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21
Logic / Re: Truth as a Property
« Last post by LouFederer on August 09, 2012, 01:03:25 pm »
Casey Enos does it again... Amazing.

22
Logic / Truth as a Property
« Last post by Casey Enos on August 08, 2012, 10:38:36 pm »
This is one of the essays I rehearsed for the logic exam, and I used this one on the exam. It scored a 70 and ran to eight complete pages. I actually consider this to be one of my best.

"When we say that a statement is true, are we attributing the property of truth to it?"
What exactly is being asked when we ask whether the property of truth may be assigned to a statement? When interpreted as being a question of the sort of whether or not a snow ball has the property of being white, it is a self-evidently an absurd notion; however when it is taken into account that we may be dealing with a very different sort of entity and sort of property, it becomes a much more problematic question. Before an intelligible answer may be given, it is necessary to delineate various theories as to what sort of entities might carry truth; what exactly "truth" is, and what sort of property we are discussing.
A common, intuitive account of truth is the Correspondence Theory, by which propositions are "true" when their structure and contents correspond to facts about the world. A traditional account having its origins in Aristotle, the correspondence theory defines a proposition "P" as true if and only if P, that is the fact which the proposition corresponds to obtains in the world. Thus, the proposition "snow is white" is true if and only if snow is white. Under this definition, which agrees well with common sense, the entities under discussion are propositional statements, which express things about facts; those being the actual entities which are true or false. Therefore the "property of truth" is the same across all propositions, it is, roughly speaking, the correspondence of a proposition to a fact. This what may be termed a metaphysical account of truth, and involves the assumption of several classes of abstract entities: propositions, facts and the property of truth itself.
Under closer examination, several difficulties begin to emerge with such a straight forward account of the correspondence theory. For one, the existence of propositions can be challenged: what is the need to postulate a category of things above and beyond the sentences and statements whose meaning they are intended to capture? Such a question can be avoided by shifting the burden of truth-bearing from propositions to uncontroversial things like sentences, however there remains difficulties with the notion of the "facts" to which they correspond. Facts are notoriously problematic as a class, because once they are accepted as existing they seem to multiply endlessly (Aristotle did not have thirty brothers, Aristotle did not have thirty one brothers...) and the invocation of "facts" above and beyond states in the world seems ontologically expensive and unnecessary. For example, snow is white without the need of any "fact" that snow is white to explain it. Yet, if "facts" are regarded simply as true statements about the world, they seem unproblematic for the purposes of defining a theory of truth. Finally, the notion of how a proposition "corresponds" is a slippery one that remains very difficult to define; however, when challenged for a definition it seems satisfactory that the correspondence between a sentence and a state of affairs is simply a primitive, indefinable function of natural languages (and not a very mysterious one, either).
In dealing with difficulties in the correspondence account, various alternatives have been offered, mostly falling under the heading of "deflationary theories", theories of truth dispensing with the notion of truth as a property. The tone was set by Frege, who began the idea of "redundancy theory" by pointing out that the use of "true" in a sentence is normally redundant; saying that "P" is the same was declaring that "P is true". To give Frege's own example, "I smell violets" is the same proposition as "it is true that I smell violets". Under this view, truth is not a property as such, rather there exist various propositions which may or may not obtain. "I smell violets" lacks any property in common with "snow is white". Ramsey agreed, noting that the word "true" normally does no work directly in a sentence, although it may be used indirectly in such phrases as "everything he says is true". Quine held a similar position , in which theories of truth are not about propositions, but rather used to allow generalization about the world. "Truth" as a predicate is what allows this function of generalization.
One of the most fully expressed deflationary theories was the "disquotional theory" of Tarski, which, abandoning the idea of defining natural language use of truth as inherently contradictory, instead looks for a criteria with which to define a coherent notion. Under Tarski's analysis, no metaphysical theories assumptions are needed, and the bearers of truth are ordinary sentences. For Tarski, a sentence is true if it corresponds to the state of affairs which will be expressed when "snow is white" is true if and only if snow is white. While the actual theory was highly technical and Tarski himself did not regard it as a deflationary theory, what is important is that it shifts the determination of truth from a "truth property" to a number of other properties of the sentence: what it refers to, whether it satisfies really occurring conditions, and if it is logically consistent.
Another deflationary theory, this one easier to grasp, is minimilism, which was expounded at length by Horwich. Attractive in its common sense approach, the minimilist account asserts that every proposition carries it own conditions of satisfaction, thus <<P> is true if and only if P>, <<snow is white> if and only if snow is white>,<<grass is green> if and only if grass is green> and so on, with no common property asserted between the cases. While Horwich himself did not deny that truth is a property or predicate, he maintained that it was one of a very restricted nature.
In the late 20th century, deflationist accounts have been predominant but by no means unchallenged. Arguments against them have hinged on the alleged inability of those theories to handle propositions which cannot be said to be true or false, and paradoxes of language such as the "lairs paradox". Proponents of deflation have invoked the use meta-languages to handle the linguistic paradoxes. However, for our purposes, regarding investigation of the idea of truth as a property, perhaps the best place to look for a resolution is not by comparing predominant theories of truth, but in examining the notion of "property" itself.
The Cambridge Encyclopedia of Philosophy defines "property" as "roughly an attribute, characteristic feature, trait or aspect". As such, it seems that all true propositions (or sentences, or statements) do share a common property, that of expressing a true statement, and they belong to the same set; that of "true propositions", as opposed to those which are false or to which a truth value cannot be assigned.
However, it should be immediately obvious that such an assignment is extremely trivial, somewhat akin to membership in a set of "all existing things". Propositions could likewise be placed in the set of all things which have no extension, clearly a technically accurate but not very enlightening division. In order to make a more intelligible division into meaningful sets, it is necessary not to look merely for universal qualities, but at how those qualities are defined. In the case of truth, it is apparent upon examination that, if the dubious admission of "facts" as a class of entities is not made, then the mechanisms by which different propositions are true or false are simply too different to be placed in the same category. 
Take the propositions:
1. 'Earth is the third planet from the sun'
2. 'Economic growth is normally accompanied by inflation'
3. '5+7=12
What makes the first proposition true is the present location of the earth in space, what makes the second true is the correlation of two states of affairs across a number previous observations, and in the third case it is a necessary truth given the rules of mathematics. The first is explained by the relative positions of physical objects; the second by the movements of abstract systems, and the third by its definition. The "truth" of each statement is dependent on things so dissimilar that it is very difficult justify assigning them the same property in more than a trivial manner. The same can be asserted for any of the infinite variety of statements which describe conditions obtaining in reality, and attempt to define criteria to fulfill the property truth will inevitably be frustrated.
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Greek Philosophy: The Pre-Socratics and Plato / Sample Answer: Zeno
« Last post by Casey Enos on August 08, 2012, 08:18:00 pm »
Another essay I wrote while rehearsing for last years exams; and actually used on the test. Every year Zeno comes up, with a slightly different twist on the question: for instance, can Zeno teach us anything positive about motion; does it dissolve Zeno's paradoxes to hold that space can be divided infinitely, and a few others.
"Can we we learn anything positive about the nature of motion from Zeno's paradoxes?"
In treating Zeno's paradoxes, possibly the single most satisfying answer was that of Doignes the Cynic, who refuted Zeno by walking around the room. In declaring movement to be impossible, Zeno is clearly running afoul of empirical evidence, and it is therefore unlikely that his paradoxes have much to say on the nature of movement. However, such hasty answers miss the opportunity to examine exactly where the fault in his reasoning lies, and therefore to learn a great deal about the tools and models with which we examine movement.
Poor treatment of dynamic processes is symptomatic o f classical Greek thought, with its focus on understanding static states. To Zeno, a finite section, be it of time, motion of space, can only be divided into finite sized chunks, although he held, oddly that the division can be performed an infinite number of times, leading directly to a paradox. Using a system of mathematics without the concept of zero and with an undeveloped idea of infinity, Zeno could not do other than generate a paradox in his treatment of both physical extension and motion. The infinitely small points of modern calculus were as unavailable  to him as to any of his contemporaries. 
Modern treatment of Zeno, as most famously presented by Russell, hinges on the idea of an infinite number of points which can be fitted, in a gap-free manner, on a line finite extension so that the addition or subtraction of points cannot cause an alteration in the size of the line. Importantly the modern calculus based solution is primarily advocated over Zeno's presentation or classical attempts at solutions, largely because of the success at calculus in building scientific models describing motion. No other set of solutions has provided such support to theories describing empirical reality, surely an indication of which direction practical handling of the nature of motion may lie.
Zeno's most discussed paradoxes are "The Dichotomy" and "The Achilles". In the Dichotomy, a runner must complete a course from point A to B. In order to reach B, she first must traverse 1/2 the distance, then 3/4, then 7/8...Each diminishing fraction must take a finite amount of time to complete; presumably as there is no lower limit to the fractions remaining yet each requires a finite time to traverse, the result is an ever growing time spiraling to infinity to traverse a finite space. The same treatment can actually be applied to the runner's first step, so that the course can not only be completed, it will not even be started. The Achilles, involving the efforts of a swift runner to overtake a tortoise who enjoys a head start, is essentially the same paradox with a more developed story line. Each time the runner arrives at the animal's previous position, it will have crawled ahead, resulting in an ever-diminishing gap that cannot be closed.
 A standard solution is point out that the continuously decreasing fractions will sum to 1;g with the  along with the diminishing amount of time required to traverse each. Such a treatment is not entirely satisfactory, although it does point in the right direction. Zeno is not dealing with a completed division which can be summed to one, but with an ongoing and never completed one that never reaches the sum of one.
Aristotle famously refuted to even consider the division into points, addressing the fact that lines may be potentially, or mathematically, divisible, yet real distances in nature do not consist of points or fractions. In this assertion he was clearly correct an established an extremely salient point about the limitations of human ability to conduct accurate analysis of nature; however in taking such a route he also closes off any access to the practical application of mathematics to analyze movement. Building the modern edifice of physics on Aristotle's foundations would be simply impossible...
Another potential solution, similar to the calculus based one, to regard the division of the line and the time required to traverse it as already complete; this time into infinitely small units, or points. As before, the runner is faced with an infinity of tasks to complete, however for each task she has a corresponding infinitely small fragment of time in which to complete it. Both series sum to one, in the same way a finite line can be divided into an infinity of points and a decimal number between zero and be assigned to each point. The key is to regard the division as already completed, not as one that occurs continuously as the runner moves and thus never arrives at its sum.
The completion of "super-tasks" of course remains controversial and has spawned a great deal of philosophical literature, most famously "Thompson's Lamp". This lamp is equipped with a toggle switch which is flicked from "on" to "off" an infinite number of times in a minute, and the question, probably unanswerable, is posed of which position it comes to rest at after the minute. However, for our purposes a better analysis is not of the end position of the switch, but the motion of the switch as it traverses an infinite number of points back forth in its movement. Under such an analysis, more relevant to consideration of Zeno, a super-task is performed every time a light switch is turned on, indeed every time this pen draws a line on the paper (*note: the actual exam paper was, of course, hand written). While not exactly resolving the problem of super-tasks, it does shed light on the irrelevance of the question to that of motion.
The third paradox of motion reported in the doxology is that of "The Arrow", which when shot from the bow will occupy a space equal to itself at any "instant". Since time consists only of instants, motion is impossible as the arrow never moves from the space it is occupying.
Again, Aristotle makes a correct answer, that the division into instants is artificial, yet again it is an answer that does not allow anything further to be learned. A more enlightening answer is that at every instant the arrow possesses "speed", that is the quality of movement, a characteristic which is carried over from instant to instant. Commentators have pointed out that in modern terms, by assigning a value of 0 to the arrow's speed at any instant, Zeno is effectively dividing by zero and thus rendering the analysis of the arrow's movement meaningless.
Another solution, similar to that of the runner, is to look at the arrow's flight as a whole, divided into an infinity of points, each one of which is traversed at each instantly, of which there are also an infinity. Since the points in both time and space are completely gap-less, the result would be a  smooth flight.
The final paradox of motion, and perhaps the easiest to resolve, is that of "the stadium", or "moving bands". As reconstructed by Aristotle, three bands of equally sized objects are presented, two moving parallel to one another in opposite directions, and both passing an unmoving one. The paradox is generated by the fact that the two moving bands pass each other more quickly than the third:
(*here there was a hand drawn diagram difficult to reproduce in type, but similar to
                                 T1:                      AAA
                                                       BBB
                                                                 CCC
                                 T2:                               
                                                           AAA
                                                           BBB
                                                           CCC
with A stationary, B moving to the right and C to the left)
In the diagram, the leading edge of the two moving bands have passed three units of one another, and only two of the stationary one.
This paradox is usually regarded as simply a serious mishandling on Zeno's part of the notion of relative speed. More charitable reconstructions involve the motion of point-particles or quantum style "jumping", unfortunately there is very little in the doxology to support such reconstructions and Zeno lacked the technical equipment to postulate points of zero size. Therefore the moving bands, at least as Zeno presented them, is probably the least edifying if the four paradoxes of motion.
As a whole, we can learn a great deal more about motion really consists of from Aristotle and his successors, such as Aquinas, who denied the actual divisibility of time and space, than from Zeno. In maintaining the use of calculus to dispel the paradoxes, we must be careful to remember that we are operating with an approximate tool. Mathematics is internally consistent only because of the definitions of the units and operators involved, just as Zeno's text works only because of the definitions in the terms used. The most important lesson may be simply that nature contains motion and it does not contain points, fractions or calculus.

24
General Discussion / recommended Course
« Last post by Fadi El Kadi on August 08, 2012, 04:38:46 am »
Hi,

I am currently enrolled in the Diploma in Philosophy and I have currently completed the Intro. to Philosophy course and I was wondering which course to take next. In the handbook for the 1st year BA in Philosophy they recommend Epistemology and modern Philosophy. Wish of the two would be the best to start off with?

Any recommendations?

Thanks,

Fadi
25
Ethics: Contemporary Perspectives / Re: Ethics: Historical Perspectives - Practice Question Response!
« Last post by waveletter on August 08, 2012, 01:12:55 am »
Hi Lou and all:

Unless you are keenly interested in Aristotle's Nicomachean Ethics, and in particular with its concept of justice as a mean, then stop reading this post now. OK, let's see how the web page formatting works on that one.

I say this because I'm launching into a reading of commentary on Book V of Aristotle's Nicomachean Ethics that is old and Greek and difficult. And, to boot, I'm neither an expert on ethics (to say the least) nor on Aristotle (to say something or other, I'm not sure what). I'm talking about the notes in J.A. Stewart, Notes on the Nicomachean Ethics of Aristotle, vol. I, Oxford: Clarendon Press, 1892.

[Oh, aside, I got this book (and vol. II too) from Stanford University's Green Library. It didn't even have a US Library of Congress index--instead it was located among quite old books, way upstairs, in a scrunched wing of the library called the Bing Wing, in a corner in fact, one that only had only texts on ancient philosophy, those with Dewey Decimal System numbers. Pretty cool. I once bumped into a guy yanking books from the shelves up there and making notes. I said, "What are you doing?" (He was pulling out old books and writing down their Dewey Decimal numbers.) He basically said, "I'm finding things that we might be able to upload onto Google Books." I thanked him (Jeremy) and told him that I often used their web-based services for Byzantine lexicography. So that's how it happens.]

Concerning Aristotle's Nicomachean Ethics 1133b32ff. On p. 472 (vol. I, op. cit.) old Stewart notes that (an anonymous paraphrasis, through Heliodorus) commentary on the Nicomachean Ethics says (my translation from the Greek; sorry) that "...but implementing justice is a mean not of a type according to the earlier virtues; for, indeed, of the others, each of the virtues is a mean of two vices, according to making a deficit and to making an excess" (Stewart, p. 472).

This is a point that I think we've already seen. Stewart goes on to remark that "Mich. Eph. has a note to the same effect--viz. that every one of the other virtues has two vices contrary to it, but justice has only one vice (adikia)...." [this would be Michael of Ephesus (11-12th century CE, who wrote a commentary on Aristotle's Nichomachean Ethics].

A little later Stewart remarks that "According to this view, then, of the passage before us [1133b32ff], the point is in the words 'he de adikia ton akron': 'justice is not a mesotes in quite the same way as the other virtues are 'mesotetes', because, although it does indeed observe a mean, "both the extremes fall under the single vice of injustice."' Is it this alone that constitutes the difference? I think not."

Stewart thinks that the difference is

(1) marked by the words 'hoti mesou estin', which we've remarked upon before, and yet
(2) a merely minor difference is signaled by the fact that both extremes fall under the single vice of injustice.

Thus, Stewart inspires Guthrie's comments on Aristotle here, and Stewart tends to dismiss the slant on this passage taken by the later commentators. Thanks! --Ron


   
26
General Discussion / Re: Split Programs
« Last post by waveletter on August 07, 2012, 09:59:22 pm »
LISP is a specialized string processing language, and, you are right, it originated in AI programming. It used to be that AI folks used LISP exclusively, but now, because of its strengths for general systems programming as well, a lot of AI engineers program in C++. Just as an example, in my previous job we worked with an AI start-up here in the Bay Area (northern Calif.) that had a generalized artificial intelligence tool that mimicked the way the brain processes visual and auditory information. They programmed in C++. Now, that being said, they had to implement a lot of the search tree methods that LISP does naturally using C++ tools of their own design, but that's what they were doing. They could replicate the functionality of LISP in C++, and they could use C++ for its own expressive power in coding up the image and signal processing algorithms that they need for the "front end" of their product.

I would suggest C or C++ (better) as a starting point into actual programming. LISP could come later, if it turns out you need it. And you might not, as things stand today.

Right. There is an area of intersection between computer science and philosophy, cognitive science. It tends to sample stuff from all kinds of disciplines: psychology, philosophy, computer science, biology, electrical engineering (sensing), and even mechanical engineering (robotics, haptics (grasping things), balance, and optimal control). Just my 2 cents. --Ron P.S. I'm reading through your sample answers. Nice work. If I can see a difference, it seems to me like you have followed a selective line of thought, and developed the arguments around that line, whereas I have tended to survey things.
27
General Discussion / Re: Split Programs
« Last post by Casey Enos on August 07, 2012, 08:35:00 pm »
Thanks for the advice!
Its the aspect of AI as a way of examining philosophy of mind that I am really interested, the exact UofL program I am looking at is called "cognitive computing" or something like that. For some reason almost all AI programming is done in a language called LISP, which runs with LINUX, so guess that is where I need to start looking.
Thanks again. If I do learn anything about programming I will go back to UofL and fix their student portal...
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Ethics: Contemporary Perspectives / Re: Ethics: Historical Perspectives - Practice Question Response!
« Last post by waveletter on August 06, 2012, 11:28:51 pm »
Hello again LouFederer & all:

I want to add a few notes on how one might salvage Aristotle's thesis that Justice is a mean. In earlier posts on the thread Louise criticized Aristotle's viewpoint with particular force, and I noted that none other that Sir David Ross also held that "The attempt to exhibit justice as a mean breaks down" [Ross, Aristotle, London: Methuen, 1923, p. 214].

It seems that Guthrie [A History of Greek Philosophy, vol. VI (Aristotle: An Encounter), Cambridge: CUP, 1981, p. 371n] is not so ready to endorse Ross's position. He writes in a footnote about Ross's statement (above): "This was denied in a long and careful note by Stewart...as later by Hardie...." Guthrie (pp. 371-2) then quotes Aristotle [1133b30]: "Just dealing is a mean between wrongdoing and being wronged, i.e. having too much or too little. Justice is a kind of mean, not in the same way as the other virtues but because it is of a mean, whereas injustice is of the extremes."

Guthrie points out that Aristotle's Greek text is "hoti mesou estin", which G. translates as "because it is of a mean" (his italics above), whereas Ross amplifies this quite a bit into "relates to an intermediate amount". The Greek words for 'the mean' are "to meson"--like the elementary particles, or as in the term Meso-America, or Mesopotamia (in the middle of the rivers)--so Aristotle is using the genitive, and it could also be translated as "from a mean". Guthrie's translation (and mine too) serves to separate the notion of justice from the kind of mean it comes from, whereas Ross tends to push justice towards that mean. Anyway, this is just a little grammatical point that shows how sometimes a knowledge of the Attic Greek is useful in exegesis.

Guthrie goes on (p. 372): "Aristotle sees at once that his first attempt at a definition in terms of the mean will not do. Just action is a mean between apportioning (whether in one's personal relations or as a judge between others) more or less than what is fair and appropriate." If Guthrie is right about this, and I'm thinking that he has a good point here, Aristotle is being quite flexible in what he considers to be a mean and how some virtue relates to the mean from which it comes. If I go back and look at Ross's further comments (see my previous post where I numbered the points; see point #11), it now appears to me that Ross is being quite unfair to Aristotle.

Here is how Hardie [Aristotle's Ethical Theory, Oxford: Clarendon, 1968, p. 182] approaches the question: "His analysis of various kinds or spheres of justice leads him to the conclusion at the end of chapter 5 [of N.E. Book V] that 'justice is a kind of mean, but not in the same way as the other virtues, but because it relates to an intermediate amount, while injustice relates to the extremes' (1133b32-1134a1). Thus Aristotle does not assert, but denies, that the application of the Mean to justice is the same as its application to other virtues. But we should not be in a hurry to decide that the doctrine here breaks down or is a failure [here Hardie notes Ross's text as I quoted above]. If Aristotle's treatment of justice as a mean is in some respects confusing and complicated, so also are both the facts to be surveyed and our ways of talking about the facts whether in Greek or in English."

I'd better stop here. I'll try to summarize later the points that Stewart makes, but his notes are rather difficult, quote a number of late 19th century authors, and are strewn with Greek. I think that the innocent-sounding sample question that Lou selected for a trial essay is really quite difficult to answer. Just look at the arguments among Aristotelian scholars! Thanks! --Ron







29
General Discussion / Re: Split Programs
« Last post by waveletter on August 05, 2012, 10:04:39 pm »
Hi Casey:

I have a couple of advanced degrees in CS, but they're from a regular university, not any online program. I can't offer too much specific advice about UoL's external CS degree.

For a BA or BS in CS, you are not expected to be able to write code or know much of anything about computers. If you can get on the web and use some basic documentation tools, like Microsoft Office, or some Linux-based tools for the same, you are ahead of the game. Most universities, and I would assume UoL as well, base their instruction on UNIX (e.g. Linux), because it's free. If you wanted to work ahead a little, you could pick up one of the PC-based Linux products, install the OS on your PC (you might have to partition the disk with a tool like Norton Partition Magic), boot up Linux, and begin to get familiar with the command, scripting, and programming environment. But, they will make you go through that in the university program, usually in an introductory course called Introduction to Computer Science or the like. You'll need to get an introductory book on UNIX.

You could also work with the Microsoft world, but you'd have to pay a little more for their programming product suite, which is called Visual Studio. You might be able to get a M/S student version of Visual Studio for a lot less. Generally, they want to see a registration card (would the UoL Philosophy card work? Hmm...), or you have to buy it at a student store on campus. You'll need to get an introductory book on Visual Studio C++ or C# programming. The one by Ivar Horton is good.

You can also download a PC scripting language, Python, for free. There are online tutorials for it, too, like Dive Into Python. This is a quite powerful programming tool, but you probably won't be learning it right away at the university.

There are a number of theoretical courses in the BSCS program, and in some schools the practical programming aspects are downplayed. My nephew just graduated from the Univ of Wyoming with a BSCS, and I was astounded at how little practical programming the kid had learned. Still, he landed a high-paying job with company in San Diego, CA, and they are giving him a thorough training in database software.

Hope this helps. Any other questions, just post them here. Uh, and try to keep away from any potentially harmful situations when you're over there. --Ron
30
Epistemology / Sample Answer: Coherentist Epistemology
« Last post by Casey Enos on August 05, 2012, 05:15:24 pm »
This is another practice essay. Every year for which I have seen examiner's reports one question was asked about foundationalist and one about coherentist epistemology. Be careful of the wording in the questions; I forget the wording on the actual exam but it was asking if inclusion in a coherent system of beliefs was sufficient for a belief to be considered knowledge. Necessary and Sufficient conditions must be distinguished between in dealing with coherentist systems;"strong cohernetism" in which a belief is necessarily justified by mere inclusion in the system is a very different proposition is a very different situation from one in which coherence merely provides sufficiency.
At the time of writing this essay I had yet to study Popper in depth, I realize now that the paragraph discussing the size of coherent systems aligns well with his theories (ie, the more propositions a system contains the more falsifiable it is and thus has more empirical content and is a stronger theory assuming that it passes experimental attempts to disprove it).
"If a belief belongs to a coherent set of beliefs, is it thereby justified?"
According to the classical definition of what it means for a subject S to know proposition P three conditions must obtain. P must be true, S must believe that P, and the belief of S that P must be justified, that is have a real basis to rule out guessing or other inadequate sources of belief. Leaving aside logical difficulties in the definition of truth, the first two clauses remain relatively uncontroversial, while it is the third which is at the heart of most of the debates in modern epistemology.
As opposed to a Foundationalist account of justification, in which a belief is considered justified by either justifying itself or not requiring further justification,   a coherentist account places the burden of justification on the other beliefs in a system. A belief must be supported by other beliefs. This defines the unit of justification not as certain beliefs held as foundations on which other beliefs may be built, but as the entire set of beliefs held. Therefore, the extent to which a belief belonging to a coherent set may be said to be justified depends entirely on the strength and consistency of the set to which it belongs. A strong, logically consistent set of beliefs large enough to account for observed phenomena will provide support for beliefs, while weak or inconsistent systems will not.
In offering a coherntist account, several pertinent questions must be immediately answered. First of all, what does it mean for a belief to cohere with a set? Obviously, for every belief in a set to deductively imply every other belief would be impossible for any set attempting to describe the world. Mere logical consistency is not enough to construct a linkage strong enough to provide mutual justification between events. Probably the best solution is to regard the notion of coherence as a primitive or intuitive one. Some beliefs, due to their subject matter, will be in closer contact with one another and require a degree of inductive support for one another, while those elsewhere on the circular chain of support will require only to be non-contradictory. For instance, one may regard physics as a network of beliefs which must be mutually supporting, while another network of beliefs, for example those of economics, are located far away from the "epistemic area" of physics and are required only to be non-contradictory with physics in order to be part of a coherent set containing both.
A further question is what scope is necessary to form a consistent set. A set of two beliefs may be perfectly consistent while not explaining very much. At the same time, human knowledge is constantly expanding, so any arbitrary number, N, of beliefs would be impossible to set as minimum; it could always be extended by the gaining of new propositions. For instance, if N was the minimum number needed for a consistent set to obtain, the extension of human knowledge by adding proposition N+1 could neither add nor subtract from the consistency of the total set or the justification it offers for the beliefs it contains, surely a counter-intuitive result. The best answer may be to regard a set as providing stronger justification the larger it is; while this introduces a controversial "contextualist" account of justification, ruling out any final definition of justification which would regard a belief as 100% justified, it supports the common sense view that systems with more cohering propositions will provide more support.
Another objection often raised is that of the "isolation" argument, which states that a coherent system may provide no real justification, since it may have nothing to do with the real world. A fictional story, for instance, may be perfectly consistent. However, it may be countered that the concern of coherent systems is not the mere consistency of any sort of statements, but the consistency of observation statements about the world. No story or arbitrary set of will approach the scope of a system of propositions describing the world. As the eminent modern philosopher WV Quine envisioned the set of human knowledge, it is a web of mutually supporting beliefs connected to the world through observation sentences. Accurate connection be absolutely ensured, but it is worked towards by the revision of propositions which become inconsistent with observation as well as the revision of propositions "in contact" with that portion of the web. This continues as necessary to ensure as close as possible adherence between observations, the world and those propositions needed to explain the observations.
The strengths of the coherence system of justification are powerful arguments in its favor. It solves the problem of an infinite regress of beliefs which must justify one another by introducing a circular system, rather than questionable "self-justifying" beliefs. In addition, a certain degree of coherntist thought is implicit even in the theories founded on its main rival, foundationalism. For a belief to be foundational, it must cohere with other beliefs to be recognized as such. For instance, if perceptual beliefs are regarded as foundational, it can only be in so far as they cohere with one another and other beliefs establishing them as foundational. Lehrer argues this position at length in "Theory of Knowledge".
In summary, the question of whether a belief belonging to a system of coherent beliefs is justified must be a qualified "yes". Cartesian justification, the sure, without-a-shadow-of-logically-possible-altenratives justification, is not possible such an account. However a great degree of justification can be obtained, providing that the system of beliefs contains networks of mutually supporting propositions on certain subjects which are not contradicting from network to network; that the system of beliefs is large enough (a somewhat vague notion) and finally that adheres to the "real" world through observation while allowing for revision through the adjustment of the propositions it contains on the basis of further observations.
Such an account, again, cannot eliminate radical skeptical alternatives, such as the "matrix", which would obtain without being observed or detected. However, within the realm of scientific and day-to-day endeavors, it can offer a very high degree of justification.
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