Ott Hulrne's Spacr euo Tnnu Dustin Gray There is no other notion in philosoph]'n'hich rs seen more clearly, and at the same time is so laden with confuslon. than that of space and time. The reason for this problem is r-oiced br-d:fferenr philosophers in different ways. The subjective narure oi ana.r'ses is most likely to blame, since a universal agreement upon the tdeas of space and time has nor yet been reached. My position ls s:np-.,, thar the mind, when passive, has no qualms with space and t:ne themselves, nor is it concerned with their principles. h :s o:-r. .,.,.lren our passions are ignited and our judgment is utilized. i.e. r.,,hen .,.,.e begin to actively rhink about space and time, that the nocon becomes confounded. Any further digression into the semanr:cs oi the issue by making an arrempt to give a final explanation of rhe ideas of space and time will always lead to a dead end. Th:s rs due to the fact that space and time are ideas of an infinite nature and can never be distinctly visited via the use of the human mind stnce :r -s itself of a finite nature. My hope is only that the reader u-ii1 agree that this predicament is well worth the exploration. The intent of this project will be to clear up any contusron of the problem via an augmenration of David Hume,s A Treanse o.r Human Nature. This will serve as a helpful analysis of the princrp.es set forth by Hume and not only will give a practicai understand.ng oi the latter's views, but also wiil elucidate my own notions of space and time. The sections covered will be 1.2.1 1.2.3 and 1.2.5: rvhlch represent Hume's core analysis of the ideas of space and time. -{s a tacit source of reference, I will include some theories offered b' Leucippus and Democritus of Abdera, who are the earliest kno*.n atomists and the first to give an accurate account of matter and extensionl. 13 I: Infinite divisibiliry in relation to the ideas of space and time Hume begins his exposition in 1.2.1 n'ith an account of the principle of infinite divisibility. He does this both to proride pertinent information in terms of, and to set a tempered platform for his further explanation of the ideas of space and time. The conclusion entailed by infinite divisibiliq: b1' Hume's account, is that if something is compounded of an infinite number of pans. it must retain the ability to be divided infinitelr: Conversell. rhe idea lve form of anything finite has the characteristic of being able to be divided into terminally finite simple parts. To gii'e a special example, think of an entity as being composed of an infinite nun-iber of parts. Must not it then be said to be of infinite extension? In a ivord, necessarily. It is a shared zenith of necessit.v that anyhing of finite extension may only be divided into perfectly simple and indir-isible parts. An idea compounded of a finite number of parts marholvever be divisible; "by proper distinctions and separations n'e ma)' run up this idea into inferior ones, which will be perfectll' srmple and indivisible."2 Hume is here alluding to his position that the mind is not of an infinite capaciry. So with ideas being the occupants of the mind. n'e can conceptually postulate the idea of arriving at the end of each idea's division. This is the claim that the imagination reaches a minimum at which any attempt at a further division of the idea brought before it could only result in its total obliteration. An obvious objection to this stance may go as foliorvs: though we may not be able to directly perceive an-vfurther division of a perfectly divisible simple, we may certainlv conceive of numerous further divisions, if only through the use of pure mathematics. This point could be further solidified by our present knowledge of sub-atomic happenings via the use of advanced visualization techniques. Hume may agree himself with the latter, but only if we were to have an immediate experience of such happenings. In a way, observing and accounting for the further divisions of previously perceived simples is a way of redefining the minima, but this would not be an entirely accurate account3. 74 1.-. Two things are important to remember. Firstly, by Hume,s account, there is always the indir.isrble simple that, conjoined with others, makes up ideas of a complex nature, and any further division will be of no use to our senses. Secondlv, even in an attempt to amplify our senses, as it n'ere. brusing a microscope, telescope, or the like, there will still be. at the base of an idea, the same indivisible simples. This is true u'hether the srmples are neurrons and electrons or beach balls and dogs. \bu mav of course conceive of a separation of the dog's parts. bur never can r-ou acrua.,r-have an immediate experience of a living dog er:srlr:g lr. such a \\-a\: This is the work of the imagination and ner.er rhe serses. -..,'itch ts cont-eniently what leads us to the nexr phase of our rnq..::n. Before anrdisagreemenr anonEsr th.,osophers in reference to infinite dir,tsibiliry'can be properir-ana}-zed. I nust erplain another relevant principle put fonh bt'Hume. He srare_s rhar whatever may be differentiated from anrthing else rs d;st:ngulshable and furtheq anything that is distinguishable ma1-be separared br the imagination. This is Hume's separabiliry principle. It essenrra_irsrates that any idea that comes before the mind that is different tron-r another is distinguishable and therefore separable into indirisibie parts via use of the imagination. This principle is foundational for Hume in that it gives justifiable trurh ro his supposrtion that the mind is finite and therefore the ideas therein are indivisible minima.Some may disagree with Hume by saying that there is no way to prove that the mind is finite and therefore could be in accord with the supposition that the mind could or could not be inherently infinite complex by virtue of being composed by an infinite number of parts. But on the same head, this objector must then admit that she is tasked with providing conclusive proof to offer for her claim of the converse, (whatever it may be). Since it is not the purpose of this essay to get entwined in epistemological circles, we will give this subject no further attention. Hume gives an example that may, for his critics, seem more plausible and give anyone offering objections something more ro consider. He discusses the divisibility of a grain of sand. He allows that one can have a conceptual idea of the infinite varying numbers 15 that could be used to define infinite divisions of a grain of sand, and even that one could have an idea of the different spatial proportions thereof.s An example of the latter would be a person having an immediate experience of a divided grain of sand seen under a microscope. Then, simply through use of her memory and imagination, duplicate (in her mind) a reflection of the origrnal sensation in as much excess as could be done by infinitelv dividing fractions or decimals. But the images of these infrnite divisions that are formed in the mind and that are identical to the impression of the original grain can only be called upon by an impression of reflection. By Hume's account, such reflections can, in no n'ar; replicate in force and vivacity, the immediate impression of sensation. Since we have never had an immediate percepdon of such divisions of a twentieth, much less a hundredth and cenainlv not a thousandth of a grain of sand (by the naked eye), u'e cannot give these ideas any empirical value. For empirical r,a1ue to be attached to any impression, it must be one of immediacy. Even the most polverful microscope would fail in displaying an infinite division of anr body to our senses. We must not fail to remember the allowance given bv Hume at the beginning of this example. "I have a distinct idea of these numbers and their different proportions."o What is meant bl-this is that the principle of infinite divisibility does have one safe har-en in which it can be comfortable in its justifiable truth. That place is to be mathematics. The proof of this can be found bv simpli dividing the half of any number on a calcuiator over and over successively. I am not sure how far modern technology has adl-anced in computational machines of this nature in haring the ability to complete this task in any extended sense. What matters for my discussion is that we can conceive of any number, (which is an abstract object, not a physical one) being infinitely divided into an infinite number of fractions.T An abstract object may not be perceived through the senses as in the case of a physical object. It would be easy for someone to say, "I am looking at a tree," and as long as the person was of sound mind, not under the influence of any hallucinogen, and was in fact looking at a tree, we could allow her 76 I I declaration to be truthful. But no one could ever declare to another. or even herself that she is Iooking at four. More imporranrh', she could never give an appropriate description since four is a concept, not an object. Four, or any other abstract object for that marrerr can only be described by objects, (i.e. 4 or if you like, f-o-u-r). and cannot not perceived in and of itself as an object. To attach anv objection to this notion would surely be a negation of the apodicric certainty of mathematics on the whole, and this I am sure. n'ould be viewed as a thorny contradiction. Hume concludes the 'grain of sand' example brshorring rhat the idea of a grain of sand is in no way able to be distingurshed. \or is it able to be separated into any number whether it be a hundredrh, thousandth, or an infinite number of inferior ideas.s For this to be possible, the mind itself must retain the requisite qua.:r.cauon of being composed of an infinite number of pans. So rhough n-e may be able to conceive of such divisions and even accurare.r' do the math, it would be a fool's errand. If something is not lmrredrarelr' perceptible to the senses we can have no immediate irnpress:on of it and thus no subsequent accurate reflection of it. Whether divisions of tdeas are nade flr.itelror infinitely, there always seems to be some degree oiunln'amongst them. If you divide a yardstick into 36 one-inch-.ong segrrents, giving you 36 pieces rather than one, thercould st:l, be said to be unires of the formerly solid yardstick. Imagine one of rhe pieces gets kicked under a chair and is found a u'eek later br'\'our spouse and she asks, "What is this?" You would surel1' replr: :\ piece of a vardstick." You wouldn't say it was a piece of rope or a piece of paper. Hume's version of this notion is that existence belongs to unity, and the former is never applicable to quantin, (or number).e Existence is, however, applicable to the unites that rhe number is composed of. For example, the Red Sox can onlv be said to be a team if it is considered that they are made up of some number of players. That is, it would be nonsensical to postulate the existence of any number while denying the existence of the unites it is composed of, thus the Red Sox could never exist as a team, if the members were not recognized as the parts (unites) of the team. Hume's ulrimate I 77 conclusion of unity is that the term itself is merelv a fictitious denomination of which the mind is capable of apply'ing to any number of objects it may collect together. II: Of time Hume's initial elucidation of time states that the concept itself is nothing more than the succession of our perceptions.l0 The property that constitutes the essence of time is that each of its parts (or moments) always either proceed or succeed one another. So, since it is easily allowed that these moments aln'ars appear as contiguous, they can never be understood as coextstent ln anr' fashion.rr Hume uses his account of infinite dirisibiiin'to shorv that time is composed of indivisible moments. This is the same line of reasoning he used in reference to the idea of ertension that lvas given in the 'grain of sand' example. He defends hrs claim bv impiying a contradiction in the idea of time being a composed of infinitely divisible moments. If this were the case. "rhere n-ould be ;, on infinite number of co-existent moments, or parts of tlree: n'hich I believe will be allow'd to be an arrant contradictlon'. -: How can we be convinced of this? Is it not posslble to imagine some fictitious elaboration of our temporai relations. even if it expressed nothing more than the devil's advocate r-len'ria the employment of a relevant thought experiment? If so. rhen n'e rvill do just that. We attempt to discover some situation in u'hich moments, or parts of time could be coexistent. Imagine something simple like a wine g1ass. \ou'imagine that said glass is situated on the very edge of a table bra man just as he leaves the room, (t1). Shortlythereafter, the man's cat leaPs onto the table, (t2) thus shakingit slightlycausing the glass to fal1, (t3). Upon hearing the noise, (t4) the man rushes back into the room, (t5) only to find his favorite wine glass broken, (t6) and his cat rvith the look of guiit in her eyes, (t7). Here we have nothing more than a simple sequence of events that occurs both temporally and spatially. For now we will focus on the temporal aspects exclusivel)'. So, the question at hand is, can there be any instance of rwo or more times 18 I being coexistent with each other as opposed to their necessary contiguous existence? The only way to conceive of t1 and t2 coexisting is to further divide each of these moments into diminished fractions of time that when divided would appear as coexistent wholes, and not halves. We could, I suppose, divide the 1.5 seconds that expired during the act of the cat jumping onto the table into tenths of a second. So then we could conceive of 15 increments of time as opposed to 1.5. Even though a further division has been made, rhus redefining the unites, the span of time remains the same. Further divisions do nothing to prove the coexistence of moments for t$-o reasons. Firstly, no matter how many times one divides a single unit of time, the unites thereof will always add up to the total of the original unit, This follows strictly on the path that Hume set forrh of unin: To contradict this would be to say that when I divide an orange into nr.o halves, I now have two oranges. Secondly, even when n'e consider the.,,ast multiplicity of divisions of a single momenr in rime. rhe sequential arrangement of time still remains. Whether rre decide to count an hour by minutes, seconds, or any other means of diusion. the distribution that we ascribe will still remain successii'e. III: Of space There is a second half to Hume's argument rhar consists of the idea of space. He defines space conciselr' as the r-arious dispositions of visible and tangible objects.t: In other rvords, the idea of space is only perceptible by means of sight and tactile reference. Furthermore, Hume's statement that, "rve therefore have no idea of space or extension, but when 'rve regard an object either of our sight or feeling"l4 simply means that space is exclusively recognized by the distance or closeness of objects in our visual or tactile fields. To solidify this argument one must only consider the perceptions of a blind man. When he meets someone for the first time, he may request that he be allowed to touch their face in order to gain an idea of what they look like. His lack of sight creates a stronger tactile sense of space since that is the only facuiry he has to 19 perceive the people he meets. The same line of reasoning would enact itself if he were to move into a nerv house. He would have to, by touch, survey all of its rooms in detail as rve1l as the decided positioning of furniture so as to ar-oid running into or tripping over things. And further, he would be n'ise to keep everything in his new home in the same layout with little variation so he wouldn't have to continually re-learn where every'thing n-as. The point of this example is to clarify the concept that sight and touch, (hearing, tasting, and olfactorysenses could be allorved as n'elI), are the only way ways that people perceive things empiricailr. These are the faculties that give us our immediate impressions. Hume considers the idea of the exisrence of a vacuum, or void in which nothing is visible or tanglble. \\-hat is empty space? The existence of a void is absolutely necessanin order to understand a plenum, or any solid matter. Without a void. n'e could not conceive of a plenum and without the latter rve could never conceive of the former. Imagine a dog in a shed. Whater-er amount of space the dog fills during the time he is in the shed is the absolute negation of the open space that surrounds him. The onI1thing that defines the negation of anl.thing is its converse. Plenum is the opposite of void. This I will call my Principle of Opposites, namelrthat if something (x) has an apparent opposite (y,) then it (r) can only be described by it (y). With this in mind, I must side rvith Hume in that a void can, and must, exist where there is no plenum. This is true especially when we consider his example of the space benveen a chamber's walls. Hume holds that the roof and floor of the chamber separate the four walls and that the latter separate the former. These six boundaries can only imply a void of extension and matter in between themls. IV: The coexistence of space and time Consider the idea of the coexistence of space and time. This may seem to be contradictory to the 'floating man' example16, but it is only due to the impossibility of the case itself. Hume feels strongly that the idea of space cannot exist with out that of time, "nor is it 20 I possible for time alone er.er to make its appearance, or be taken notice of by the mind."tz For how could we have an idea of time without perceiving objects that constitute its succession? Even more impossible would be the exisrence of space with out that of time since we couid never see objects interacting with other objects without time present to srrucrure the objects'motions in a contiguous manner. One could object. horveve4 that it could be possible to perceive a succession of sensations of reflection. Imagine someone simply thinking of n'hat one did yesterday. Whether it was wakino up, grocery shopping. or going to a movie, it may be said that a person would be erper;encing a succession of impressions that have no spatial location n'harsoever. But what must be kept in mind is that every reflection and or memory is simply a recollection of something that n'as nor onhspatially located somewhere, but was also temporally sequenrial. For example, I see a car drive down the street from point A to po:nr B. The idea of space is necessary to realize the distance rhat constitutes the two points in which the car may be at or in benteen. -\rtd more importantly, time is necessary since we could never tnagine the car traveling forward from point B to point A, only the con','erse is sensible to the mind. So even if months passed from rhe actual occasion and a person were to call upon this impression of reilection and mix and match the moments thereof, they u'ou1d onlr-be lnaccuratelv reconfiguring the moments via use of the rmaginauon. Thev could never have an immediate experience of something .n thls mixed up manner. V: Conclusion As I mentioned in the beginnrng of this enquiry I hold that the only method that we matimplement ro erase confusion concerning the ideas of space and rime is simply to give none of the mind's attention to the notions themselr.es. How can this be possible? Prima facie, this line seems so fallacious and contradictory that to even consider it would be completely impractical. But if one considers that space and time are simpiy the framework of, or 27 perhaps the mechanisms that structure the way we perceive and recollect our impressions in the mind, my point gains legitimacy. This is the theory in which I hold to be the most sensible since space and time are given to us a priori, but are manifested in experience and experience alone. Space and time may be infinitely existent, but the only recourse we have to understand ',vhat space and time do is through experience (rvith a finite mind). Immanuel Kant suggests that a priori cognitions such as space and time are stimulated b)'erperience but never satisfied by it.18 The reason this is relet'ant ro the current topic of discussion is that we can never have an1idea of space and time, but rather that it is what struffures all of our rhoughts and ideas that are originally initiated by experience. Kanr holds that our minds are divided into two sections; one of outer sense (sensibilin-) and the other of inner sense (understanding). Stimuli are gir-en ro the sensibiliry via the sense organs and synthesized in rhe understanding \']a subsumption under innate concepts such as unin: realin'. cause, and existence' The outer sense is spatial since u'hat it deals lvith is the spatial location of what it perceives and the inner sense is temporai since what it deals with is perceptions cognized in contiguous relation to each other. Kant would sa1'that space and time are the a priori conditions of our mrnds. Though Kant's subsuming of perceptions under concepts may nor be in complete accord with Hume's ideas of space and time, it is imporranr to yisit another philosopher's relevant theories to broaden the scope of the project. The question norv is: could Hume himself be said to be in agreement with my position? Consider this statement: "nor is it possible for time alone er,'er to make its appearance, or be taken notice of by the mind."re He does not give validity to the notion that if five notes are played on a flute, the span of time in which they successively occur is a sixth impression. Rather, Hume sees time not as an impression at a1i, and thus not an idea; I would say that time Structures our impression and ideas. As for space, we have no direct impression of it. We can only perceive what does or doesn't occupy ir. We can have no idea of space and time in and of themselves, 22 I though we may (and do) have impressions that are given from space and time. This is because space and time should be understood as the structure or framework of our minds'workings with perceptions that are immediately perceived via the senses and then subsequentl,v transformed into impressions of reflection for later use only. Endnotes 1 2 J 4 5 6 7 8 9 10 11 72 13 74 15 16 The First Philosophers, translated by Robin Waterfield, 165. David Hume, A Treatise of Human Nature, 23. This point rvill be revisited shortly. See Berkeley, Principles of Human Knowledge: Three Dialogues. David Hume, ATreatise of HumanNature,23. rbid. rbid., 2s. rbid., 23. rbid., 25. rbid., 28. rbid., 26. rbid. rbid., 28. rbid. rbid.,41. I believe that Hume rvas probably influenced by the ideas set forrh by the early atomists, Leucippus and Democritus. They held that the universe is made up of atoms, and the lack thereof that constitute the plenum and the void. "Leucippus and his companion Democritus say that the elements are rhe full and the void, by which they mean what-is and what-is-not" (Waterfield). They roo felt that plenum and void were necessarily codependent. To rake this idea one step further we can consider Hume's floating man example. In a thought experiment, he alludes to a man that is suspended in the air and moving to and fro by means of some 'invisible power'. The entire time he is floating about, he has no idea of extension. He does however retain the idea of time since, as he floats along moving his appendages, there is an idea of 23 77 18 19 contiguous motion. In this instance the idea of time does not necessitate the idea of space for the floating man' But this is, of course. not a plausible scenario. rbld., 28, Immanuel Kant, The Critique of Pure Reason,727 Al. rbid. Works Cited Hume, David. A Treatise of Human Nature. Oxford University Press' 2000 Kant, Immanuel. Cririqu e of Pure Reason. Cambridge University Press,199B Waterfield, Robin (translation). The First Philosophers: The Presocra.tics and Sophists. Oxford University Press' 2000 24 I