Thursday, 26 May 2011

Chris Port Blog #264. A Classic Example Of How Empiricists Can Get Themselves Into Trouble... Which came first, maths or the universe?

© Chris Port, 26th May 2011

The following discussion is a verbatim record of my involvement in a comment thread on The Richard Dawkins Foundation for Reason and Science (Official) Facebook page. It's a classic example of how empiricists can get themselves into trouble without metaphysical perspective...
S: "I have just had a thought that may bear some examination and may be a problem for theists, though they will have a facile way out. It has just occurred to me that Mathematics is something that exists in effect outside of the universe and simply is. Completely immutable, absolute, existent before time or the big bang, defining everything there after, and built upon rock solid axioms. Like “god” Mathematics is eternal and self existent though sadly has offered no opinion as to how Noah should have built the ark."
Me: "The word ‘exist’ may be leading you astray here. Mathematics is the study of quantity, structure, space, and change. It is overwhelmingly probable that these phenomena exist independently of our minds. However, mathematics is the study of the phenomena, not the phenomena themselves. Mathematics is the attribution of consistency in the mind. The universe itself is as indifferent to mathematics as it is to beauty. Without consciousness, mathematics would not exist."
S: "It would but without consciousness it would not be acknowledged, gravity at sea level was still around F=MA has always been the case, and the universe is mathematics made function. I see where you are coming from but these relationships or more simply say prime numbers, are there whether they impinge on our consciousness or not. And these relationship or rules will be consistent when and where ever, though F may not equal M A. And looking why back I pulled back from claiming that these relationships can exist pre existence, but would insist on them being latent. Any way it was only a thought I had while driving a bus around in circles earlier today. A possible atheist god if you like, so I'm not living or diieing on its verifiability."
Me: "I think that you may be falling into a classic teleological trap (getting things back to front).

Teleology is the supposition that there is purpose or direction in natural processes. To say that “the universe is mathematics made function” is to infer that mathematics preceded the universe, and that the ‘purpose’ of the universe is to give mathematics physical form.

I would argue that in reality it is completely the other way around. The universe came first. Mathematics is our expression of patterns that we observe in it. These patterns are relationships attributed by our minds, not inherent properties. The only inherent properties of the universe are the four basic force charges and the ways in which they interact with each other. Everything else in the universe is an ‘emergent property’ rather than an expression of function."
‎"... as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." ~ Albert Einstein.
S: "OK I give up, it was only a thought and I wouldn't dream of giving the universe function. But I won't budge on 1+1=2, when ever and where ever."

Me: "I once thought that I would never budge on Descartes’ “Cogito ergo sum” (“I think therefore I am”). Unfortunately, science has revealed this to be almost completely wrong! It would be now more correct to say “A thought, therefore something having it”…

I won’t argue with 1 +1 = 2. That’s true in as far as it goes. It just doesn’t go very far. It doesn’t mean anything (other than being a trivial axiom).

Logical consistency, as exemplified by mathematics, has some shaky claims on ‘truth’. 1 + 1 = 2 may be true, but that doesn't mean anything other than 1 + 1 = 2. To ask what it means is meaningless. You either accept it or you don't. If you do, it doesn't mean anything. And if you don't, then (mathematically) you can't say anything else. Kurt Gödel's incompleteness theorems prove (in the mathematical sense of the word) that there is no complete and consistent set of axioms for all of mathematics

Only in aesthetics and ethics will you find meaning - and (I suspect) it is meaning that people want from their truths, rather than mere pedantic consistency.

Maths is not a meaningful language because its notation has no subtext or context. It communicates nothing. However, its self-referential expansion to develop consistent patterns of logic (which some find elegant and beautiful, expressing infinite complexities in pithy formulas - like poetry but with numbers) hints at something deeper...

Truth is intangible. Like the humble electron, it is affected by our clumsy measurements. Once you realize that it cannot be grasped, only then have you truly understood it. Truth, like humanity, is inherently paradoxical, a probability waveform. Confused? If so, good. Like quantum theory, if you think you understand it, then you don't! That's a good starting place for science and art...

Truth, logic and consistency are human constructs. We attribute importance to them for various practical, moral and aesthetic reasons. Pattern recognition and consistency have evolved in our species because they were useful survival traits....

So, once, was religion. Whether it is now a help, a hindrance or a harm is currently the subject of much heated debate. The real question is whether science and religion are actually talking about the same thing.

Richard Dawkins is happy to allow artistic fiction to tell us meaningful truths about life (he is a cultured, aesthetic writer) but he is not happy to allow religion to do the same because (a) he believes it is a fiction posing as a truth, but more importantly (b) because he believes it is harmful. Art, if you like, is a ‘good’ lie and religion is a ‘bad’ lie.

Even in its benign, compassionate form, he believes that religious belief acts as the thin end of the wedge for irrational indoctrination (often without choice) and, ultimately, an intolerance of scientific methodology.

In essence, there is no middle ground or fence to sit on. I agree with most of what he says, but I do see some gaps in communication. We have a good old dialectic here: science versus religion, each making moral claims about what is ‘good’ for humanity.

Is there a synthesis, or do we have to jump one way or the other? I would plead for some breathing space to allow Wittgenstein’s ‘language games’ to develop a more ‘artistic’ dialogue. Stop worrying about ‘reality’ (whatever that may be) and start analyzing how we communicate.

T: "I'm short on time and my posts haven't been working here, but Chris, how do you solve the problem of unity out of the diversities when it comes to logic/math? If we are contriving these realities [individually] how do they work as a unity?

Me: "It’s a fascinating area of study. Does the recurrence of similar patterns in different systems suggest a metaphysical role for mathematics? The problem then would be an inference that physical forms are an expression of mathematical functions…

My initial solution to this ‘problem’ is simply to suggest that there is no problem!

Starting from the four fundamental forces, why shouldn’t localized systems arrive at similar ‘solutions’, even at different scales? The diversity of emergent properties is the result of slight inhomogeneities in the quantum state of the early universe. Time, expansion and chaotic (complex) interactions have provided a wide variety of phenomena for us to study. We use mathematics to model their forms and behaviour. Some physicists have even speculated that chaos theory may give rise to new ‘emergent’ laws of physics, but the gist of String/’M’ Theory seems to be that all matter and energy is just variations on a fundamental theme.

Unity in diversity only seems to be a problem if you think that this is an underlying ‘design’ feature. I would cite the Weak Anthropic principle and say “That’s just the way it is, otherwise we wouldn’t be here to see it”.

As a very simple example, many different types of forces tend to be transmitted equally in all spatial directions. One consequence of this ubiquitous behaviour is that the pattern of a circle or sphere is likely to recur throughout nature at different scales. If mathematics starts to develop self-consistent variations on the component relationships of circles and spheres, it shouldn’t really surprise us if we start to discover more and more apparent similarities in different phenomena. Basically, the more complex mathematics becomes, the more opportunities it creates to find patterns. That’s what maths is designed to do.

Whether this recurrence of patterns suggests anything deeper actually leads us away from numbers towards language and metaphysical discussions (which I suspect you wish to avoid!). For example, if I was to claim that the ubiquitous recurrence of ‘God’ in different localized cultures inferred that there must be something like ‘God’ in nature, I suspect you would retort that all it actually reveals is people’s general urge to invent explanations. A diversity of religions does not make a unity in a deity.

Once the concept of ‘God’ is invented, this can lead us into all sorts of teleological traps. I would say that ‘unity in diversity’ is actually just another variation on this theme. We invent a notation designed to find patterns. We then map that notation on to the physical universe. We are then surprised to find recurring patterns in the notation. I don’t think that’s a problem. I think that’s what we were looking for, so we found it."


Mathematics - Unity in Diversity

The Significance of Unity and Diversity for the Disciplines of Mathematics and Physics 

Functions and Mathematics

T: “Nice Google. Now, please explain how, if we are [individually] [making] mathematical truths, subjectively, how they are united into a coherent [objective] system."

Me: "Because that's what we've designed the system to do. If it's not consistent, its not maths. You're starting to slip into Wittgenstein's 'category errors'.

Mathematics (unlike language) is specifically designed to be consistent and coherent. The universe, by existing, is coherent. The ‘laws’ of physics are consistent and (quantum theory of gravity aside) mostly coherent down to the Planck scale. To map a coherent system onto a coherent universe, then claim that the universe is somehow a manifestation of the system, is to confuse two different categories of coherence. They are physically unrelated. They just look similar. Fortunately, the consistency and coherence of our mathematical system enables us to make testable predictions about the consistency and coherence of physical systems. There is a ‘family resemblance’ concept at work here. But they are not the same thing at all."

T: “You didn't answer the question, my friend;)"

Me: "I have answered it. I've just not answered it on the terms you've suggested ;)

Coherence gets more ‘fuzzy’ at the quantum scale. Quantum mechanics is the most consistently accurate scientific theory ever devised. Heisenberg was dismissive of attempts to understand what was ‘physically’ going on. As far as he was concerned, all that could be claimed about quantum mechanics was that the maths worked. The uncertainty principle, and the strange interference of measurement and even consciousness on quantum level 'events'/probability waveforms, are still profoundly incomprehensible to us. As a lyricist physicist, I derive a wry satisfaction from this. Maths is designed to be ‘perfect’, yet the universe (so far) eludes perfect notation. There is, of course, no such thing as an objective system.

T: “Great! Can't answer, so you pull the old QM card....gotta love it!"

Me: "All roads lead to foam...

Although (strictly speaking) non-sequiturs, you may find the following 'family resemblance' posts amusing when pondering some of the discrepancies between numbers and 'reality'...

Marty Gull - Targets

Monkey Dust - Government School Targets
My training is in aesthetics rather than mathematics. However, borrowing from perturbation theory, perhaps another way of clarifying the apparent subjectivity/objectivity ‘problem’ of unity in diversity is to transpose an aesthetic methodology onto an empirical impasse. I’m not suggesting that the two are directly analogous, simply that clarity of thinking in one discipline can sometimes lead to clarity of thinking in another discipline.

I'll post the different perspectives one at a time to avoid overwhelming you with data. We'll need to consider: Simple Objectivism, Simple Subjectivism, Simple Relativism, Sophisticated Objectivism, Sophisticated Subjectivism, and Sophisticated Pragmatic Relativism...
Simple Objectivism (Recognizing the rules of composition).

Simple objectivism depends simply upon the observer's recognition of the ‘rules’ of composition (consistency in this case) and not on any supposed feelings aroused by them. Indeed, the satisfaction or pleasure experienced by the observer is supposed to arise from their skill in recognition.

'Whatever the peculiar causal conditions… the … features…are themselves independently perceivable. This gives the ... [phenomenon] a certain critical autonomy.' (David Cooper).

However, Cooper then goes on to describe a basic problem with simple objectivism. The evaluative force of a judgment claims more than that the phenomenon possesses certain qualities. It also claims that the phenomenon merits attention and thus ascribes a value which is not inherent in the phenomenon itself. Where does this value come from? One possible answer is that, while the rules of the phenomenon may be objectively observed, the values given to it may arise from a simple subjectivism.
Simple Subjectivism (I know what I like but do I need to know why?).

According to simple subjectivism, the judgment does not depend upon the rules of composition in the phenomenon but in the pleasure or displeasure that perception of the phenomenon happens to arouse in the spectator. This implies that one spectator experiencing pleasure and another spectator experiencing displeasure from the same phenomenon would not be contradicting each other.

However, as Cooper notes: '... we are normally expected to try to show that the judgment rests upon features which render our response a justifiable one'. By what rules, to what indisputable court may we appeal to justify our judgment? Are all judgments only relative to each other?
Simple Relativism (Is one judgment as good or as bad as another?).

Simple relativism (often referred to as dogmatic or vulgar relativism) proceeds from the rather pessimistic premise that, since we cannot incontrovertibly prove universal judgments, all judgments must logically be equally valid (or worthless).

Cooper argues that this 'anything goes' approach is doubly inconsistent. It self-defeatingly allows for universalist theories and also implies the existence of a supposed universal standard of which all theories must fall short.

It is impossible to find a system which could possibly exist in a self-enclosed way; certainly it is theoretically difficult to define what it would look like.

It seems then that, in their simple versions, theories of objectivism, subjectivism and relativism are all flawed by their lack of predictability. Objectivism cannot predict values, subjectivism cannot predict judgments and relativism cannot predict anything. It thus remains for us to consider whether a finer, more sophisticated version of one of these theories might be threaded through the eye of our ontological needle.
Sophisticated Objectivism (All in the imagination?).

Sophisticated objectivism was developed by the eighteenth-century philosopher Immanuel Kant in his Critique of Judgment. In some ways, it is a fusion of simple objectivism with simple subjectivism.

While Kant claimed that objectivist judgments demand agreement from everyone without exception, he also allowed that the determining factor of some viewpoints was the feeling of contemplative pleasure or displeasure aroused in the mind of the spectator (a simple subjectivist viewpoint).

Kant linked these two seemingly mutually exclusive viewpoints by giving this paradox the structure of an 'antinomy' (a contradiction existing between two apparently indubitable propositions).

The key to understanding how these opposing viewpoints can co-exist is in Kant's emphasis on the 'free play' of the imagination. In essence, this means that the spectator's imagination is free to introduce concepts which are not inherent in the phenomenon and then rationally defend such a judgment by reference to these concepts.

An important consequence of Kant's 'free play' of the imagination is that different spectators can only be perceiving the same phenomenon in so far as they possess the same faculties of understanding and their imaginations operate identically.

However, it is difficult to refer to any particular attribution to justify one's assessment other than a sophisticated subjectivist perspective of what is pleasurable or displeasurable.
Sophisticated Subjectivism (Colours and aesthetics - 'seeing red'?).

Sophisticated subjectivism was skilfully defended by the eighteenth-century philosopher David Hume. In Of the Standard of Taste, Hume drew an analogy between colour judgments and aesthetic judgments whereby even the subjectivist occurrence of colour in the observer's mind still allows for standards in assessing the appropriateness of particular colour judgments and the capacity of the observer to make such a judgment.

For example, we would be sceptical of the colour judgment of someone who was known to be either blind or colour-blind.

It is worth remarking here that it was correct for Hume to attribute the occurrence of colour to subjectivism rather than objectivism. As the twentieth-century philosopher Bertrand Russell showed in The Problems of Philosophy, we cannot say that objects 'possess' colour. Colour is simply the result of light-waves in one part of the spectrum being reflected off an object and into our eyes while light-waves in another part of the spectrum are absorbed either by the object itself or by the intervening medium. In astronomy, physicists use this technique (known as spectroscopy) to deduce the characteristics of interstellar phenomena.

While there is a relatively uncontentious agreement on colour judgments, this does not so clearly hold true for other judgments. Even if it did, this would not be equivalent to a claim of universality. By its very nature, a subjectivist mode of assessment must allow for the possibility that not all spectators will arrive at the same judgment.

'Unlike the objectivist, a defender of subjectivism, including the sophisticated variety, cannot maintain that a judgment, if correctly made, must hold for everyone without exception... To those of us whose sensibilities may happen to be governed by totally different principles from the majority's - always a possibility for a subjectivist - the judgments of discriminating spectators within that majority can have no logical force.' (David Cooper).
Pragmatic Relativism ('Local' truths).

The problem with simple or dogmatic relativism was that, in adopting a form of Nietzchean nihilism, it inadvertently implied that there ought to be a set of universal criteria which all theories fail to meet. How can we fail a theory for failing to include a non-existent quality?

By way of contrast, pragmatic relativism does not condemn any one judgment for failing to be universal. Nor does it imply that any judgments should be universal by giving a despairing, post-modernist equivalence to all judgments. It simply recognizes the de facto existence of different judgments.

While judgments are relative to distinct practices, they are not objectivist (they do not demand agreement from everyone) and they are not subjectivist (they can be defended as impersonal, localized 'truths').

The main attraction of pragmatic relativism is that it is an essentially modest theory (it does not assert its supremacy over other useful theories) and allows us to be receptive to competing judgments by emphasizing their differences rather than their similarities.

The main failing of pragmatic relativism is that, in failing to acknowledge the superiority of any one mode of judgment (including itself) it cannot arbitrate between competing judgments.

Therefore, while pragmatic relativism may be useful in discussing different perspectives, it is unable to provide us with any conclusion.

Despite the inherent inconclusiveness of pragmatic relativism, it is a nimble enough perspective to enable us to avoid the logical pitfalls which open up before each of the other perspectives discussed.

For myself, I would therefore proceed to examine the apparent phenomenon of unity in diversity using a sophisticated pragmatic relativistic perspective rather than an empirical one. Perhaps mathematics (and, annoyingly, religion), have an underlying aesthetic overlap? Truth is beauty and beauty is truth. Then it gets a bit complicated..."


  1. "Unity in Diversity!" Sounds like an Orwellian party slogan, but it's actually a philosophical conundrum. It makes the 'chicken and the egg' riddle look like simple scientist's play.

    After 2,000 years of eggheads coming up with some VERY st...range answers, scientists claimed to have cracked the riddle last year. It's the chicken...

    "It had long been suspected that the egg came first but now we have the scientific proof that shows that in fact the chicken came first."

    Stephen Hawking claims the egg came first...

    Any man who talks like a TV advert gets my attention. Now I know that the ultimate purpose of the universe is to get me to sign up with British Telecom.

  2. On the 'redefinition' of God...

  3. Toward Orwellian Mathematics: The Virtual Impossibility of the Number ‘3’

    PROBLEM: “Prove that you have an IQ over 9000! Name a number which doesn’t include a 3! Bet you can’t!”

    (CAVEAT: names such as ‘Dave’ are mathematically unacceptable).

    SOLUTION 1: The number of possible answers is 3.

    If we forsake negative integers, the number of possible answers is, ironically, 3: 0, 1 and 2. All higher integers 'include' 3 as a subset (e.g. 4 = 3 + 1, 5 = 3 + 2 ...)

    SOLUTION 2: It is virtually impossible for you to give the answer ‘3’.

    Let us reject my earlier analysis and go with a more 'commonsensical' (an inherently dangerous concept) concept of the digit '3' being excluded from appearing in any of the bases. There would then be an infinite number of possible answers excluding '3'.

    Because the set of correct answers is infinite, the statistical probability of someone selecting the finite incorrect answer of '3' is so small as to be practically (another dangerous concept) non-existent.

    So if someone does select such a virtually (another dangerous concept) non-existent answer, what does this say about the role of consciousness (another dangerous concept) in mathematics?

    COMPLICATION: It gets more complicated when you then realize that the set of possible incorrect answers must also be infinite...

    CRITICAL FRIEND OBSERVATION: “Then I guess you have to apply the "re-normalisation" technique used in quantum physics - using the plus and minus infinities to cancel each other out!”

    RESPONSE: “Which means that there is no correct answer?”

    CRITICAL FRIEND OBSERVATION: “I'm no quantum scientist (really!?) so I don't understand how it works exactly, but I know that it is used to get a definite answer once infinity enters the equation, by cancelling them out leaving you with the remainder.”

    RESPONSE: “But if the set of correct answers is infinite, and the set of incorrect answers is also infinite, then the re-normalised remainder must be precisely zero...”

    CRITICAL FRIEND OBSERVATION: “Chris, I guess you have to work out the ratio of correct answer to incorrect answers on a finite scale… Which, I guess is 9:1… Because no matter how far you go into infinity, the ratio will remain the same… Although not sure if that really works or not.

    SOLUTION 3: "All infinities are equal, but some infinities are more equal than others".

    It's a tricky area. A useful starting point is Cantor's theorem...

    However, this has attracted some controversy...
    "what had it done to anyone to make them angry with it?"

    Douglas Adams wisely observed that the creation of the universe "has made a lot of people very angry and been widely regarded as a bad move..."

    He then went on to note that the universe has no imports, exports, population, art or sex.

    This is likely to make a lot of people angry. Not least the digit 3 which may (quite justifiably, I feel) feel unfairly excluded… I suspect that, somewhere out there, there must be an Orwellian theorum of mathematics. Something along the lines of "All infinities are equal, but some infinities are more equal than others". Out of such inequalities, whole universes may erupt...

  4. "I myself think that all of the reasons that lead people to say things like that have very little merit, and that people have just been misled, largely by mistaking the mathematics they use to describe reality for reality itself. If you think that mathematical objects are not in time, and mathematical objects don't change -- which is perfectly true -- and then you're always using mathematical objects to describe the world, you could easily fall into the idea that the world itself doesn't change, because your representations of it don't." ~ Tim Maudlin, Philosopher of Physics, New York University

    'What Happened Before the Big Bang? The New Philosophy of Cosmology'
    Ross Andersen, The Atlantic, 19 January 2012


    Sam Harris (world famous neuroscientist philosopher) is offering his critics a chance to put up or shut up. He's offered a cash prize of $20,000 (about £12,800) to anyone who can convincingly refute his central argument for a scientific morality.

    Assuming no-one can refute him, there's a consolation prize of $2,000 (about £1,280) for the most interesting response.

    See FAQs in link for further details. Closing date for entries is 9 February 2014, so you've got time to buy his book and boost his royalties.


    Hmmm… Traditionally, science has been regarded as descriptive and morality as prescriptive. But science is also predictive. So, in Sam’s moral landscape, do good* predictions = good** prescriptions?

    * Falsifiable
    ** Beneficial

    Possibly. But if they’re truly equivalent, does it work vice versa? This leads out onto some very thin ice…

    The real question is always “Cui bono” (to whose benefit?). So I suspect that Sam’s thesis could only be refuted by reference to de facto cynicism rather than de jure principle (i.e. selectivity and performativity)


    I don’t actually want to refute Sam’s thesis (fortunately for me). I just want to qualify it (modesty is my only flaw). But, in order to qualify it, I’ll have to fail to refute it in a way that grabs his interest. So, all I’m really looking for is a fascinating aesthetic conundrum at the heart of his argument…

    See also:

    Can Science Answer Moral Questions?

    First Draft PhD Proposal

    Woolwich Threads

    A Crash Course in Aesthetics

    Metamodernist Case Notes on a Think Tank Thread: Why Us and Why Now?

    Notes on Metamodernism: The Pit and the Pendulum...

    The Name of the Ghost

    Teachers Talking Rot (1 of 2)

    Teachers Talking Rot (2 of 2)

    See also: "Perhaps description is the key?"

    Marty Solves One of the Problems of the Universe

  6. WG: If morality evolved for the purpose of fostering community, can we deduce anything about what is moral/immoral without committing the naturalistic fallacy? If so, what?

    Naturalistic fallacy

    CP: Assuming evolution (and discounting intelligent design) we would be committing a teleological fallacy if we claimed that morality evolved for any purpose.

    See Teleological Argument

    It would be less erroneous if we simply claimed that community evolved as a successful survival strategy. From this we can deduce that morality evolved from a natural hierarchical pecking order into etiquette.

    See Etiquette

    The problem of the 'Naturalistic Fallacy' arises because of a manmade distinction between natural and manmade.

    This distinction seems to be an inverted form of the anthropomorphic/pathetic fallacy.

    See Pathetic Fallacy

    Man (i.e. homo sapiens) evolved IN the natural world. However, our intelligence evolved as another successful survival strategy. Eventually, this sapient differential resulted in misrecognition. We began to see ourselves as SEPARATE from the natural world.

    However, this separation is a fallacy. In (physical) reality, sentience is an emergent phenomenon. The artificial is still part of the natural world.

    From our initial premises, we can deduce that morality (i.e. evolved etiquette) can only exist in higher level consciousness. Therefore, we can deduce that morality is a complex emergent property.

    After that, we can only deduce that we are playing Wittgensteinian language games.

    See Language-game (philosophy)

    In 'The Moral Landscape', Sam Harris proposes we should discard cultural relativism and quantify these language games in terms of 'the well-being of conscious creatures'. It's a logical deduction and a valid premise.

    See 'The Moral Landscape'

    Whether his arguments are sound is still up for grabs though.


    CP: If morality is ‘the well-being of conscious creatures’, then consciousness must precede well-being.

    This is a one-way logic gate. We can talk of consciousness without well-being, but it makes no sense to talk of well-being without consciousness.

    Ergo, existence must precede essence (sans Sartrean Free Will).

    Ergo, survival must precede morality.

    But survival of what? Individuals, communities, genes, or memes?

    These qualities are entangled and interdependent. But which is most important?

    Ironically, we cannot be equitable from first principle here. Unfortunately, we do not live in a deathless paradise. Therefore, in the physical universe, we can only talk of survival and morality in terms of priorities (e.g. dilemmas or conflicts of interest).

    The scientific method can quantify well-being. But can it qualify existential priorities? If not, then a scientific morality without aesthetic qualification has no system of prioritization.

    Ergo, does ‘scientific morality’ encounter similar inconsistencies to those identified in Gödel's Incompleteness Theorems?

    Raatikainen, Panu, "Gödel's Incompleteness Theorems", The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), Edward N. Zalta (ed.)