly. In any case, the contemplation of the world sub specie aeterni is not a mystical notion (6.45): rather, as will be illustrated shortly, it is our average-everyday way of being-in-the-world. None of this, however, takes away from the mystical-like significance of contemplating the world sub-specie aeterni; rather, it is merely to state that such significance is far closer to us and more frequent than we often notice –significance as such, is something which we take for granted. Feelings such as timelessness, presentness, and eternity, are not outlandish, ineffable, or rare; instead, they are our default/fundamental way-of-being.
How can we speak about the contemplation of the sub specie aeterni as contemplating the world in terms of its infinite essence –amounting to an understanding and engagement in-the-world in terms of the Being of things — in a clear manner? And how can doing so illuminate that such contemplation is our average-everyday way of being-in-the-world? Firstly, we need to look at what Spinoza means in his Ethics by the word “intuition.” As I have written elsewhere,
Intuition is that which “proceeds from an adequate idea of the formal essence of certain attributes of God to the adequate knowledge of the essence of things.” (E2P40S2) That is, intuitive knowledge is an understanding of things in terms of their Being. Intuitive knowledge for Spinoza is the highest –and most irreducible — form of understanding; when our idea of something is equivalent to God’s idea of it, that is an adequate idea through intuition. “Intuition is more immediate than immediacy; it is affirmative identification, the self-reflexive identification and knowledge of God and his modes [or Being and things in terms of their Being].” (Dutton, 4e) Intuition is a necessary human characteristic, as “any human mind has an adequate idea of God’s eternal and infinite essence.” (E2P47) (Lehewych 6–7)
“Intuition” is notoriously obscure –and it will be elucidated in plainer terms shortly. Saliently, however, what is revealing about intuition is that it is an understanding of things in terms of their Being. How is this related to contemplating the world sub specie aeterni? Intuition “proceeds from an adequate idea of the formal essence of certain attributes of God to the adequate knowledge of the [NS: formal] essence of things.” (E2P40Schol2) Therefore, not only does intuition pertain to the Being of things, but to Being in general (i.e., God). And the way intuition is presented is a way which doesn’t have any correspondence to time:
It is of the nature of Reason to regard things as necessary and not as contingent. And Reason perceives this necessity of things truly, i.e., as it is in itself. But this necessity of things is the very necessity of God’s eternal nature. Therefore, it is of the nature of Reason to regard things under this species of eternity (E2P44).
It is intrinsic to intuition to perceive things under a species of eternity, according to Spinoza, as the Being of things entails the essence of God (Being), which is itself eternal and infinite. (E2P44Cor 2)
The only explicit example Spinoza gives of intuition is the following: suppose we are given the simple string of numbers 1, 2, and 3; “no one fails to see that the fourth proportional number is 6.” (E2P40) What this example illustrates is that intuition is a pre-cognitive, complete and immediate, reflexive grasp of things. Intuition doesn’t entail pre-emptive reasoning or empirical analysis. What other examples might exist of intuition? What is another way of grasping things in terms of their Being? Heidegger’s notion of circumspection from Being & Time is extraordinarily helpful here. “Circumspection is the pre-theoretical and precognitive grasping and understanding of equipment.” It is a form of “seeing,” as Heidegger describes it. To illustrate these matters in clearer terms, think of the following example: I am currently writing this essay in a café; when I entered the café, I grasped for the doorhandle to enter into the café, so I can write this paper. Now, I did not inquire upon or think about how to grasp the doorhandle; rather, I merely grasped it in a reflexive and in a manner that entailed no thinking –if “thinking” consists of, “[a] logical picture of the facts.” It was not necessary for me to have a representation of the doorhandle, nor was it necessary for me to have made an explicit linguistically expressed decision to open it and enter the café. Such actions are reflexive, in the moment, and pre-cognitive. Such is the primary way in which we interact in the world. Simply put, when we are enacting our ordinary skills and actions out in the world –whether it is sitting, socializing, hammering or grasping door-handles — , it is our a priori reflexive pragmatic engagement with and “sight” of the world and the things in it which constitutes our seeing/contemplating/using them in terms of their Being; such is what “circumspection” is.
Just as Heidegger does with circumspection, Spinoza too believes intuition is a form of reflexive seeing “in one glance.” Intuition, thus, includes circumspection under its umbrella of possible ways of Being/seeing/contemplating. Circumspection, therefore, is a contemplation, seeing, and way-of-being towards things under a species of eternity, as intuition is synonymous with sub specie aeterni. Intuition and circumspection are ontological facts about human beings (Dasein) which gives us further insight into Being in general/puts us in a better position to inquire upon such a matter, according to both Heidegger and Spinoza. (E5P30)
What sort of insight into human ontology might we make in light of all of this, then, regarding contemplating the world/Being-in-the-world sub specie aeterni? It is an insight which is antithetical to Wittgenstein’s regarding sub specie aeterni: namely, that it constitutes our average-everyday Being-in-the-world –the kind of Being which is closest to Dasein. (94) This is due to circumspection being a constituent element of our average everydayness –as, in terms of how we deal with things, we do so in a circumspect manner “proximally and for the most part,” rather than in a non-circumspect and “theoretical” manner. The contemplation of the world sub specie aeterni is not something that is far away from us or abnormal. Rather, it is our default way of existing; and it is our default way of experiencing and dealing with things in the world.
Circumspection, however, isn’t the only mode which our average-everydayness takes. It also takes the form of care. With care in the form of solicitude, for instance, we treat other human beings as such, (i.e., as beings who we are with, who also experience the world, and who are also capable of being concerned with Being in general and the Being of other beings) is not something we do in a theoretical or though-out matter. Rather, doing so is a pre-cognitive reflex which we simply cannot help doing. In order for one to treat Dasein as something other than Dasein, something very abnormal would be required –whether it be a pernicious form of ideology or even a psychiatric disorder. So too with care in the form of concern: while we are hammering a nail, we are wrapped up in the hammering, without thinking about the hammering in an explicit sense. The phenomenology of contemplating the world sub specie aeterni, in this sense, is simply our deep embeddedness in the world, with others in the world and in our dealings with entities in the world. Wittgenstein in the Investigations alludes to similar examples that fits into this picture:
But can’t the meaning of a word that I understand fit the sense of a sentence that I understand? Or the meaning of one word fit the meaning of another? — Of course, if the meaning is the use we make of the word, it makes no sense to speak of such ‘fitting.’ But we understand the meaning of a word when we hear or say it; we grasp it in a flash, and what we grasp in this way is surely something different from the ‘use’ which is extended in time!
That is to say, we grasp the meaning of words in a reflexive and pre-cognitive manner. This is also noted with activities that are as simple as reading: “Try this experiment: say the numbers from 1 to 12. Now look at the dial of your watch and read them. — What was it that you called “reading” in the latter case? That is to say: what did you do, to make it into reading?” (Investigations: 161) Likewise, there is a strong case to be made that rule following in the Investigations is also synonymous with intuition and the everyday comportment of Dasein — “Just as we comport ourselves with equipment unreflectively for the most part, we also follow rules unreflectively: in order to follow a signpost, obey a command, perform an arithmetical calculation, I need to act, not to reflect on the grounds for my action.” (Egan 7)
The main point here is that there is nothing special/mystical about any of this. It is, indeed, quite normal. It is so normal that you have been experiencing it the entire time you have been reading this paper, by your very reflexive grasp of the words which I am using to write it –indeed, can you even help but grasp or fail to grasp what is being written here (can you even help the fact that you grasp English writing in general? No. Now it might be argued that this idea is null, due to Heidegger’s rejection of fixed essences. However, as I’ve written elsewhere, Heidegger and Spinoza are in agreement with reference to essences.
§ 4: A True Understanding of the world under Sub Species Aeterni as the Pre-Cursor to Agency and Virtue
The significance of overturning sub species aeterni as a “mystical concept” rests in the following:
The aspects of things that are most important for us are hidden because of their simplicity and familiarity. (One is unable to notice something — because it is always before one’s eyes.) The real foundations of his enquiry do not strike a man at all. Unless that fact has at some time struck him. — And this means: we fail to be struck by what, once seen, is most striking and most powerful.
What is most profound and significant –i.e., all which falls under the category of our contemplating the world sub specie aeterni (i.e., our average everyday Being) — in our lives is that which we take most for granted. Feelings of timelessness, being present, and eternity, are ones that always seem profoundly remote. The utility of traditional practices like meditation is that they intrinsically demystify the idea that such feelings are abnormal, mystical, or even profound; is what is commonly referred to in Buddhism as Vipassanā (insight). These practices do not give us special access to feelings of timelessness, eternity and being present –it is intrinsic to these feelings that no one has special access to them, as, they are our default way of Being. Rather, they are simply tools for insight into the fact that these feelings constitute the very ordinary nature of [our] reality; such practices are similar to what Edmund Husserl (Ideas I: Section 24) referred to as a phenomenological epoche. It is similar in the sense that, in order to see the true nature of [our] reality, we must suspend our judgment of it in terms of how we ordinarily perceive it –Husserl calls ordinary perception the natural attitude, which is basically seeing the world in terms of physical things/entities, like tables, chairs, people, etc.
One might rebut: “who cares?” Truly, why does any of this matter? Fundamentally, it matters because philosophy, along with other disciplines, makes great efforts in over-analyzing, and mystifying that which is proximal and ordinary — doing so to that which is significant, but not significant in a way that warrants such over-analysis and mystification. (298 & 314 Investigations) Philosophy, in a sense, inculcates what Heidegger refers to as fleeing from anxiety and inauthenticity; anxiety is what brings about a collapse to the pragmatic-teleological of our being-in-the-world, which is caused by our attention being drawn to the higher-order end of this structure –Heidegger calls this “for-the-sake-of-which.” This higher-order end, when we look at it clearly, has two possible outcomes, both of which are disheartening to say the least: (1) an infinite regress because this higher-order end is not attainable or (2) we are confronted with a project or an end that does not contribute to this higher-order end. In either case, what “anxiety arises from [is] the recognition of the ultimate groundlessness of all our activities.” What this anxiety amounts to, really is a confrontation with the fact that “we may be alien to ourselves.” In some sense, anxiety is simply a glimpse at what self-awareness and individualization looks like –the embrace of which is truly the source of freedom from inauthenticity and falling into Das Man (which akin to Nietzschean notions of “following the herd.”) “Fleeing” from anxiety consists of turning to “inauthenticity,” by interpreting one’s own Being through the lens of what everyone else is doing and thinking. Fleeing is when we understand what we do via common notions of “what it is that people do,” rather than through authentic self-analysis –i.e. from fleeing from what is significant, yet close and quite simple (i.e. the fact that our everyday being-in-the-world is oriented by care), towards that which is far away and opaque. Philosophy has this fleeing effect not just on how we view ourselves and therefore, our ability to operate authentically in the world, but on other extremely important matters. Philosophy’s failure to understand –or even want to understand, as Heidegger noted — what our average everydayness is and consists of has grave consequences. Namely, it leads ignorance on matters such as ethics and other important disciplines, because it renders such disciplines as either unspeakable or self-evident (which is what I take Wittgenstein means when he says that ethics “shows itself.”)
To focus in on ethics, once we gather insight regarding the true nature of the/our world –namely, that the feelings associated with sub specie aeterni consist of our average everydayness — we become more capable of virtue –another thing we can, will, and must speak about in a clear manner. Think about the following: how are we to cultivate virtue if we delegate ethics into the realm of the unspeakable? Should I just guess how to act? When I am told that “it is wrong to hurt others,” should my rebuttal be, “well, since you speaking about an ethical dilemma, there’s no point in listening to you because you can’t speak about ethics,” with the corollary that, “since the ‘pain’ of ‘others’ can’t exactly show itself (Investigations 293) — whatever this ‘pain’ is to others, might very well be nothing (either way, I cannot see it, but only see other’s supposed reactions to it) — I have no need to care about how I act towards others?” I do not believe that we would take too kindly to such a response, and for good reasons.
There is much in the way of value and gain to be had in speaking in good faith about ethics; in light of this, to mirror Russell once again, one cannot help but feel a sense of “intellectual discomfort” at the prospect of ethics being ineffable. Moreover, one cannot help but feel a sense of moral irresponsibility in accepting such a prospect –as Hannah Ardent rightly pointed out in her coining of the “banality of evil,” that immorality arises from complacency, thoughtlessness, disengagement, shallowness, and the blind surrender to cultural norms.
The pre-requisite for reliably acting in a moral manner is adequate knowledge regarding the true nature of reality. The argument given in E5P32 of Spinoza’s Ethics beautifully ties this idea together, but it requires some unpacking. Intuition, by Spinoza, is the most perfect understanding of God (Being) that is possible for humans –as, it entails an understanding of the formal essence of God. Therein, our best understanding of Being consists of affectively grasping the being of entities, which is what intuition consists of. According to Spinoza, knowing God is the greatest virtue that is possible for us. (E4P28) Why might this be? Firstly, it must be understood that nothing can be or be conceived of without God –that, everything which is, is in God. (E1P15) God, therein, is Being in general, as Heidegger might say, and God is the ground for the possibility of all things and their intelligibility. Now, what might it mean to know God adequately? Spinoza’s summing up of this is essentially that insofar as we are embedded within a Dasein-like mode of being, — which he describes as “acting”, “seeing in one glance,” and “thinking” — and that we are aware of ourselves in light of this, and the power which it gives us, that is when we understand God adequately. (E2P42 & E3P1) Our ontological orientation in-the-world –engaging in it in terms of the Being of things — when uninterrupted, is when we understand God. We do not understand God, by contrast, when we merely understand the world as a totality of “things,” via having our sensory organs externally affected –for example, God is more fully understood when I use the chair (i.e., an understanding of the chair’s Being), but is far less understood when I contemplate the material composition of the chair. When we understand God, our way of being-in-the-world entails our actively engaging in it concernfully, towards persevering in our Being –towards attaining our teleological ends. “No man can desire to be blessed, to act well and to live well, unless at the same time he desires to be, to act, and to live, that is, to actually exist.” (E4P21) The sign that we understand God, by Spinoza, is that we are acting and thinking with greater power –that is, our thinking and acting entail a greater ability to reach our teleological ends and a greater ability to be virtuous. Indeed, understanding God is perfectly compatible as manifesting into Heideggerian authenticity –as, such authenticity necessarily allows for a greater ability to think and act autonomously. What this teleological-end ultimately amounts to insofar as we are operating according to reason (intuition) is a striving for understanding [God] –understanding, being the foundation of virtue. (E2P40) This sort of understanding is necessarily affective –our Being is oriented in the manner of Spinozistic intuition when we understand God. For how can one be virtuous without the ability to act and the ability to concernfully deal with and things and other beings and engage in the world in terms of the Being of things? How can one seek to understand [God] when one is fleeing in the face of anxiety, wherein one cannot seek to truly understand anything? How can we engage in the world honestly, when we refuse to understand ourselves and the important aspects of the world around us, by supposing that such things are ineffable? We can’t.
But how can we understand God’s formal essence? By affectively grasping our own “essence”, which by necessity, is a mode of God’s essence. What does our “essence” consist of? According to Spinoza, it is our conatus, which “characterizes all things as objects of care” and “it makes us ‘live in continuous change” towards achieving our teleological-ends. This essentially amounts to Heidegger’s notion of our Being-in-the-world and our authentic acceptance of it — “an inescapable pragmatic teleology that is inexorably tied to the world that we inhabit.” Inasmuch as we orient ourselves in this manner, we can be said to have an understanding of God. The more “intuition” we have –the more continue to simply engage in the world as Dasein. The more we understand this, the less susceptible we will be to the sway of passivity inducing ideas, such as mysticism and an overly-theoretical engagement with the world. For virtue is something necessarily requires you to engage in the world in a manner that entails understanding entities in terms of their Being –for instance, to treat Dasein as anything other than Dasein in one’s everyday life, is to treat them as an “object,” which as Heidegger notes in his essay on technology, is a route to treating people as a resource to be exploited, rather than an end in themselves, as Kant would rightly have it. Failing to understand yourself is the route to coming short of achieving virtue.
Virtue arises out of intuition, because intuition illuminates the determinate necessity of all things –so too with the thrownness of all things. In light of this such an insight, we are capable of overcoming passive affects that have their origin in the notion that somehow, we are the makers of our own Being and fatalism; rejecting fatalism and total self-determination makes passivity-inducing-affects like worrying and hoping about the past, present or future non-sensical; for one is no longer regarding things temporally under intuition –but rather, as determined and capable of autonomy. (E5P29Schol) Imagine living in a way that no longer entailed constantly looking over your shoulder at illusory strings of imagination and memory? One would be far more capable of doing good under such conditions –both towards oneself and towards others. Blessedness –the greatest joy of the mind — is this very capacity for greater power over one’s actions and thoughts (wherein, the betterment of one’s own being is made a top priority) and the virtuous consequences which follow from it –as, if everyone is doing well and acting virtuously, one’s own life will improve as well. None of this is possible, however, if we make sub species aeterni out to be something that is ineffable and mystical –so too with notions of an “authentic self,” and “ethics.”
Thus, we do ourselves justice in demystifying the notion of sub species aeterni. From the context of the Tractatus, once we grant that logical propositions can talk about states-of-affairs and logical form –negating the necessity to yield to finitism — , we no longer need to speak about contemplating the world sub specie aeterni as something ineffable –but rather, as something we are in and doing almost all the time. Our ability to affectively grasp this fact allows us to increase our power to autonomously think and act within a structure of rationality; doing immoral things in light of such affective grasping –which entails understanding the deterministic necessity of all things — becomes impossible –for, immoral things are most often guided by hatred, and hatred truly makes no sense once we realize that nobody is the maker of their own Being –they did not choose to be the way they are. Hatred is a form of ignorance, which can only be remedied by understanding. The consequences of the answer to the question of “how ought we to live our lives” fairs much better when we negate the illusion of ethics being ineffable, wildly profound, and mystical. We ought to do the same with other so-called “mystical” notions if we ever want Wittgenstein’s philosophical aim of “shewing the fly out of the fly-bottle” (Investigations 309) to succeed.
 For the sake of brevity, the rising and setting of the sun is understood and determined by the axial tilt of the Earth, which is a mathematical notion. The measurements of the axial tilt of the Earth are mathematical ways of representing (i.e. saying) the rising and setting of the sun (i.e. something which is shown.) Indeed, the very visual phenomenology of the sunrise and set — the beautiful sights that are shown to us — is something which can be measured mathematically — i.e. Represented mathematically.
 Dawkins does not say explicitly what he means by “evidence.” This footnote is intended to fill in this gap, as merely stating “the weight of the evidence” is far too vague in this context. Generally speaking, in the world of science, there is what might be referred to as a “hierarchy of evidence.” At the lowest rung of this hierarchy –i.e. the lowest quality form of evidence — is anecdote and tradition. An example of the former might be “well, this diet worked for me, so it must work for everyone;” an example of the latter might be “my father and my grandfather ate butter every day and they were healthy, so it must be healthy for everyone to eat butter every day.” Anecdote and tradition are poor quality forms of evidence in the sense that their conclusions are drawn from too many unspecified variables and conditions which are not controlled. Next on the hierarchy is observational research. Observational research is when scientists study phenomena in their ordinary environment, collect data on their observations and look for connections between different observed variables. Observational research is only able to establish correlations, not cause and effect. Randomized control trials (RCTs) are next on the hierarchy; RCTs are basically when scientists take a group and divide them into two or more groups. In doing so, they keep conditions the same amongst the groups, barring one group, wherein the conditions are different –these conditions are the ones the researchers intend to study. RCTs’ highly-controlled nature makes them capable of establishing cause and effect relationships. Finally, the highest quality research on this hierarchy are meta-analyses, which essentially consist of a group of studies that are systematically analyzed (i.e., studied) through complicated statistical analyses, so as to give us an idea of where the overall weight of the evidence on a given topic lies. It is this lattermost form of evidence which Dawkins is surely speaking of, when he talks about the overwhelming weight of the evidence proving the validity of evolution by natural selection.
 pp. 165–166.
 I’d like to make an imperfect, but rather clear, example here, as what is being said still may not be clear. It might be helpful to think about what “the Being of things entailing the essence of God” means from a more modern, materialistic standpoint: I’ve often heard astrophysicists say that we are made of “stardust.” The only real grasp of how our universe as we know it (i.e., not as an infinitesimally small “nothing”, but as an infinitely large something) “began” is through our observations of the big bang. All of the elements of every human body –and every finite body for that matter — derives from the elements of first stars that formed after the big bang, when they exploded from going into a supernova. From the perspective of pure extension or materiality, the essence of the big bang resides in all finite beings. Similarly, in a purely ontological sense, Spinoza believes that because everything derives from God and is in God, all things contain the essence of God. This example is only partially correct in the sense that God has an infinite amount of attributes –one of which is extension. Hence, we can get a vivid image of part the essence of God within all finite things, through considering God through the attribute of extension.
 Which is ontologically undergirded by our teleological concerns –such concerns are something which Wittgenstein in the Investigations rightly notes, are largely out of our control: see sections 337–338 of Philosophical Investigation.
 Investigations; 337–338.
 This being “far-away” and “opaque” is quite nicely illuminated by Wittgenstein’s ideas around private languages and private experiences. That, what it is that others are and how they understand what they themselves are, is something that is quite far away from me –they might not even have a beetle in the box, in the way that I do; or, they might not experience ‘pain’ the way I experience ‘pain.’(Investigations: 293) By contrast, what I am and how it is that I can understand what I am, is something proximal –so much so that I most often take it for granted.
 Ethics, to my eye, is more salient in this context, but I believe that everything said here about virtue is also applicable to developing Heideggerian authenticity –as, the less we flee in the face of anxiety, the more capable we will be of self-analysis and therefore, authentic modes-of-being (which, incidentally, allows for greater autonomous thinking and acting, therein clearing the way for “virtue” as Spinoza conceives of it.)
 “Thought” for Spinoza is not primarily theoretical. Rather, it is primarily affective.
 It ought to be noted here that Spinoza and Heidegger clearly depart here on the point of virtue –the former embracing it and the latter eschewing with it.
 Thrownness and determinism are perfectly compatible, and both are also compatible with the notion of “freedom.” For Heidegger, we can see this in his balance between thrownness and projection and for Spinoza, we can see this in his denial of the freedom of will and his valiant efforts at freeing humans from “bondage.”
 It can plausibly be asserted that the Tractatus denies the ability to talk about the “self.” For, the talks about the self in 5.6 through 5.641 are extremely unclear. “Everything that can be said can be said clearly.” (4.116) If we are to treat the Tractatus as a consistent document, it readily follows from 4.116 that we cannot speak about the “self.”
[i] P= Place; T= Time.