Category Archives: metaphysical
The other day on the bus into work I was thinking to myself ‘How do I know what the world really looks like?’
Since I have had to wear corrective lenses since I was nine I have no memory of what the world looked like without needing my glasses. Without them the world appears as an amorphous gathering of globules of varying colours all merging together seamlessly. A world without form. But how do I know this is not what the reality is actually like? Without memory of perfect vision I can only rely on, as I am not able to perceive the world through another’s eyes, I have only the word of the optician to believe. And of course the optician would not necessarily tell me the truth if it meant he’d be able to charge me for another pair of expensive lenses and a frame to house them.
I can of course ask you about how you see things, assuming you all have twenty-twenty vision. Then again can I trust you to answer me honestly? And even if you do answer me honestly how then can you prove what your telling me is true? As I already said I have no means of seeing through your eyes to back up your words.
So is it actually possible to purpose any certain truths about the nature of the external world given this predicament? Maybe there is no such objective external world, merely a collective approximate of gathered subjective overlaps? Your views on this topic would be much appreciated so please feel free to comment 🙂
First off a big Happy New Year to you all and I hope 2014 brings you a proprous year ahead 🙂
To kick off 2014 here is some medieval philosophy, a look at the problem of universals has debated between William of Ockham and Boethius. It was this argument that helped push metaphysics forward from the classical teachings of Aristotle and Plato into its next age where it would soon make way for Renaissance thinkers to revive philosophy in a glourious burst of light surging forward Western Civilisation:
In his categories Aristotle says that things can be named in three ways: equivocally, univocally and derivatively. By equivocally he means two things that have a shared name but their definition is different like a bear and a cuddly bear, they are both animals but plainly are not the same thing. Univocally is when two things share a name and a definition like cat and dog, they are both animals and share that name and definition. Finally things that are named as derivatives are objects that get their name from an unrelated subject like a musician, a musician is still an animal and a human etc. they just happen to play a musical instrument but they do not fit into the category of music (Categories 1). There are also two types of speech, simple and composite, this is pretty straight forward, simple is individual words like ‘cat’, ‘dog’, ‘eats’, and ‘sleeps’, and composite is when they are combined to form sentences like ‘the cat sleeps’ and ‘the dog eats’. The other semantic confusion that is cleared up is that when he writes ‘present’ he means a thing being incapable of existing without it’s subject, like colour (Categories 2).
Aristotle then goes on to discuss the four fold division (Studtmann 2007). Firstly when something is predicable of a subject, but never present within it e.g. ‘cat’ is predicable of an individual cat and is never present in the subject. Others are present in a subject and never predicable of a subject like the tabby pattern of a cats coat, it is present in a tabby cats coat but without the cat there would be no tabby pattern. The third possibility is being present in an subject and predicable of a subject, Aristotle’s example here is very good, he says that knowledge is present in the human mind and at the same time is predicable in grammar. Lastly there are things that are neither present in the subject or predicable of a subject like an individual cat. (Categories 2)
Section 3 of the categories discusses how predicates work and how they relate to genus and species. “When one thing is predicated of another, all that which is predicable of the predicate will be predicable also of the subject” (Categories 3). So a cat is predicated of an individual cat, and at the same time ‘animal’ is predicated of ‘cat’ and therefore it’s predicable of the individual cat as well, this is because a ‘cat’ is both ‘cat’ and ‘animal’.
If we look at the genus ‘animal’ and ‘knowledge’ as examples to help the explanation. ‘four footed’, ‘has a tail’ ‘aquatic’ are all differentiae of the genus ‘animal’, and whilst ‘knowledge’ is not defined by the same differentiae does not stop it from having both ‘knowledge’ and ‘with tail’. This shows that genera are different and co-ordinated, and their differentiae can be different in kind. Genuses are subordinate to each other in a certain respect, they can also share differentiae because “the greater class is predicated of the lesser class” (Categories 3). For instance ‘cat’ will be part of the genus ‘animal’, ‘with instinct’, and ‘living’ but we know that ‘living’ will contain the genius ‘animal’ which in turn will contain the genus ‘instinct’. This means that all differentiae of predicables will also be differentiaes of subjects. (Categories 3)
Aristotle’s fourth chapter in the categories does warrant a mention, more to list his categories and clear up a few semantics than to clear up his argument on universals. His ten categories are substance, quantity, quality, relation, place, time, position, state, action and affection. Statements that only contain one of these does not involve an affirmation of that statement, a combination of the categories must be present to be able to get a positive or negative statement. Every assertion has to be true or false meaning that composite statements cannot be true or false because they have no quality to judge them on as they are not quantified in any way.
Boethius was an Italian philosopher writing around 480-524/5. He translated Aristotles logical works from the Greek to Latin to give more people access to them. Among these he translated Aristotle’s categories and Porphyry’s third century Isagoge (meaning ‘introduction’) to Aristotle’s categories, this is where the problem of Universals is first bought up, Porphyry says “I shall decline for the present to say (a) whether, if they subsist or are posited in bare understandings only, (b) whether, if they subsist, they are corporeal or incorporeal, and (c) whether they are separated from sensibles or posited in sensibles and agree with them.” (Spade 1994 pg20). Porphyry says that there are five main categories or predicates; genus, species, difference, property and accident and also their possible combinations. These come from Porphyry who states that there are three levels of Aristotelian predication, the first is the genus and their differences, the second species and how the differences from the first level influence this, and the third is the subject or substance of which they are predicated (Categories 1b15-24). These possess the properties of accidents and essentials. Species and genus are secondary substances, that can be predicated of the subject or substance proper (Categories 2a13-18). Each increase in generality must have a corresponding decrease of substantiality, within the category of substance, because it is in the primary substance that these individual substances are predicates.
In his secondary commentary Boethius first argues that the likenesses of members of a species is what the mind tells us constitutes said species, secondly that a genus is made of similarities that are perceived in our mind between member species, and, thirdly that both genera and species exist only in our minds but they must be thought of as real or else they would be empty and inconsequential.
In section 10 Boethius said that “Genera and species either exist and subsist or are formed by the understanding and by thought alone” (Spade pg 21). This outlines the problem that Boethius faces. He then puts forward his arguments against universals, he says that their existence is not possible because things that are common to a number of objects at the same time cannot possibly be one. Boethius then argues that if there are more than one genera which gets round the separability problem there will still be no genera that everything belongs to. This would result in each individual thing having it’s own genera as must each similarity, by this Boethius means that if an object is both red and round e.g. a ball and there is a balloon that is both red and round then there needs to be a genera for red and for round as well as one for ball and one for balloon etc. this process unfortunately continues ad infinitum and is the main problem with this theory.
Boethius follows this with the case for universals,if genera and species are grasped by understanding alone, and that these understandings come from subjects, then they are not in understanding alone but actually exist in reality. He quickly counters this with the claim that if this understanding comes from the object itself, but not as it is in itself, then the understanding itself is false and that as genus and species don’t exist, then debating the existence of the five predicables must be discarded. He claims that it is “not inquiring about a thing that exists, or about a thing about which something true can be understood or stated” (Spade pg 23).
Boethius’ solution agrees with Alexander (of Aphrodisias), false reasoning does not necessarily occur when we misinterpret a subject, but occurs when composition is mistaken, when we compose something in our brain that is not possible in nature e.g. horse and horn results in unicorn, we know this is a false impression. But if division and abstraction is where this understanding arises from, then the object is not understood in the way that it is in itself, but the understanding is still not false. This is because there are several things which exist only as part of something, if they are separated from that object they can no longer exist but our minds can see them separately even though they cannot be e.g. the marking on a tabby cats coat, it cannot exist apart from the cat. The sense faculty gives us all the incorporeal things which subsist within such objects, the mind then sees the incorporeal qualities along with the corporeal ones and can separate them or join them as it decides. This is because the incorporeal qualities are separate from the corporeal ones even if they cannot be separated and both still exist in physical reality.
Boethius says that because of that, genera and species can be found in both corporeal and incorporeal things. When found in incorporeal things then an incorporeal understanding of the genus is gained. However if the genus and species of corporeal things are observed then the mind separates them and sees them as pure form. Everything we learn from incorporeal qualities is not false and falsity should not be assumed, in fact it is through the minds division and abstraction that we can discover what is actually true. Therefore things like this are understood separately from sensibles but they do exist in corporals and sensibles, this means that they can be observed and their individualities understood. Because of this when we think of genera and species the information we consider is always sourced from the individual objects they exist in. “For example, from single men, dissimilar among themselves, the likeness of humanity is gathered.” (Spade pg 24). This similarity is the species and this likeness which cannot exist except in the species or it’s individuals is what makes up the genus.
Consequently these things exist in singulars and are thought of as universals, so species is simply the likeness of if individuals that are unlike in number whilst genus is what the mind gathers as the likeness between species. “This likeness becomes sensible when it exists in singulars, and becomes intelligible when it is in universals” (Spade pg 25)
Boethius gives succinct answers to the three questions that Porphyry decided to omit from his Isagoge. The answer to (a) is that both genera and species are understood one way and subsist in another. For (b) he says that they are incorporeal but are a part of sensibles and therefore joined to them but they are understood as individuals that are separate from the individual objects. Finally for (c) Boethius outlines Plato’s theory that these exist as universals but contra to what both Boethius and Aristotle say, Plato thinks that they also exist as physical entities separate from their original objects, where Aristotle thinks that they are understood as incorporeal and universal whilst subsisting in sensibles as parts or qualities of objects, not apart from them.
William of Ockham begins by setting up the case for realism, before arguing against it until he is in a position to advance his nominalist account. Ockham is the author of ‘Ockham’s Razor’ which is a simple rule where we must not multiply entities beyond necessity; this rule allows Ockham to build on the Aristotelian criticisms of Platonic Ideas within the third man argument.
To do this he uses three main arguments. The first argument concerns single substances in regard to universals. A universal cannot be a single substance else every single substance would require a universal. This cannot be the case else universals would be meaningless. Also there is no reason for some single substances to have universals and not others. This leads to his second argument. If single substances are not universals then universals must contain multiple single substances of the same type, but this would be a collection of particulars rather than a universal so this does not work either. The other way to understand this would be as multiple universal things. However as has been shown with Platonic forms this leads to infinite regress and as a result is still not a satisfying answer. This again leads us to the final argument, if universals are neither single nor multiple substances, it appears to lead to a dead end. Ockham suggest a novel way of resolving what universals could be. He poses the idea that universals can be a single substance within multiple single things. If we take the universal cat and apply this idea , two objections arise, the first is that the universal will pre-exist each instantiation of itself, so the cat would exist before the cat exists. This clearly is not an option. The objection is that when a cat dies part of the universal will be destroyed with it. Again this doesn’t work.
So Ockham comes to the conclusion that universals do not have substance, they are incorporeal to tie it in with Boethius’ terms. Ockham argues that the universal is not a product of the mind but is really in the things that share it as it is one and the same in each, and is really distinct from each of them. A second argument of his follows the same point but rejects it is one and the same but multiplied an argument similar to Boethius’.
Later on Ockham changes his argument again so that all that remains from the original position is the only difference between universals and particulars is the difference in our reason not in reality.
After this Ockham starts to advance his own theory on metaphysics by claiming that universals are inside the mind and they are only universal in the sense of being predicated of many. A claim which reflects Aristotle’s nominalist position,
Ockham’s next stage is to pose the question ‘Is a universal really outside the soul, distinct from the individual, although not really distinct?’, this question is an attack against Scotus who argued that universals are the subjects existing outside the soul where are different from the individual but only because each is made of a different type of material.
Ockham answers his question by saying that anything which is individual by nature cannot be universal, which contradicts Scotus’ argument. Ockham then goes on to demonstrate how a substance can either be or not be a universal but never both as it breaks the law of non-contradiction, if (on the off-chance) that it is possible for universals and particulars to be one and the same then one will be left incomplete due to the nature of the other, thus we end up with something that is less that what we grasp of it.
Ockham provides four ways that the universal nature causes contradiction either: it is a particular, or it is a numerical unity, if not then it is a universal, and finally if none of the first three then it must be a less than numerical unity. By rejecting the notion that it is a singular Scotus argues that the nature of the substance is prior to the contradiction so that its nature and contraction form two separate things. Hence the nature is not a numerical unity, yet is numerically one breaking the law of non-contradiction. Therefore it must be a universal in which case the nature of the universal is less than universal (according to Scotus). Hence the nature of a universal cannot be singular, numerical or universal leaving only the possibility that it is less than numerical but still many things.
One of the prevalent theories of Ockhams time was that of Walter Burley who was like Scotus a moderate realist. He appeared to try and soften both Ockham and Scotus. Burley agrees with the first half of Scotus’ argument but not the later here he reverts to Aristotle by saying that the “Indiscernibility of Identicles is our chief criterion of distinction among real things.” (Kretzmann 1982 pg423).
Burleys next step is to state that universals exist or partake in many particulars and are defined, but that particulars do not and are not defined either. This means that for Burley universals and particulars are distinct from each other. He still holds that different categories are distinct from one another and like Scotus thinks that these differences and indeed similarities must also have something in common but that this thing is again distinct.
Added to this Burley states that it is universals and individuating principles that make up particulars, but that they do not separate the particular, instead “The whole universal (secundum se totum) exists in each of it’s particulars and is not numerically multiplied by its existence in numerically distinct particulars” (Kretzmann 1982 pg423).
Ockham has two main criticisms of this theory, firstly that arguing that universals and particulars are distinct and that “both the nature and the contracting differences exist in reality as constituents of a particular and they can exist in reality only as such” (Kretzmann 1982 pg414) would mean that universals can exist without particulars and vice versa. Now the one side of this is perfectly acceptable, for example courage can exist without an individual particular exemplifying it at a particular moment. The second statement taken from this by Ockham that he rejects is that the individual adds to the nature of a thing and that added with the universal which then makes the ‘one’ this leads to the statement that given that there is no universal nature there is no reason why God should not preserve what is added. Whilst these criticisms are interesting and do apply, they do not dismiss Burleys position completely, they more cause him an inconvenience
For Ockham, the only universal entities it makes sense to talk about are universal concepts, and derivative on them, universal terms in spoken and written language. Metaphysically, these universal concepts are singular entities like all others; they are universal only in the sense of being predicable of many. So to conclude it is stated that there are particulars and universals, however universals exist only within the mind and particulars within nature, therefore Ockham is a nominalist and agrees with Boethius.
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- P. Boehner, Ockham: Philosophical Writings (Edinburgh: Nelson, 1957; repr. Hackett, 1990)
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- J. Marenbon, Medieval Philosophy (London: Routledge, 2007),
- J. Marenbon, ed., The Cambridge Companion to Boethius (Cambridge: Cambridge University Press, 2009)
- M. J. Loux, Ockham’s Theory of Terms: Part I of the Summa Logicae (South Bend: St Augustine’s Pres, 1998)
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Given that time travel is an actual possibility for the sake of this argument I would like to broach the subject of relationships.
Lets imagine that our time-traveller; Mr.X; embarks on a relationship witha stunning young blonde; Miss.Y; from London in the month of May 2013, now it turns out things didn’t exactly work out between them (insert whichever reason you want here).
After some travelling around in the 15th century to get over the breakup he returns to May 2013 and finds himself in a London bar where he meets a brunette in her thirties; lets call her Miss.Z; and tries again at having a relationship believing the time is right to let go and move on after the Miss.Y incident.
Unfortunatly whilst Mr. X is out of town…and in fact of the time zone…Miss.Y and Miss. Z happen to meet up and discuss their new boyfriends…turns out they work together in the same office block and decided to lunch together that day. They soon come to realise that Mr.X is in fact seeing both Miss. Y and Miss. Z simultaneously. But is he two-timing?
Well to answer this we must first realise that what we are talking about is a problem involving three seperate time streams. First is Mr.X’s where he has gone from being single, in a monogonous realtionship with Miss. Y, break up wtih Miss. Y, single again, in a monogonous realtionship with Miss. Z. In his time stream at no point has in been with both Miss. Y and Miss Z simultaneously so within his time stream he has not cheated on either of them.
Let’s now examine Miss.Y’s perspective she has gone from single to in a realtionship with Mr.X, find out he is in a relationship with Miss. Z, break up with Mr.X, single. So it seems to her he has wronged her by seeing her workmate whilst seeing her.
Finally there is the viewpoint of Miss.Z to take into account. Miss.Z’s time stream shows her going from single, in a relationship with Mr.X, discovery of Mr.X dating Miss.Y. Again Miss.Z has every reason to believe Mr.X has not been as faithful as he thinks he has.
So has Mr.X really been two-timing? Or does the fact that his time stream proves he has never dated both simultaneously let him off the hook?
It would appear that Mr.X is both two-timing and not two-timing simultaneously. Yet even taking this stance proves its own problems, the most obvious of which being that it breaks Aristotle’s famous law…that of non-contradiction. The law of non-contradiction states in its third form (its logical form as opposed to its ontological or psychological forms) “The most secure of all beliefs is that mutually contradictory statements cannot be jointly true” [Aristotle, ‘Metaphysics’, 1011b]. So in order to resolve this problem we must accept one of the following:
- Mr.X is two-timing
- Mr.X is not two-timing
Seeing as we cannot hold both the primary problem rears its head once more. Has Mr.X really been two-timing? Or did Aristotle, in devising his law, fail to realise that there could be some examples where it is necessary to hold contradictory statements can both be true simultaneously?
The German philosopher Immanuel Kant throughout his book Critique of Pure Reason argued that time and substance are permanent, this being the case then they must be the foundations for an objective understanding of the world as opposed to the subjective understanding we are currently following based on our perceptions of phenomena. He also argues that for us to make the connection between the manifold of subjective perceptions and objective understanding we require a synthetic unity which comes to us in the form of cause and effect a tool of cognition which combines phenomena with a priori reasoning. But just how valid are Kant’s arguments? It would seem the evidence supports his claims although a small number of philosophers fear what would happen should we gain access to an objective understanding of the world and try to put us off any attempt from moving towards it.
Kant established a set of three analogies named the ‘analogies of experience’ in order to demonstrate that “experience is possible only through the presentation of a necessary connection of perceptions”, or in words experience is the a posteriori synthetic unity of all our perceptions merged into one single consciousness. Kant goes about proving this by making three arguments revolving around the three aspects of what he terms the ‘inner sense’ or ‘inner intuition’, to which we commonly refer to as time. These three aspects of time are thus; permanence, succession and community, with each relying on the former aspects in order for the whole argument to remain valid. Before evaluating Kant’s arguments within the analogies it is best to first give a brief summary of the arguments.
Throughout the first analogy Kant argues “in all variation by appearances substance is permanent, and its quantum in nature is neither increased nor decreased” the reasoning behind this claim is that all our appearances occur within, and only within, time, therefore time must itself be a permanent fixture in the universe allowing substance to flow in sequence or form unities leading to the ever changing appearances we have. He also adds that even though time itself cannot be perceived only conceived as it is the inner sense then it must be a priori to the universe and all substance within it both of which must therefore be a posteriori by necessity. Kant also argues that substance is permanent by referring to an example about smoke, “substance endures and only the accidents vary” as when wood is burnt it leaves smoke and ash but the total mass of the smoke and ash will always be equal to the mass of the wood prior to it being burnt, hence substance is a permanent fixture yet its form changes in time. Since it is only accidents that vary then it must be the case that, for Kant at least, “our apprehension of the manifold of appearance is always successive, and therefore is always varying. Hence…apprehension alone…can never determine whether this manifold considered as experience is simultaneous or sequential…unless something underlying in experience is there always.” Or in other words, the combination of our perceptions will change from moment to moment so our understanding of the world alone is not enough to construct knowledge of how the external world really is as it fails to grasp the constants hiding within it. So the first analogy Kant has argued that substance and time are the only constants in the universe with all other things undergoing change and for this reason we cannot understand the world by empirical means alone.
The second analogy is dedicated to the temporal mode of succession in which Kant tries to convince us that “All changes occur according to the law of the connection of cause and effect” because all appearances succeed one another because we apply our cognition to connect our perceptions in time, thus cause and effect is a synthesising product born out of our cognition. However Kant later adds to this point “But a concept carrying with it a necessity of synthetic unity can only be a pure concept of understanding” thus cause and effect is a key part of our faculty of understanding and therefore needed if we our to obtain knowledge of phenomena, this is because when we perceive phenomena we never actually perceive the object in itself. For example say you were to read the analogies within Critique of Pure Reason you would not actually be perceiving the book itself, only the manifold of all the appearances it presents to your sense of perception, thus objects in themselves remain unknown to us. This isn’t the only thing Kant believes to be beyond our comprehension he also states that “an actuality succeeding in empty time…cannot be apprehended any more than empty time” the reasoning behind this is that to have empty time there must be non-existence yet in the previous analogy he concluded that substance is permanent, hence persists in every point of time making the notion of empty time absurd, from this we can make the inductive leap that cause and effect (probably) relies on substance being permanent. To conclude Kant has argued that cause and effect is the necessary synthetic unity binding time to phenomena via succession which relies on the permanence of substance if a posteriori knowledge of phenomena is to be possible.
The final analogy is concerned with community. Kant uses this analogy to argue that “All substances insofar as they can be perceived in space as simultaneous are in thoroughgoing interaction” meaning that existents although seen to be existing individually, yet simultaneously, are actually existing within a community where they constantly affect one another within each instance in time. For Kant “Things are only simultaneous if their perception can…succeed one another reciprocally” for example placing a ball on a cushion would cause an indentation in the cushion as the indentation makes room for the ball being placed upon the cushion, thus both occur within the same instance. This led to Kant arguing that “substances in space cannot be cognized in experience except under the presupposition that they interact with one another…Therefore every substance…must contain within itself the causality of certain determination in the other substance and simultaneously must contain within itself the effects of the other substance’s causality”, hence substance must contain every possible connection of cause and effect within it simultaneously so that they can be perceived as if they are in constant interaction with one another. In conclusion every substance affects all other substances as all other substances affect the substance first in question, thus substances are held in a community linked by cause and effect within time.
Gardner argues “The Analogies proceed to show that the…categories of substance and causality perform a transcendental function…tied specifically to the circumstance that we are subjects…in time” because when thinking about objects as being things outside our representations we must think of them as existing within time, but beyond the assumed mental flow of our representations. If we cannot do this then objects, that is to say substance, falls back into the temporal flow making then vulnerable to change which goes against Kant’s argument that substance is permanent. Following from this we can assume that Gardner is trying to support Kant in the claim that substance is, in fact, permanent. Yet Kant holds that time and substance cannot be perceived only conceived making them a priori as Scruton argues “every category corresponds to a principle, whose truth is presupposed in its application” and is therefore a priori, hence how the world is objective via necessity even if we cannot perceive it to be as such.
This notion of having time and substance as beyond perception, yet permanent and objective, implies that there must be something else outside, and beyond, phenomena where all objective knowledge must reside. Scruton states this to be the case as “we find causes only by postulating a realm of enduring things”, Kant adheres to this by referring to a realm of objective knowledge which he calls noumena, thus we now have what Gardner referred to as the ‘transcendental function’ of Kant’s analogies. The transcendental function being the analogies were set up in order to prove the existence of noumena in what would seem to be a dualistic epistemology similar to Plato’s concept of the Forms in the intelligible realm and substances in the sensible realm. Gardner also accepts the notion of an objective realm as all things are bound by a single objective nature, he argues “we inhabit a world…in which all objective empirical facts have a particular form, and all appearances collectively compose ‘one nature’” or a manifold which Kant would say lights up an a priori resemblance to that form within noumena, as opposed to being a relative, and therefore subjective, manifold as Hume argues for.
One argument against Kant is ‘if this knowledge is beyond our perception maybe there is a good reason as to why this is the case’ a view held by Prymus who argues that “madmen were feared because it was supposed that they were driven crazy by stumbling upon hidden secrets of the universe…knowledge that no human could comprehend” so for any of us to gain access to noumena would prove dangerous. We have been given warnings of this within popular culture, for example in the sci-fi series Doctor Who an evil villain known only as ‘The Master’ when placed in front of the temporal schism to see time for what it is in itself lost his mind and began plotting away against creation. Similarly in the video game Final Fantasy VI we encounter a clown called Kefka who after being infused with magic to enhance his knowledge of the universe becomes homicidal as he attempts to reduce creation to a state of non-existence. Prymus argues the reason as to why objective knowledge makes us act in such a way is because objective knowledge makes us ‘arational’, that is to say we become entities outside the sphere of rationality (neither rational or irrational), whilst outside this sphere we realise “most of us see existence as necessary, as an imperative…existence is really only…a hypothetical imperative” meaning that existence is only necessary so long as it adheres to our idea of what we seek in the world.
However Prymus’ argument on first sight doesn’t seem to correspond to Kant’s analogies but only to his concept of there being a realm known as noumena, nor does it argues against any of Kant’s arguments as being true. But if we were to take Prymus’ use of the word existence in her essay and ask ‘what is existence?’ then we can answer it by looking at Aristotle who argued that existence is what exists and what exists is substance. Thus we can now deduce by the logical procedure that if X is equal to Y and Y is equal to Z then by necessity X must be equal to Z to state that existence is substance. Now we can see that Prymus’ argument actually relates to the first analogy where Kant argues that substance is permanent. Now if these warnings are true and someone does gain access to noumena and tries to destroy substance then they would also take down cause and effect and the interaction between substances making knowledge, be it a priori or a posteriori impossible. We can therefore conclude that we should not seek objective knowledge but be satisfied with the subjective empiricism offered to us by Hume, unless Kant is mistaken.
Kant originally set up the analogies in response to Hume’s arguments of cause and effect in hope that it would disprove Hume, but just what was Hume’s argument? Hume argued that “It is evident, that there is a principle of connection between the different thoughts…in the mind…To me, there appear to be only three principles of connection among ideas…resemblance, contiguity in time and place, and cause or effect”. It appears that Hume, like Kant, accepts that time must be permanent and cause and effect must also exist if knowledge derived from our perceptions is to be obtainable. However this is where the similarity draws to an end as for Hume knowledge must only be based on empirical methods, and therefore we can only hope to achieve a posteriori knowledge which is subjective due to our own relative experiences of the world, the reasoning behind this is that if “we must enquire how we arrive at the knowledge of cause and effect…knowledge of this relation is not…attained by reasonings a priori” it is only through our experience of phenomena that we conceive the concept of cause and effect, for example if given two billiard balls we would never accept that the first would cause the second to move if it rolled into it unless we had seen this to be the case on a number of previous occasions so that it became a fixed continuity of how things are in accordance with the laws of Newton’s physics. Yet Hume never accepts that cause and effect exists as part of phenomena as it can not be perceived, instead it is a cognitive synthesiser uniting two separate events together consistently to produce a manifold of presentations. So if we cannot perceive cause and effect yet it still does the same job as Kant believes it does, then we can say that cause and effect lies within noumena along with time and substance, thus Hume and Kant although go about it by alternative methods seem to reach similar conclusions as to the nature of time, causality and substance.
To conclude even though Kant set off to argue against the subjective empiricism of Hume he actually constructed a set of arguments similar to Hume based upon a transcendental empiricism (otherwise known as transcendental idealism). A framework supported by, to some degree, Plato, Scruton, Hume and Gardner. However as Prymus pointed out there may be hidden dangers lurking within this realm of objective knowledge, so it might be advisable to remain contented with the subjective empiricism of Hume until we know as to whether there is any truth in Prymus’ claims or if they are just scare tactics to keep us all in the dark about how the world really is.
- Aristotle, 2004, Metaphysics, London: Penguin Classics
- Gardner. S, 1999, Kant and the Critique of Pure Reason, Abingdon (Oxfordshire): Routledge
- Hume. D, 2008, An Enquiry Concerning Human Understanding, Oxford: Oxford University Press
- Kant. I, 1999, Critique of Pure Reason (Abridged (Translated by W. S. Pluhar)), Indianapolis: Hackett
- Kant. I, 2007, Critique of Pure Reason (Reissued Edition (Translated by Smith)), Basingstoke (Hampshire): Palgrave Macmillan
- Plato, 2007, The Republic (second edition), London: Penguin Classics
- Prymus. K, 2009, ‘Kefka, Nietzsche, Foucault: Madness and Nihilism in Final Fantasy VI’, in Beaulieu. M and Blahuta. J, ‘Final Fantasy and Philosophy the Ultimate Walkthrough’, New Jersey: John Wiley & Sons Inc, pp 20-33
- Scruton. R, 2001, Kant a Very Short Introduction, Oxford: Oxford University Press
 Kant. I, Critique of Pure Reason, 1999, B218
 Ibid, A182
 Ibid, A184
 Ibid, A189
 Ibid, B234
 Ibid, A192
 Ibid, A211
 Ibid, B257
 Ibid, B258-B259
 Gardner. S, Kant and the Critique of Pure Reason, 1999, Pg. 171
 Scruton. R, Kant a Very Short Introduction, 2001, Pg. 47
 Ibid, Pg. 51
 Gardner. S, Kant and the Critique of Pure Reason, 1999, Pg. 177
 Prymus. K, ‘Kefka, Nietzsche, Foucault: Madness and Nihilism in Final Fantasy VI’, in Beaulieu. M and Blahuta. J, ‘Final Fantasy and Philosophy the Ultimate Walkthrough’, Pg. 24
 Ibid, Pg. 27
 Hume. D, An Enquiry Concerning Human Understanding, 2008, Pg. 16
 Ibid, Pg. 19
Since the rise of science fiction a few decades ago physicists have started to look into the possibilities of time travel, however physicists being physicists have approached this subject from a somewhat blinkered viewpoint by trying to deal with it from a purely scientific way of thinking. Because of this physicists have managed to make little headway into proving as to whether we can time travel, however if we abandon the physicists scientific style and rely solely on logical thinking it is possible to prove, and demonstrate, that time travel does exist and everyone single one of us is in fact a time traveller.
The Oxford English Dictionary…that excellent record of the one of the greatest languages we have in the world today…defines travel as being “go from one place to another; journey along or through”. So if we now unpack the term time travel using this definition we end up with a concept that means ‘the ability to go from one point in time to another; to journey through time”. This does seem to be no different to the usual conception of time travel but it lacks one thing, normally we expect time travel to mean being able to move from one point in time to any other point in time under the definition just given no such ability is alluded to.
So from this I shall now move onto my demonstrative proof. We as beings living within a temporal framework go about each day in our lives moving from one day to the next, one hour to the next, one minute to the next, in short one point in time to the next satisfying part one of the Oxford Dictionary’s definition of travel, now for the second part the medium we move through when doing this is time hence we are travelling through time satisfying the latter clause. Therefore is it possible to conclude that time travel does in fact exist and that we are all time travellers despite having no special adapted machines…like The Doctor…or superhuman powers…like Hiro Nakamura.
I now end by thanking you all for your time in reading this and wish you all the best of luck with your time travelling adventures. Adieu.
- Hawker. S (editor), ‘Oxford Mini Dictionary’, 2002, Oxford University Press: Oxford
 Oxford Dictionary, pg.655
Ever since the philosophers of ancient Greece there has been an ongoing debate about metaphysics, a debate that has moved through into the medieval era and even into modernity. The nature of this debate is whether the philosophic school of metaphysical realism; as upheld by Plato; or the philosophic school of nominalism; as upheld by Aristotle; shows us the true nature of reality. On the one hand we have the belief that reality consist of things ordered by their abstract counterparts whilst on the other side of the debate it is believed that reality only consists of concrete things and to talk of such abstract ideas is an absurdity. The answer to this debate is elusive but via studious contemplation it becomes apparent that truth lies with the realists in that reality is governed by a set of abstract entities known as universals. Before proceeding any further it is necessary to provide a brief outline as to what is meant by metaphysical realism and nominalism, firstly what is metaphysical realism?
Metaphysical realism is the set of beliefs explaining how reality is built up in two layers, particulars and universals. Loux explains metaphysical realism as being the belief “where objects are similar…there is some one thing that they share or have in common”, therefore we can think of reality as consisting of concrete objects which occupy a single set of spatial co-ordinates, for sake of example call them Α, Β, Γ, but for the realists there is a second layer to reality, the realm of abstracts. These abstracts are capable of occupying multiple sets of spatial co-ordinates simultaneously. It is in the realm of abstracts similarities between Α, Β, Γ resides in the form of universals, which shall be named Φ. So long as Α, Β, Γ share a common attribute they share the same relationship with Φ, this relationship allows us to understand how they differ from each other to allow knowledge to become possible.
One philosopher to argue that reality was defined by a set of universals was Plato who proposed that knowledge can only be truly grasped by obtaining an understanding of what he called the Forms. Plato’s theory of the Forms is most famously put forward in The Republic where Plato claims that “for all the sets of particular things which we have regarded as many; and we proceed to posit by contrast a single form”, which means that Plato is suggesting that particulars can be grouped by a common characteristic, which takes shape as a Form residing in a realm beyond our sensory perception, A similar view is held by Kant later on when talking about the noumenal. For Plato the sensory realm, or “the twilight world of change and decay” cannot hold knowledge just doxa (opinion) as particulars are always in a state of flux, a view first proposed by Heraclitus some years before when claiming that “It is impossible to step twice into the same river”, thus knowledge of particulars without reference to the universal is nothing more than subjective opinion.
However unlike some realists Plato does not go as far as to say that the universals and particulars exist in entirely separate realms, although upon first sight it may appear this is exactly what Plato implies. In fact Plato proposes that the realm of the Forms and “the twilight world of change and decay” are actually both joined together as he explains in 476a of The Republic; “That, since beauty and ugliness are opposites, they are two…And as they are two, each of them is single…but they seem to be a multiplicity because they appear everywhere in combination with actions and material bodies”, this could be interpreted to mean that even though it may seem that universals and particulars exist separately governing different aspects of understanding they are really co-existing with each other as the universals reside within the particular and the particular can only be indentified so long as the universals exists within it. Hence what we have a monist based realism where universals and particulars are two dimensions to the same object.
On the other hand we have nominalism, according to the Stanford Encyclopaedia of Philosophy “The word ‘Nominalism’…in one sense, its most traditional sense, it implies the rejection of universals. In another…it implies the rejection of abstract ideas.” So it becomes quote clear are nominalists believe that reality only exists of particulars. In the first instance the nominalists would accept that abstract ideas exist, such as numbers and other non-spatiotemporal objects, but only in the sense that they, like all objects, must be particulars. In the second instance the nominalist would accept that universals exist but the only universals are non-spatiotemporal objects whilst everything else is a particular. Either way what is certain is that nominalists claim that real objects can only be concrete particulars, where they differ is what non-spatiotemporal, or non-concrete, objects can be classified as, therefore “Nominalism, in both cases, is a kind of anti-realism”.
In support of the nominalist theory of reality there is Plato’s pupil Aristotle, who in The Metaphysics attempts to prove why the Forms are not a feasible way of looking at reality. One criticism Aristotle makes against the Forms is “But above all one might raise the problem what the Forms…might contribute to the eternal things or to things that come into being and are destroyed…And indeed they do not contribute in any way”, the point being made here is the Forms do not actually add anything to the particular they represent not do they add anything to the particulars existence nor take anything from it, therefore the Forms have no value and should not be taken as serious train of thought when describing reality. Aristotle later adds to this criticism “it would seem to be impossible that the substance should exist apart from that of which it is the substance” meaning that the universal could not exist in a realm outside our own as anything that exists does so within the sensory realm in the form of substance. Although as it has already been explained Plato did not claim that there were two separate realms but that they both co-existed as one, thus it could be argued Aristotle misinterpreted Plato’s teachings and therefore misunderstanding Plato’s monist realism.
However by accepting Plato as a monist it does suggest that Plato holds some nominalist leaning, as by claiming that universals and particulars are two dimensions to the same object then they must co-exist within each other. This would mean that there is no such thing as an independent universal entity residing beyond the sensory realm. Therefore if this be the case then it would better to think of universals, in Plato’s monist realism, as abstract ideas from here on as to avoid confusion.
Even though it appears that Aristotle is a nominalist by looking at several other passages in The Metaphysics it is possible to see the outlines of a realist system coming through. In 1006b Aristotle says “all properties are accidents…we can draw the distinction between substance and accident” by properties Aristotle means attributes such as beauty, which Plato argues are Forms, and by substance Aristotle is referring to matter which is the building blocks for particulars but yet is a universal in itself., this can be further supported by Aristotle’s claim that “in the case of things that are, the primary object is substance” which leads on to “everything is connected to the primary”, hence everything that exists is substance and substance must be the first cause for everything.
So what actually is substance? To answer this it must first be asked what exists? The answer to which can be found within the teachings of Parmenides who said “It must be what can be spoken and thought is, for it is there for being”. So what exists is anything that can be spoken and thought of, in which case as long as we are able to conceive or universals, be they Forms or the notion of substance, then universals exist. Furthermore as Aristotle argues that substance is the first cause for everything, and substance can be considered a universal then it follows that universals are the first cause for everything, or at least everything concerned with knowledge. Even the Pre-Socratic thinker Anaximander believed that there was such a thing as a first cause, and therefore a universal, as he claimed “the first principle and element of existing things was the boundless”, this ‘boundless’ would later become known as substance after Aristotle published The Metaphysics.
Another philosopher writing on this problem is the medieval thinker Boethius, who takes Aristotle’s arguments on genera and species and places them under scrutiny. One way of interpreting what is meant by these two terms is to rename genera as universals, as Aristotle claims that substance is a genera, whilst species are particulars, as all else comes from substance. Boethius argues that “genera and species cannot exist. This is understood on the following grounds. Everything that is common to several things at one time cannot be one.” By this it is meant that if a universal exists, as is believed, in all particulars resembling it simultaneously, then substance cannot be a single entity but multiple entities because “it cannot happen that although it is a whole in several things at one time…in itself it is one in number.” Boethius later goes on to argue “Now if a genus is one in number, it cannot be common to many. For one thing if it is common, is either common by parts…or…it passes into the use of those who have it”, or in other words a single entity cannot wholly exist within a multitude of other existents for this would mean that the former would not be a single entity but a multitude in itself. This is an argument very similar to Aristotle’s which goes “how is one Form to come from many Forms? …if they share the Form, then many absurdities will follow, but if do not, then they will neither be like each other”. This argument is a direct attack against Plato’s theory of the Forms as universals the former part making the point already stated earlier, with the latter part stating that if a single universal does not stand above particulars holding the attributes that create their resemblance then how are we able to distinguish between particulars? Thus if we cannot do this then knowledge falls down as we would have to constantly re-learn what each existent is whenever we come across it, also this being the case any concept of language would become meaningless as we would not be able to exchange views on matters reducing communication down to the wriggling of a little finger.
After looking at both sides of the argument it would seem that truth lies within metaphysical realism, despite the efforts of Boethius and Aristotle who attempted to propose a nominalist doctrine, as without the existence of universals any concept of knowledge and language would become impossible leaving us only with subjective opinion but no way to communicate these opinions between each other to build any truth from them. Even the nominalists acknowledge this difficulty has they claim that universals may not exist but abstract ideas (i.e. substance) do, so that we have a starting point to build upon. Or abstract ideas don’t exist but universals do. Either way the nominalists still end up falling back upon some sense of metaphysical realism, thus leaving the view on shaky foundations. Even if we were to take Plato’s monist idea and say universals and particulars are two dimensions of the same thing then they may eliminate the notion of universals existing independently, however it still leaves open the possibility of abstract ideas which now exist within things. Thus we remain with a metaphysical realism, albeit one with more sympathy towards nominalism.
- Aristotle, 1998, The Metaphysics, London; Penguin Books
- Kant. I, 2007, Critique of Pure Reason (Reissued Edition Translated by Smith), Basingstoke (Hampshire); Palgrave Macmillan
- Loux. M. J, 2007, Metaphysics a Contemporary Introduction (3rd Edition), Abingdon (Oxfordshire): Routledge
- Plato, 1993, Phaedo, Oxford; Oxford University Press
- Plato, 2007, The Republic (Revised 2nd Edition), London; Penguin Books
- Spade. P. V, 1994, Five Texts on the Medieval Problems of Universals, Indianapolis; Hackett
- Waterfield. R, 2000, The First Philosophers, Oxford; Oxford University Press
- http://plato.stanford.edu/entries/nominalism-metaphysics/ [accessed 23rd October 2009]
 Loux, Metaphysics a Contemporary Introduction (3rd Edition), 2007, Pg. 17
 Plato, The Republic (Revised 2nd Edition), 2007, 507b
 Plato, The Republic (Revised 2nd Edition), 2007, 508d
 Plutarch in Waterfield, The First Philosophers, 2000, Pg. 41
 Plato, The Republic (Revised 2nd Edition), 2007, 508d
 Plato, The Republic (Revised 2nd Edition), 2007, 476a
 Aristotle, The Metaphysics, 1998, 991a
 Aristotle. The Metaphysics, 1998, 991b
 Aristotle, The Metaphysics, 1998, 1006b
 Aristotle, The Metaphysics, 1998, 1003b
 Aristotle, The Metaphysics, 1998, 1004a
 Simplicius in Waterfield, The First Philosophers, 2000, Pg. 58
 Theophrastus in Waterfield, The First Philosophers, 2000, Pg. 14
 Boethius in Spade, Five Texts on the Medieval Problems of Universals, 1994, Pg. 21
 Boethius in Spade, Five Texts on the Medieval Problems of Universals, 1994, Pg. 22
 Boethius in Spade, Five Texts on the Medieval Problems of Universals, 1994, Pg. 22
 Aristotle, The Metaphysics, 1998, 991b
During the seventeenth century the French rationalist René Descartes constructed a series of sixth short essays known as ‘The Meditations’, in which Descartes proposed to demolish all his beliefs in order to make way for certain truth upon which he could build all further knowledge upon. Descartes points out in ‘The Meditations’ that the only certain truth must be of the metaphysical, thus this must be the root for all knowledge. Since certain truth, for Descartes at least, comes from metaphysics then it knowledge must have a metaphysical cause, hence Descartes spends some time throughout ‘The Meditations’ trying to prove that it is necessary for God to exist since God is the only metaphysical entity we can rely on to be non-deceiving and therefore use as the root system for the tree of knowledge. Descartes uses a set of three arguments to prove God’s existence; however these arguments turn out to be partly unsuccessful as we can only prove that God exists as an idea.
Descartes’ first causal argument claims we can prove God exists because any idea we hold must be true as we cannot prove false that we have the idea of it and no idea can be any less true than another since they are all ideas of equal existence within our minds. However since we hold minds of a finite capacity then we can only conjure up ideas of finite things, such as hippogriffs or phoenixes, anything greater than our finite capacity must have been placed within our minds by a greater entity. Since God is of infinite nature then it would be impossible for us to devise such an idea by ourselves and so the idea of God must come from another entity, also the idea must come from something of equal capability to the object in question, so God being infinite must have been the idea of an infinite mind and since God is the only infinite source we can hold the idea of the only answer we can rationally deduce is that God created himself, thus it is necessary that God exists in order for us to hold the idea of him.
The second casual argument begins by Descartes asking how he came into existence of which he poses three ways; himself, his parents or some first principle. He dismisses himself from the equation by stating that if he created himself he must hold an infinite power to do so since only an infinite power can create itself due to its nature of being infinite but during the first argument he had already claimed his was of finite nature. He then moves on to refute the claim that it must be his parents which caused his existence, since they would need to have been created by their parents who were in turn created by their parents and so in creating a state of infinite regress unless some first principle proves to be the ultimate cause. This proves, in Descartes eyes, that he must have been created by some first principle, which he names as God, and since he was created by this first principle it is necessary that it exists as something that does not exist could not create something that does, thus God exists through necessity.
In the fifth meditation Descartes puts forward a third and final argument, known as his ontological argument, which goes as follows: whenever Descartes imagines the idea of God he always imagines God as having a “supremely perfect being”, thus by this definition God must hold all attributes that entail perfection, including omnipotence, unconditional honesty, benevolence and also existence. Since God is ultimately perfect then God must exist since by definition God is perfect and by perfect we mean existing. Descartes then completes his argument by using a set a set of analogies to prove that the nature of a substance cannot be separated from the substance, therefore both nature and substance are mutually dependent. One of the analogies is of a geometric nature as Descartes takes the idea of a triangle, by nature a triangle has three angles and “that its three angles are equal to two right angles”. The second analogy made is between a mountain and a valley, both are mutually dependant since there cannot be a mountain without a valley. From this line of argument Descartes concludes that God exists because he relies on his existence on order to maintain his perfection, just as the existence relies on God being perfect otherwise existence would not be necessary.
Sorell in page sixty-eight of ‘Descartes a Very Short Introduction’ states the arguments employed by Descartes in proving God’s existence are nothing more than circular argument, a form of sham-reasoning, since Descartes claims that he can only prove God’s existence by using clear and distinct premises, but Descartes also claims that he can only come across clear and distinct premises after he has proven God’s existence. This being the case then there are only two possible outcomes. One being that there are no clear and distinct premises so we shall never be able to prove God exists, because the only premises that we cannot hold any degree of doubt about are those of clear and distinct nature. Hence we can only ever doubt that God exists, to be certain either way it impossible. The other possibility is that there are clear and distinct premises and so we can prove that God exists but the certainty of the used premises do not rely on God’s existence, consequently God’s existence is not necessary for our capability of holding certain truth about anything, this refutes Descartes claim that God is the foundation needed for his metaphysics which is to be the root system to his metaphoric ‘tree of knowledge’. French scientist Pierre Petit also pointed out that it is difficult to accept Descartes claim that all humans hold an idea of God and God was necessary for certainty about all other knowledge, since even “the most dedicated atheists” could hold with absolute certainty the Earth and Sun existed without needing God to exist. Following Sorell’s and Petit’s claims we can rationally conclude that either God doesn’t exist, or if he does we cannot be certain and it is also unnecessary that he exists.
Further criticisms of Descartes’ arguments come from Jorge Secada. Secada says the first casual argument “assumes knowledge of God’s essence before it [the argument] can draw its inference. As with the ontological argument, it too follows the essentialist path.” By this Secada means Descartes is guilty of assigning the attribute of existence to God before actually proving that God exists in order to hold said attribute. This is a dangerous position to put oneself in since if it turns out that God doesn’t exist then he has misplaced the attribute since only existents, or substances as Descartes calls them, are capable of holding attributes, consequently if God does not exist then Descartes reasoning would fall down allowing refutation for the remainder of Descartes arguments. Secada also raises a concern with Descartes claim that only infinite entities could create themselves out of nothing and all infinite entities are perfect, but Descartes acknowledges his imperfection therefore he cannot be infinite. What Secada puts forward is the possibility that Descartes was infinite only decided to relinquish some of his perfections in order to create himself as a finite entity, having done this it was seem logical that Descartes would forget about his previous infinite self due to the newly acquired finite memory he had given himself. Even though this does propose that God is unnecessary it does raise the question why choose to be something less perfect? A plausible answer is we would do so because we had a reason for doing, only this reason remains unknown to us so it cannot be the case and therefore we can go someway to refute Secada on this occasion and accept Descartes’ proposal that we are incapable of creating ourselves, and thus some first principle must be our creator.
There is another concern we can make with Descartes arguments based on the claim that God is a “supremely perfect being”, if God is, as he is claimed to be, perfect then he would hold the attribute of being unconditionally benevolent, however this is not the case since we can see injustice happening in the world all the time, in fact the contemporary poet Churchill speaks about one particular type of injustice in his poem ‘Home’ which is to do with bullying. We can see this in the lines “watching outside nervously. Will they? Won’t they? Crash! Another window gone.” An unconditionally benevolent God would not allow such a social injustice to occur and therefore God cannot be unconditionally benevolent. The point of this being that if it is possible that God is not unconditionally benevolent then it is also possible that God fails to hold other attributes that are necessary for perfection since God would have been proved to be imperfect. One attribute Descartes assigns to his concept of a perfect God is existence, but since God might possibly be imperfect then it is plausible to claim that it is possible that God fails to hold the attribute of existence in which case we can conclude that God does not exist. Although this conclusion is shaky as it is founded upon hypothetical reasoning, which has not been proven to be either true or false, thus we cannot use it as sound evidence against Descartes but merely as inductively forceful or unsound evidence.
However there is some support for Descartes assertions from the cosmological argument for the existence of God as put forward by Saint Thomas Aquinas in his Five Ways. Aquinas’ First Way states that “there must be a first cause of all change, since nothing changes itself” and that we cannot have a series of causes leading to an infinite regress. This supports Descartes second causal argument as far as it proves that Descartes must have been caused by a first principle and not his parents, as the latter suggestion leads to infinite regress which is an illogical position. However what this first principle is remains unnamed, Aquinas only argues that it is what we call God he does not claim that it is God. Hence the first principle does not have to be God but some other infinite entity, perhaps even Anaximander’s apeiron. In fact if we look back upon what has preceded this section of the argument then we know that the first principle exists but it is nowhere mentioned that it must be perfect, only that God is perfect and it may be the case that God is not the first principle, in which case the apeiron might be the first principle since as it does not need to hold benevolence as a attribute allowing room for injustices to occur. Therefore, following Aquinas we can say that a first principle exists and that it is often called God but the existence of any such God is still questionable as the first principle may actually be something other than God.
To conclude it seems unlikely that God exists since we are capable of doubting God’s existence based on the injustice argument mentioned above and the dubious reasoning Descartes uses as highlighted by Sorell, not only this but following Sorell and Petit we can also see that God is unnecessary and since Descartes and Aquinas both claim that all existents require a necessary reason for existing then we have no reason for God to exist. On the other hand we should not completely dismiss Descartes arguments since there is certainty about the necessity for a first principle, and as Aquinas points out this is often called God, so what Descartes refers to as God in ‘The Meditations’ is not God as such but just a name for the first principle. Thus as long as God is used as a name for the first principle and we do not assume God is an actual entity then we say that God exists as an idea within our minds and any external God is unnecessary and cannot exist.
- Burns. E & Law. S, ‘Philosophy for AS and A2’, Routledge, 2004
- Descartes. R, ‘Discourse on Method and The Meditations’, Penguin Classics, 1968
- Gaarder. J, ‘Sophie’s World’, Phoenix House, 1995
- Secada. J, ‘Cartesian Metaphysics’, Cambridge University Press, 2000
- Skirry. J, ‘Descartes a Guide for the Perplexed’, Continuum, 2008
- Sorell. T, ‘Descartes a Very Short Introduction’, Oxford University Press, 2000
- Wise. P et al, ‘POP! The Power of Poetry’, Young Writers, 2006
 Pg. 123, Burns. E & Law. S, ‘Philosophy for AS and A2’, Routledge, 2004
 Pg. 143, Descartes. R, ‘Discourse on Method and The Meditations’, Penguin Classics, 1968
 Pg. 52, Sorell. T, ‘Descartes a Very Short Introduction’, Oxford University Press, 2000
 Pg. 150, Secada. J, ‘Cartesian Metaphysics’, Cambridge University Press, 2000
 Pg. 123, Burns. E & Law. S, ‘Philosophy for AS and A2’, Routledge, 2004
 Pg. 477, Wise. P et al, ‘POP! The Power of Poetry’, Young Writers, 2006,
 Pg, 109, Burns. E & Law. S, ‘Philosophy for AS and A2’, Routledge, 2004
The matter concerning tomorrow’s sea battle is a complicated one which features in Aristotle’s book ‘De Interpretatione’, also known as ‘On Interpretation’. Aristotle tries to resolve the problem by using his own theory of logic, the rules of which he sets out within ‘Prior Analytics’. The problem can also be answered by referring to Platonic fatalism which would argue the case that since chance and free will have no effect on anything then what is true now must be true tomorrow and so tomorrow’s sea battle is necessary. However by analysing Platonic fatalism and finding it faults, and then applying Aristotelian logic then this is not the case since tomorrow’s sea battle is not necessary but it is possible.
According to the concept of Platonic fatalist time moves on a set path totally independent of the effects that occur within it, thus what was true of yesterday is true of today and shall be true of tomorrow and every day then on. In this sense fatalism can be described as pre-determinism. Platonic fatalism rests upon a set of three assumptions. The first assumption is what is commonly known as the principle of bi-valence, which is the principle whereby all assertoric statements can only ever be true or false, there is no possible third option, in between state or degrees of relative truth/falsehood. Secondly once a statement possess a truth-value it cannot change no matter what effects occur upon it, hence what is true yesterday is true today and will be tomorrow, thus we should not waste energy trying to intervene with the way the world works since any such attempt will bear no effect on the pre-destined path time is set to take, instead we should take contentment with being inactive and the consequences of our inaction since there is nothing we can do otherwise. The third assumption is a hidden premise to the argument and comes to light under after Aristotle scrutinises the concept. The third assumption fatalism is based on is if something is true then it must be necessarily true. It is this concept Aristotle refutes within his works ‘De Interpretatione’ and ‘Prior Analytics’.
Aristotle proposed that free will must hold some importance otherwise why would we be granted such a useless faculty? If fatalism was true then Aristotle would be forced to accept that both deliberation and free will were useless tools of the mind, this would have proved detrimental to his works on ethics which relied on such faculties. Aristotle also questioned fatalism on the grounds that the first two assumptions are faulty; to begin with the principle of bi-valence if accepted meant that it becomes impossible to change our position on any subject since truth-values cannot change. Secondly if something is true it does not follow that it must be unconditionally necessary for it to be true, for example if Mr. X went into a pet shop and come out the proud owner of a puppy then it is true that Mr. X brought a puppy but not necessarily true that Mr. X brought a puppy as he could have equally used his free will to purchase another form of pet. Aristotle puts forward a third argument to refute this third assumption which goes along the lines of, just because X is true it does not follow that X is unconditionally necessary. In order for a statement to be necessary then we must give it its correct temporal justification, this asserts the importance of time’s effects on truth-values, opposite to the Platonic view.
By looking at Aristotle’s refutation of Platonic fatalism as given above it becomes possible to begin to understand Aristotle’s approach towards the sea battle problem. But there is still more information needed in order to get a complete understanding of Aristotle’s position, and this is the theory behind Aristotelian logic. According to Aristotle “all sentences are meaningful…but not all make statements; only those in which truth and falsity are found do so” so for Aristotle the only sentences that are meaningful are ones that hold a truth-value of some description, these meaningful sentences are what Aristotle calls propositions, or to quote his definition of a propositions exactly “A proposition, then, is a statement affirming or denying something…this is either universal or particular or indefinite”, by universal Aristotle means what applies to all or none of the term, whereas particular refers to propositions which make use of a soft quantifier such as some, few or many, finally indefinite propositions are those which propose no quantifier at all. Aristotle claims that propositions must consist of a terms which Aristotle said “I call a term that into which the proposition is resolved”. Now this has been established it is possible to begin to understand Aristotle’s method for resolving the problem concerning tomorrow’s sea battle. Aristotle argued that logical certainty about any given matter could be found through deductive reasoning based upon arguments constructed from two propositional premises leading to a propositional conclusion; this method is known as syllogistic reasoning or sullogismos, with the described form of argument named as a syllogism.
According to sullogismos then if the two given premises are universal affirmative propositions then it becomes necessary for the conclusion to follow, this being the case then the argument for tomorrow’s sea battle should look something like this. It is always true now that a sea battle will occur tomorrow; it is also always the case that when something is true now then it be necessarily true tomorrow, therefore the sea battle will always happen tomorrow as it is necessary. The same situation occurs whenever two universal negative propositions are used as premises although since the problem is concerned with a conditional then it must be assumed that the argument is being based on affirmative propositions.
According to Aristotle in ‘Priori Analytics’ if a proposition is a universal then it must work not only forwards but backwards for example “if it is admissible for no garment to be white, it is also admissible for nothing white to be a garment”, this is what Aristotle refers to conversion and can be applied to all first figure syllogisms. First figure syllogisms are those which follow the structure of all A are B, all B are C therefore all A are [necessarily] C. If the rule of conversion is to be applied to the proposed argument as given above then the argument should look like this. It is always the case that tomorrow’s sea battle is necessary, it is always the case that when something is necessarily true tomorrow the it always true now, therefore it is true now that there will be a sea battle tomorrow. Once the argument has been converted it starts to reveal it weak points as the new first premise can be disproved by adding an additional premise which counters it for example ‘today a letter came through declaring that a cease fire had been agreed so tomorrow’s sea battle has been called off’, this would mean that it is no longer the case that tomorrow’s sea battle is always necessary since we have introduced the possibility of it being false (of course the letter could be a hoax as part of a stratagem to lower enemy defences). What this has effectively done is reduced the conclusion from a universal proposition to a particular proposition since with the additional premises added to the unconverted argument the conclusion follows as such: the sea battle might happen tomorrow as it is possible, although equally it might not happen tomorrow as this is also possible.
Aristotle agrees with this since as “it might equally well happen or not happen, since what is as chance has it no more thus than not thus” by which he means that nothing is pre-determined as Plato would have his followers believe but everything is down to free will and chance, but he extends this view to claim that within this theory of a random chaotic fate there is actually some order since everything that happens does so for a reason, because “it is not because of the affirming or denying that it will be or will not be the case…it was necessary for this to happen…everything that happens happens of necessity”. Hence it doesn’t matter whether the syllogism only produces a conclusion where tomorrow’s sea battle is only possible and not certain, if it happens then it is only because it happened due to necessity; it had a reason for happening.
This idea that things happen only if they have a reason to happen which then makes the event necessary does start to resonate back into Platonic fatalism since if everything if left to chance which is then ordered then there must be something which is manipulating the chaos as to bring it to order, this being the case then there must be some plan drawn up otherwise there would be no way of knowing whether things are running to order, in which case everything is pre-determined. Aristotle even admits this as he said “everything that will be, therefore, happens necessarily so nothing will come about as chance”. By using the phrase ‘will be’ Aristotle if implying that this is to be the case whenever referring to propositions about the future, which provides a loophole for Aristotle to avoid the criticism of sounding hypocritical by refuting Platonic fatalism but then supporting it as he could claim that free will can only change the truth-values of things in the present and all things in the past are now fixed and all things yet to be can be pre-determined based on evidence we hold in the present, however whatever we pre-determine will happen in the future might not happen it only will if it is necessary.
Barnes agrees with this idea of future propositions must be pre-determined and present propositions are changeable due to free will since if propositions about the future, he argues, follow the rules laid down for sullogismos then either outcome is true because of the possibility of either outcome to occur and the lack of certainty than it will be one or another, thus within the present it not necessarily true for the future proposition to be true or false. But propositions about the past must hold a particular truth-value and therefore must be necessarily true or false depending on that truth-value. This then makes any future proposition based upon those concerning the past necessarily true or false depending on the truth-value of the past proposition since the past is fixed according to Aristotle and Platonic fatalism. Therefore if it is true now that a sea battle will happen tomorrow then tomorrow’s sea battle is possible but not necessary as the proposition concerns the present and not the past, hence free will and chance is still capable of changing the course of events.
To conclude, the matter concerning tomorrow’s sea battle is a confusing one which proves difficult to resolve by means of sullogismos. Nevertheless a conclusion is possible to be obtained, since it is possible that tomorrow’s sea-battle might not happen, which was proven by the ability to add a counter-statement in as an additional premise and based on the argument proposed by Barnes then it becomes arguable that tomorrow’s sea battle is not necessary because there is a significant lack of evidence that may appear between now and then to alter the truth-value of the argument, which is; ‘if it is true now that there will be a sea battle tomorrow, then tomorrow’s sea battle is necessary’. Although since the transition from sullogismos to syllogism is a mistranslation there may be more rules, such as those concerning inductive reasoning, or epagoge, which could prove the case to be otherwise.
- Aristotle, ‘De Interpretatione’ in Barnes. J, ‘The Complete Works of Aristotle [Vol. 1]’, Princeton University Press, 1984
- Aristotle, ‘Priori Analytics’ in Barnes. J, ‘The Complete Works of Aristotle [Vol. 1]’, Princeton University Press, 1984
- Barnes. J, ‘Aristotle a Very Short Introduction’, Oxford University Press, 2000
- Barnes. J, ‘The Cambridge Companion to Aristotle’, Cambridge University Press, 1995
- Bowell. T & Kemp. G, ‘Critical Thinking a Concise Guide [second edition]’, Routledge, 2005
 Aristotle, ‘Priori Analytics’, 24a16
 Aristotle, ‘Priori Analytics’, 24b16
 Aristotle, ‘Priori Analytics’, 25b10
 Aristotle, ‘De Interpretatione’, 18b8
 Aristotle, ‘De Interpretatione’, 18b39-19a4
 Aristotle, ‘De Interpretatione’, 18b15
Is Time Real
The question ‘is time real?’ may at first glance seem simple, requiring nothing more than a single word answer…yes. However here lies a difficulty if we answer ‘yes time is real’ then we have the complex problem in trying to explain exactly what time is. We often use the term time in expressions such as ‘I ran out of time’ as if time is something limited, yet on the other hand we say ‘there is all the time in the world’ which infers that time is something unlimited, already we have ran into problems as something cannot be limited and unlimited simultaneously. We also make use of the phrase ‘time stood still’ indicating that time must have been in motion to begin with again this can be problematic as if time is unlimited then it would consume all of space and therefore have nowhere to move making a locomotive unlimited time implausible. Equally if time is static then it causes problems for change as things are normally said to change as time moves on, consequently for change to be possible some form of locomotive time must be present.
On the other hand if we answer ‘no time is not real’ we have an equally challenging task ahead of us as we must disprove all arguments that claim time to be either limited or unlimited, locomotive or stationary, or in fact any argument that posits time with an attribute. Having successfully done that we must then work out why we refer to time as an existing thing if its only attribute is non-existence, here lies yet further difficulty. Hence to answer either way this question is far deeper that it first appears.
From what has been said so far it would seem that the only plausible options open to us are time is a locomotive limited entity, time is a stationary and either limited or unlimited entity, or time is a non-existent. By looking at various arguments put forward for both the defence that time is real and for the case that time is not we shall come to realise that time is actually time is part of a four-dimensional framework which subsists as part of our cognition, or in Kant’s words, inner sense which allows us to experience the physical world and make sense of it, therefore time is real.
To begin let us first examine the arguments against the notion that time exists beginning with those of Conee and Sider who say “we ordinarily conceive of time as being something that moves…the problem with this way of thinking is that time is the standard by which motion is defined; how then could time itself move?”  If time does move, then it must move though some secondary time. Let us call time t and this new secondary time t’ now if t moves through t’, t’ still being a form of time and time being something which moves, then t’ would have to move through a further form of time t”. Now following this on would result in an infinite regress argument since every time we introduce a further form of time we would require an even further form of time, hence any notion of a moving or flowing time becomes absurd and so time must be static.
Conee and Sider also argue “time is just one of the dimensions of space-time”  and “time has a special direction: past to future”, this could be taken to be contradictory to the previous argument in which time is proving to be static as anything which has a direction must be moving. However this is not the case, by direction they are not talking about direction of travel but the direction in which it points, for example if I were to stand stationary the way in which I would face would be my direction yet I am not moving, this is the same for time. From these two arguments we can come to the conclusion that both Conee and Sider believe time to exist as a static entity which is part a four-dimensional space-time framework.
There also seems to be two concepts of time known as A series and B series, and it would appear Conee and Sider are both advocates of the A series notion of time. McTaggart clearly explains how each of the two notion differ in his essay Time “I shall give the name…A series to that of positions…from far past through…to the far future…the series of positions which runs from earlier to later…I shall call the B series”. However McTaggart does not support either of the two series instead he denies the existence of time, he argues “we perceive events in time as being present…this merely subjective…a constant illusion of our minds” by this he means that what is present relies entirely on the subject and their temporal location. For example as if I were to say ‘presently I am writing this sentence’ then by the time you come to read it the statement will be rendered false as I wrote it in what would then be the past. Therefore any system of time based upon past, present and future will be completely subjective and therefore illusory, hence A series time cannot exist.
But what of B series time? McTaggart claims that “if then a B series without an A series can constitute time, change must be possible without an A series…but this is impossible…if there is any change, it must be looked in the A series” the reasoning behind McTaggart’s claim that B series time is impossible is because subject x in b series time would be earlier than subject y and must always be this way in accordance with the notion of B series time then time never progresses and if time fails to progress then change fails to happen. Thus B series time cannot offer change only A series time can, but A series time cannot exist so neither can B series time as the latter depends on the former.
Loux states “we may concede that there are things that are not in time. Philosophers have claimed that God, is not a temporal being, and it has been argued the abstract entities like properties, propositions and numbers are outside time.” If this is true and things do not exist outside of time then they must not change as only things within time change, yet we have heard of God changing form in the Bible as one night in a stable in Bethlehem God became human in the form of Jesus. If the Bible is an accurate historical document then this goes against the notion that time is essential to change as if change can occur outside of time then time is no longer necessary for change, and thus time need not exist.
The idea of time not existing is far from being a modern notion, the Pyrrhonian Sceptics in Ancient Greece, along with the Stoics and Aristotle who shall be mentioned a little later, also denied time’s existence. The sceptical argument denies time on the grounds that if it exists it must be either limited or unlimited yet it cannot be either since “if limited…there will be a time with no time…which is absurd” but “if unlimited…past and future exist, each of these will be present. But it is absurd”. So what we are left with is a time which is not limited but not unlimited, or in other words something that both is and is not, with the is in this case meaning limited. Yet to have something that is and is not the predicate posited to it breaks the law of non-contradiction therefore time can not possibly exist without breaking this law.
The Stoics held the belief that the cosmos was “the god himself who…being the craftsman…taking substance as a totality back into himself in certain temporal cycles”, by which they meant the universe was caught on a temporal loop which ends and begins anew, a theory now taken by physicists as the big bang followed by a big crunch. This notion of time being looped is detrimental to the B series theory of time especially given that the Stoics also believed that “the cosmos, governed by reason, has the best possible organization, this is repeated in each cycle”. Leaving us with a repetitive time which with every passing cycle will play out exactly as the previous did, the reason this is detrimental to B series time is the fact that for B series to work x must be earlier than y and must always be earlier than y, but under the Stoic concept of circular time we get x being earlier and later than y. This contradicts the B series view on time and therefore if time is circular as the Stoics believe then B series time cannot exist.
However the Stoics do not deny time entirely, they “thought that time is incorporeal… a thing conceived of as existing on its own”but it was also unlimited and infinite, infinite because it was looped and therefore has neither beginning nor end and unlimited because it could not be traversed in its entirety as once the ‘end’ is reached you will find yourself back at its ‘beginning’, that is the dawn of a new cycle. This usage of the word unlimited gets around the Pyrhhonian use of the word as the Stoics do not take it to mean something which can be extended infinitely in all directions but merely impassable, thus an unlimited time can exist regardless of the Pyrhhonian criticism.
When discussing the fundamental principles of the cosmos Aristotle has this to say “if any one of them were infinite, the others would have been destroyed”, time being one of the fundamental principles of the cosmos then if it were to be unlimited then it would be extended in all directions pushing everything out of existence, this includes space and substance yet as space and substance continue to exist alongside time then time cannot be unlimited, as the Pyrrhonean Sceptics led us to believe. Another of Aristotle’s arguments against time is critical of A series time as it shows how the past and future are not real, thus proving that the flow of A series time is not plausible. Aristotle’s claim comes like this, “some of it has happened and does not exist, and some of it is in the future and does not yet exist…it would appear to be impossible for anything which consists of things that do not exist to exist itself”, the claim can be explained quite clearly as if time exists of non-existent sections then the only thing that can exist by combining these non-existents must be non-existence and therefore A series time cannot exist.
So far we have looked at the arguments that time does not exist, and what cannot exist cannot be real. From what has been said we can now say that is seems unlikely that B series time can exist, but for A series time although the evidence suggests it does not exist McTaggart’s claim that A series time is subjective and therefore an illusion of the mind could be interpreted to mean that A series time subsists as a product of mind, in which case A series time is real whereas B series time is not. Now we shall look at the arguments for time’s existence beginning with looking at the revised version of B-series time.
It would seem B series time has already been condemned however there is a revised version which may bring it new life. This new version of B series time like its earlier format removes the idea of tense from time so there is no past, present or future but also removes the ideas that time as a flow from earlier to later. Instead “defenders of the new B-theory…take time to be just another dimension along with the three spatial dimensions”, so the revised B series suggests time to be part of a four-dimensional space-time framework as supported by the likes of Conee, Sider and Smart.
Smart is an advocate of static time as part of a four-dimensional framework claiming that “our notion of time as flowing…is an illusion which prevents us seeing the world as it really is”. For Smart time is just another dimension to the three spatial dimensions so as things pass through the three-dimensional ‘cube’ that is space it also moves through this extra dimension known as time and if we were to dissect time into slices we would observe space and all forms of substance within changing, but time itself is not changing only space is changing and its temporal location along the fourth dimensional plane. So what Smart suggests is we ought to remove the notion of a locomotive time as being the cause of change, which requires a change in language, one which is without tense as opposed to the tensed language used for A series time. “If we are going to eliminate the notion of change we had better…eliminate…words such as ‘past’, ‘present’ ‘future’ and ‘now’”. Having a language without tense would result in statements such as ‘I am typing this now’ into ‘I am typing this on the seventh of February 2010’, hence all statements using the terms ‘now’ or ‘present’ must be replaced by referring to the precise temporal location within the temporal plane. The same can also be said of statements using terms such as ‘past’ and ‘future’. Consequently it would seem the revised B series notion of time is more plausible than its predecessor, although it does require a change in the way we use language otherwise we shall remain in the shadows as to the true nature of time.
Loux provides further support for the revised B series notion of time as he says “there can be little doubt that…contingent beings…appear to have their being in time” and McTaggart “fails to show that the B series taken by itself is not a proper temporal framework”. Proposing that time exists as an eternal principle which acts as “a dimension along with the three spatial dimensions”, even though this sounds a lot like the revised B series notion of time which sees time as part a four-dimensional framework but Loux adds that it is eternal, a concept he calls eternalism. Eternalists argue time to be an eternal existent, one which cannot have an ending, not to be confused with unlimited which implies it can stretched out in all directions time can only be stretched along its dimensional axis, which it can be forever according to eternalists.
Epicurus argued that time is neither substance nor predicate but a predicate of predicates, as he said in the two fragments; “nor must one predicate anything else of it, as though it had the same substance as this particular thing” and “Epicurus says that time is a property of properties”. By this what is meant is that time is incorporeal but is also something which cannot be posited to things instead it exists outside the boundaries of substance and predicate in realm of its own. It could then be argued that this realm in which time exists is the realm of cognition making time a substance of mind; hence time does not exist but subsist.
Kant was another strong advocate that time was real having believed that “time is a necessary presentation that underlies all intuitions…all actuality of appearances is possible only in time. Appearances…may go away; but time itself cannot be annulled”. So for Kant time is not something which happens to be real, but it is also necessary and cannot be removed, so just what does Kant mean when he claims time is a presentation? Unlike others such as Smart who argue time is objective Kant claims “time is not a universal concept”, in fact he argues “time is merely a subjective condition of our intuition…time is nothing”. Although what Kant means here by nothing is not something which is non-existent, instead Kant suggests time is an entity without substance, thus it cannot be part of the realm of phenomena, which is the physical realm. Time is an entity of cognition and being an entity of cognition it must subsist as a product of mind or as Kant calls it ‘inner sense’. This view can be seen clearly in the Critique of Pure Reason where he states “time is not something that is self-subsistent or that attaches to things as an objective determination…for if time were self-subsistent it would be actual. But if on the second alternative…then it could not precede the objects”. A view supporting Epicurus’ idea that time is neither substance nor predicate, we also see support from McTaggart that A series time is subjective and cannot exist, yet McTaggart fails to deny time as a subsistent, so perhaps there is some truth in Epicurus’ and Kant’s claims that time subsists as a substance of mind.
To conclude it seems to be the case that time is real, and it is a four-dimensional space-time framework, and therefore only the revised B series concept of time is real. However there is some convincing evidence suggesting time subsists as revised B series time. Since any form of space/time framework we have is going to be a man-made device created by our cognition then time could only ever be a substance of mind and therefore only be real in the sense that it subsists as opposed to existing as part of the physical world we experience through our senses. Furthermore time is static and unlimited only as far as it can stretch along its dimensional axis for all eternity.
- Aristotle, 2008, Physics (Translated by Waterfield), Oxford: Oxford University Press
- Conee. E and Sider. T, 2007, Riddles of Existence a Guided Tour of Metaphysics, Oxford: Clarendon Press
- Gerson. L and Inwood. B, 1997, Hellenistic Philosophy Introductory Readings (2nd Edition), Indianapolis: Hackett
- Kant. I, 1996, Critique of Pure Reason (Abridged (Translated by Pluhar)), Indianapolis: Hackett
- Kant. I, 2007 , Critique of Pure Reason (Reissued Edition (Translated by Smith)), Basingstoke (Hampshire): Palgrave Macmillan
- Loux. M. J, 2007, Metaphysics a Contemporary Introduction (3rd Edition), Abingdon (Oxfordshire): Routledge
- McTaggart. J. M. E, ‘Time’, in Loux. M. J, Metaphysics Contemporary Readings (2nd Edition), 2008, Abingdon (Oxfordshire): Routledge, pp 341-350
- Sellars. J, 2006, Stoicism, Chesham (Buckinghamshire): Acumen
- Smart. J. J. C, ‘The Space-Time World’, in Loux. M. J, Metaphysics Contemporary Readings (2nd Edition), 2008, Abingdon (Oxfordshire): Routledge, pp 383-394
- The Holy Bible accessed at http://www.biblica.com/bible/verse/?q=Luke%202:1-20&=yes (21:36 05/02/2010)
 Conee and Sider, Riddles of Existence a Guided Tour of Metaphysics, 2007, pg. 44
 Ibid, pg. 50
 Ibid, pg. 50
 McTaggart, Time, 2008, pg. 351
 Ibid, pg. 351
 Ibid, pp. 352-353
 Loux, Metaphysics a Contemporary Introduction (3rd Edition), 2007, pp. 205-206
 Luke 2:1-20
 Sextus Empiricus, Outlines of Pyrrhonism, 47.141
 Ibid, 47.142
 Diogenes Laertius, 7.137
 Sellers, Stoicism, 2006, pg. 99
 Sextus Empiricus, Adversus Mathematicos, 10.218
 Aristotle, Physics, 2008, 204b22
 Ibid, 217b32
 Loux, Metaphysics a Contemporary Introduction (3rd Edition), 2007, pg 224
 Smart, The Space-Time World, 2008, pg 385
 Ibid, pg 386
 Loux, Metaphysics a Contemporary Introduction (3rd Edition), 2007, pg 206
 Ibid, pg 212
 Ibid, pg 213
 Diogenes Laertius, Letter to Herodotus, 2.72
 Sextus Empiricus, Adversus Mathematicos, 89. 219
 Kant, Critique of Pure Reason, 1996, A31
 Ibid, B47
 Ibid, A35
 Ibid, B49-A33