Thursday, 26 March 2020

Mind-Independence and Value

Over at The Electric Agora, Daniel Kaufman posted an interesting essay on morality and objectivity (here), which carries on a debate he has been engaged in with Spencer Case.  I left the argument below in the comments there, but thought I would repost it here as it does constitute something that I take to be an implication of views I hold elsewhere.
Here is an argument for a kind of realism about moral values (in what follows 'Real' with a capital-R means 'mind-independent').
First premise: realms of what you call the objective but non-Real have the following property: the rules, norms, and facts involved are what they are in virtue of acts of human deliberation and decision. There are publicly accessible facts concerning the rules of tennis, for example, but they are subject to revision by us: should a governing body, or sufficient numbers of people, decide that there are new rules, then there are new rules. 
Second: in order for there to be realms whose rules/norms/facts are determined, at least in part, by human deliberation and decision, then human beings must be the kind of creatures who can deliberate, and that requires that we have a certain kind of structure, for the truly structureless cannot give rise to anything, let alone deliberation. The nature of this structure cannot be determined by acts of deliberation, for the latter depend on that structure for their existence. 
Conclusion: there is structure to human beings that is Real, i.e. mind-independent. Let us assume for now that this structure is biological.
Here is a neo-Aristotelian take on all this. It is plausible to suppose that biological structure leads to objective facts about human beings, and so can determine, for many aspects of being a human, that there are some conditions or states (the virtues) that lead to flourishing and some (the vices) that diminish flourishing: some things promote health, for example, whether we like it or not (eat your vegetables). So, in reasoning about moral matters, i.e. how to live best as a human being, the realm of the Real will be a factor – not necessarily the only factor, but one nonetheless. Hence, we can conclude that moral reasoning must be at least partly Realistic.
This seems rather persuasive to me. All the same, I in fact lean toward subjectivism when it comes to most of what is contained in actually existing moral codes, which generally strike me as the attempted universalization of local, contingent, and historically conditioned preference-sets. People who argue about morality often seem to think that their own success can be attributed to the specifics of their moral or cultural or social code – which are, therefore, projected outwards – but it seems more likely that, since most systems include some people who flourish, it is something that is common to all systems that grounds well-being, and that is what contributes to flourishing given our nature. Put another way, most moral argumentation seems to be conducted without considering human nature, and so is like arguing over Einstein’s Field Equations without considering physics or math. 
So I guess I would say that I lean toward *theoretical* Realism about values but, in most cases, *practical* subjectivism. This is, admittedly, a strange position (though perhaps something not too far from Plato).
Anyway, if you have any interest in formulating a response I would be interested in it, but I found your essay interesting and though-provoking regardless.

Wednesday, 18 March 2020

Special Relativity, Entropy, and the Direction of Time

Assuming that, as far as perception and experience are concerned, space is a three-dimensional, and time a one-dimensional, projection of a four-dimensional space-time, the following question arises: why does the brain, a material organ, break down a four-dimensional, relativistic space-time into three spatial dimensions and one temporal dimension? There is really only one answer that suggests itself, and it is that as biological products of natural selection our survival depends on tracking entropy: we need to find pockets of low entropy in order to discover sources of work that we may employ in order to maintain our own relatively low entropy, and since the entropic gradient is aligned along the temporal dimension, it is to our benefit to evolve to single out that dimension from the other three in order to focus on it and thereby be able to track entropy. That is, it is important to our survival that we find low entropy systems in order to secure energy.

This seems straightforward enough but it does, however, raise a deeper question: why is entropy organized along the temporal dimension alone; why not along another dimension, or two or more dimensions? Why did evolution find it necessary to endow us with perceptual and cognitive faculties that see the world as a three-dimensional array of material and objects that are evolving in a fourth dimension rather than some other way?

We know that in Minkowski space-time, neither spatial distances nor temporal durations have geometric significance on their own: only their combination in terms of Einstein’s Interval Formula:

     I2 = dt2 – ds2

has physical significance. What this entails is that there is no preferred set of spatial axes for the universe, no sense in which one can be right or wrong in labelling one direction “east” rather than “north” or “up” rather than “sideways”, and so on. All such spatial directions are significant only in relation to an observer; the universe itself doesn’t single out a particular direction in space.

Accordingly, if entropy increase were to be correlated with a spatial axis, it would be impossible for evolution to track it because it is impossible for physically real correlations to exist in relation to one or more spatial axes. The pattern of entropic increase would simply disappear from all spatial perspectives except one, i.e. from those corresponding to the rotation of the particular choice of axes. If a pattern is deeply dependent on a directional convention in this way, then there is no way for the non-directed, probabilistic processes of evolution to latch onto it, for there is, in reality, no probabilistic pattern to be detected: the pattern would be an observer effect, just like some works of art are constructed so that only when looked at directly is an image visible; all other angles show no discernible pattern - there is no pattern inherent to the image itself in such a case. In essence, if entropy were to be aligned with one or more spatial axes, the pattern of the second law of thermodynamics would simply disappear with movement in space, rendering impossible to have both freedom of movement and the ability to track entropy.

Given the non-directionality of space, entropy increase could not be aligned along any spatial dimension, so there could be no fitness relevant pressure to track any such gradient spatially. The only remaining option is that what we evolved to detect, namely the entropy gradient, is aligned with the fourth, temporal, dimension. But how could this be the case? According to (I), temporal duration frame-dependent – how much time there is between any two events will vary, though in such a way as to preserve the interval, I, between them. Moreover, the direction of time does not make an appearance in (I) since whether we put a positive or negative sign in front of the (frame-dependent) measure of time will make no difference to the interval because the value for time is squared in (I). This is one of the senses in which it is thought that Relativity counts against the common-sense notion that time passes from past to future.

If we leave things here, however, then we are faced with a problem: we know that entropy is coordinated with the temporal dimension, but if that dimension lacks an inherent direction, then there is no reason for entropy to uniformly increase or decrease along it: any such pattern would only be apparent, like a spatially oriented second law of thermodynamics, that exists only from some points of view. So if there is a genuine entropy gradient along the temporal dimension, which would account for our having evolved to single out time from space, then we must conclude that as a matter of fact, if not mathematical necessity, the fourth, temporal of the universe is inherently directed or asymmetric.

However, precisely because the temporal duration is squared in (I), it makes no difference to the mathematics of the interval to suppose that there is an objective, physically significant direction to time. In other words, even if there is a real difference between +t and -t, the interval will wash that out by squaring the value. So, the mathematics of Special Relativity is not impacted by the assumption that time is directed in the following sense: at each four-dimensional space-time point, a unique direction is defined, from the past light cone to the future. We can think of it as an array of vectors originating at the point and directed toward each point on the interior of one half of the light cone only; alternatively, we can state that between any two time-like separated space-time points, there exists a vector that defines the past-future orientation. This way, local temporal asymmetry is relativistically invariant and from the frame of reference of the surface of the Earth, there is a genuine pattern for the non-directed mechanisms of evolution to stumble upon and register for future iterations of variation-selection-inheritance.

In other words, the very fact that the four-dimensional, invariant Interval is broken down by the brain into a three-plus-one dimensional cognitive-perceptual model provides excellent reason to believe that the direction of time is not an illusion but, rather, a relativistic invariant.

Why does this matter? Well, it matters because there is a strong current of argumentation in the philosophy of time/physics to the effect that both the passage and direction of time are illusory, mere mental projections onto a fully symmetric underlying physical reality. If the foregoing argument is correct, then this is unlikely to be true simply because it would be unable to account for the fact that evolution reached a wide-spread and relatively stable equilibrium in constructing human beings to experience and understand the world as 3+1-dimensional rather than 4+0-, 2+2, or 1+3-dimensional. More fundamentally, it cannot account for the fact that entropy is aligned with any of the dimensions in (I) at all: if there is no fact of the matter as to which direction in space-time is locally future-oriented, there would be no entropic gradient in the first place for evolution to eventually track. In other words, without an objective temporal direction, there could be no entropic gradient at all since from one temporal perspective the universe would consist of mostly improbable transitions and that perspective would have to be considered equally valid compared to the opposite perspective in which probable transitions are the rule. But any viewpoint according to which a highly probable and highly improbable set of transitions need to be considered equally valid must surely be incorrect.

So, it seems that the best way to view the implications of Relativity Theory for the debate over the nature of time is that it combines with the theory of evolution to suggest that Einstein-Minkowski space-time includes a temporally oriented vector field defined at every space-time point that determines the future light cone from that point. The vectors themselves are perhaps to be viewed as unit vectors with frame-dependent lengths determined by the time-dilation implied by Lorenz Transformations.

The upshot for the philosophy of time is that a naturalistic picture of time that combines Einstein-Minkowski space-time with Darwinian evolution is not only compatible with asymmetric, i.e. directed, time but in fact demands it. In short, the direction of time is not an illusion. Furthermore, so long as we can define temporal passage in terms of directed temporal ordering, then this view is compatible with objective temporal passage as well. Since, as I’ve argued elsewhere, there is no problem with a deflationary, relational conception of temporal passage, we can conclude that the Theory of Relativity is no threat to the idea that time genuinely passes from the past toward the future.

Wednesday, 22 January 2020

Understanding as an Alethic Concept

One of the ways in which I have defended the value of the humanities is by reference to understanding, as in “the humanities help to improve our understanding of ourselves and our environment, and this is important”.   This is both initially plausible and helps to lay out a kind of value that is distinct from the gathering of knowledge, which the sciences seem to do better than the humanities. 

One advantage of taking this route is that “understanding” is a rather wide-ranging term that has many meanings, so people can import various, positive, interpretations into the phrase “improve our understanding”.  This is, of course, also a disadvantage, for it renders the basic defence ambiguous.  So what does it mean to say that the humanities improve our understanding?

Among the rather familiar and straightforward meanings of “understanding” we could list:

·      The knowledge of linguistic meaning: e.g. “x understands English”
·      A sympathetic or gentle approach or demeanour: “x was very understanding of y’s situation”
·      An informal agreement: “x and y came to an understanding”
·      A belief state that is the result of inference or observation: “I understand that you have changed jobs”
·      An assumption, perhaps unspoken or hidden: “it is understood that everyone will speak respectfully at department meetings”
·      A cognitive ability: “it is impossible for non-human animals to understand that moral obligations exist.”

When it comes to the value that humanities offer, I think, however, that the best meaning is something along these lines:

·      To understand something, P, is to realize or learn the significance of P; e.g. “I understand that this is a very complex issue that impacts x, y, and, z and will require further investigation”

That seems to capture what the humanities are after: to discover and impart methods, tools, writings, interpretations, and arguments that will allow us to learn something of significance about something, which may be that that something is in fact significant.  So, understanding, will result when some argument or analysis makes clear to us: (1) that P is significant/important; or (2) what is significant/important about P.

This indicates that understanding is similar in certain respects to explanation.  An explanation, E, of P makes P clear to us or, as I would say, enables us to see why or that P is true, either by entailing P, rendering P probable, or fitting P coherently into our prior body of knowledge.  
In the case of explanation, however, E can explain P even if E is false.  For example, Aristotle explained why material bodies sink in water by appeal to (1) hylomorphism, which includes the claim that bodies (“substances”) include an immanent form; (2) a theory of space that is structured formally, with “earth” at the center, surrounded by, in order, “water”, “air”, and “fire”; and (3) a principle which states that anything with form F will naturally seek space that is F.  Given (1) – (3) it follows that rocks, “earth”, will sink because the “earth” form of space is below the “water” part.  So, (1) – (3) are explanatory.

They are not, however, true.  Accordingly, I suggest, Aristotle’s explanation cannot provide us with any understanding of the motions of bodies. In particular, it cannot offer any additional understanding than what was contained in the prior observation that rocks fall in water, fire rises in air, and so on.  Aristotle’s attempt to move from those straightforward observations to a systematic elucidation of what is going on when bodies move ultimately fails for the simple reason that it is, so we currently believe, false: we no longer accept his account of the structure of space and reject his formal account of attraction (bodies don’t naturally move, we think, but instead naturally continue in their current state).  So even though Aristotelian physics neatly explains motion in virtue of providing a set of propositions that entails a great deal of what we observe, it does not offer understanding of motion.  This is, of course, not unique: it is straightforward to construct a set of propositions that are false but entail or make probable some other proposition that is known to be true.

Let’s consider a made-up case in which x is afraid of the dark and posits that this was caused by x’s abduction by extraterrestrials one night years ago, which left a deep-seated fear that is brought to the surface in the dark.  This would explain the fear: the proposition that x was abducted combined with the proposition that this was traumatic and that trauma can leave a lasting fear that is associated with the time of day during which the initial event occurred, entails or renders probable a current fear.  However, x does not in fact understand why the fear exists, if the abduction never occurred.  Further, a non-occurrent event cannot increase x’s awareness of the significance or importance of the fear: the abduction proposition adds nothing on that score either (no more than supposing x’s fear is caused by unicorns or magic).

What this suggests is that the understanding sought by the humanities is in fact an alethic concept: whatever it is that increases understanding must be true.  The same applies for a good explanation, so understanding is something like a good or correct explanation of the significance of something.

If this is right, then it immediately raises a question: how can the humanities improve our understanding if they do not either: (1) discover the truth, at least in part; or (2) apply truth-preserving methods to previously discovered truths?  In the absence of truth, there can be no understanding, so the humanities must either be able to determine the truth or else take the truth and derive something from it that clarifies the importance of something.  

In the latter case, this process of derivation must be truth preserving or probability/coherence increasing; otherwise it will not in fact increase our understanding.  It may of course be possible to do something in addition to determining the truth or an alethic consequence from what is known.  That is, the process of increasing understanding may involve deriving something, P, from something known as well as situating this truth in some kind of context that is enlightening.  But again, if this context is not factual, situating a truth in it cannot improve our understanding, so there is a kind of alethic constraint at all stages of the process.

So, if all this is roughly along the right lines, then any humanities project aimed at improving understanding must, at least in part, either discover the truth or else work with the truth to derive further truths that are significant or can be contextualized with other truths in such a way as to produce an improvement in our awareness of the significance or importance of something, which must also be of genuine or true significance, for otherwise we have no understanding (if something isn’t truly significant, then we cannot really understand its significance.)  

In short, if we want to improve our understanding of P, then:

1.     P must be true
2.     The theory (story/account/proposition/…), T, that improves the understanding of P must be true
3.     T must have some truth preserving or probability raising relation to P (otherwise it cannot help us see that/why P is true)
4.     T may also do more than (3): for example it ay relate P to a context, C, or another understood proposition, Q.
5.     If (4), then C or Q must be true as well.

I don’t, in other words, see how the appeal to “understanding”, in the defence of the value of the anything, gets a discipline off the hook of either being truth-producing or at least truth-preserving.  So, any field that aims at understanding must employ methods that have one or both of these properties.  This, of course, includes the humanities.

One worry about (1) – (5) above is whether it is compatible with a robust notion of fictional truth, i.e. one in which fictional propositions can be literally and directly true, as in “that Centaurs have four legs is true” instead of “that Geek myth-makers said that Centaurs have four legs is true”.  If one takes it to be true that Centaurs have four legs, then presumably we could offer a study to increase our understanding of Centaurs themselves, which seem never to have existed, rather than our understanding of their story-tellers, which do or did exist.  This seems awkward.  I am not sure how much of a problem any of this is, but it seems to me to have a rather felicitous implication: there is reason to adopt an indirect account of fictional truth in which propositions about fictional entities are in fact about the acts and thoughts of writers and story-tellers, in which case the study of mythology can aid in our understanding insofar as it aids in our understanding of human beings who make up tales and the societies and times in which they live.  This seems perfectly respectable, so long as it is alethic in the ways mentioned above.

Friday, 1 November 2019

More on "Theory" in the Humanities

This is a follow up to the previous post that cast a skeptical eye on the ability of the humanities to produce knowledge or meaningful understanding.  I want to comment here on the possibility of constructing a humanities based “theory” to elucidate the world, ourselves, or the relation between the two.

To see deeper into the problem with the assumption that something such as a theory emanating from a humanities discipline can reliably provide information about the world – including the mind of an author – I will consider the description of one such theory, Derrida’s deconstructionism, as provided in the Stanford Encyclopedia of Philosophy (SEP).  What is deconstruction according to this article?  One of Derrida’s earliest answers is described as follows:

Simply, deconstruction is a criticism of Platonism, which is defined by the belief that existence is structured in terms of oppositions (separate substances or forms) and that the oppositions are hierarchical, with one side of the opposition being more valuable than the other. The first phase of deconstruction attacks this belief by reversing the Platonistic hierarchies.

Supposing that Plato’s alleged hierarchies are mistaken, it is unclear what value there is in reversing them.  The reversal of a false hierarchy isn’t necessarily a true one.  For example, if we reverse the false hierarchy, men are superior to women, we get the equally false, women are superior to men.  Moreover, if Plato himself is guilty of some form of complex fiction writing, i.e. failing to engage in anything other than his own abstractions that lack grounding in reality, then reversing them is to similarly play in the realm of fiction, much like analyzing Tolkien’s works for hierarchies among Orcs, and then reversing them; what could that possibly teach us?  Perhaps it could teach us something about the opinions of the author of the reversal, but without both more context and a relatively sophisticated psychological theory applicable to the author, it is not easy to say what would be learned here.

The SEP entry continues:

On the basis of the reversal… we can see that something like a decision (a perhaps impossible decision) must have been made at the beginning of the metaphysical tradition, a decision that instituted the hierarchy…

This is plausible.  Decisions – assumptions, presuppositions, etc. – as to the rules and axioms of investigation must be made prior to any inquiry.  It does not follow, however, that such decisions are arbitrary, unfounded, unjustified, or not conducive to discovering the truth.  They may be just the right decisions required to uncover the structure of reality, and the reasoning they initiate may be logically sound.  What this means is that there is no reason to believe that the mere act of reversing the result of such decisions will lead to a better account of reality. 

Now let us turn to the second phase of deconstruction:

The previously inferior term must be re-inscribed as the “origin” or “resource” of the opposition and hierarchy itself.

There are a couple of problems here.  First, as just noted, because the need to rely on “decisions” – axioms, rules, etc. – in order to get inquiry off the ground does not entail that the decisions are bad or conducive to falsehood, it follows that we cannot assume that any hierarchy that results is necessarily wrong.  Hence, to elevate what Plato saw as the less valuable of two parts of a hierarchy – say matter over form – is not necessarily to do anything important or revealing.  Nor does it follow that the inferior term must have some fundamental or central role in the creation of the hierarchy.  Perhaps Plato elevated form over matter because he was in fact obsessed with the material – maybe he feared the physical body – and felt some paradoxical need to overwhelm it – put it in its place – in his theory; but perhaps not.  The mere fact that there is a decision here tells us nothing, because similar decisions are required for any inquiry, including Derrida’s. 

In general, from the fact that a hierarchy is incorrect, it doesn’t follow that the previously inferior term is the origin of the hierarchy itself.  Consider:

            Non-human animals are more intelligent than humans.

This is, apparently at least, the wrong way around, so we must reverse the hierarchy:

            Humans are more intelligent than non-human animals.

It does not follow that re-inscribing “non-human animal” as the “origin” of this opposition and hierarchy is correct, or even makes any sense.  On the contrary, it appears that if anything it is a preference for, or bias toward, the human that is the origin here.  At any rate, it is the relation between the two that is the cause of the hierarchy, not any one on its own, so to propose a theory of reversal and inversion on a priori grounds is simply suspect.

Secondly, unless we assume that Plato himself discovered something deep and true about the essence of reality in his hierarchical oppositions, he just messed up the order, any act of inversion will tell us nothing.  So… how do we know that Plato was right here?  Suppose someone divides the world into red things and geometric objects, making the latter more important than the former.  This clearly seems to be a hierarchy that tells us nothing about reality, so inverting it so that the red things are more important will similarly tell us nothing. 

Well, perhaps I am not properly considering the nature of this re-inscription, so: 

How would this re-inscription or redefinition of appearance work? Here we would have to return to the idea that every appearance or every experience is temporal. In the experience of the present, there is always a small difference between the moment of now-ness and the past and the future… this infinitesimal difference is not only a difference that is non-dualistic, but also it is a difference that is, as Derrida would say, “undecidable.” Although the minuscule difference is virtually unnoticeable in everyday common experience, when we in fact notice it, we cannot decide if we are experiencing a memory or a present perception, if we are experiencing a present perception or an anticipation… Insofar as the difference is undecidable…[it] destabilizes the original decision that instituted the hierarchy.

There is certainly work in the experience of time that suggests that any particular experience is a structured mix that combines perception of what is occurring at that time with memory and anticipation (see, e.g., Horwich 1987) – experience has content that is temporally structured to include a past, present, and future component.  What is not clear, is whether there is no way to distinguish these at all; even fuzzy boundaries can be boundaries, and who knows what cognitive science might discover.  Moreover, it is unclear why this undecidability would invalidate Platonic arguments about, say, the form of the good, or the nature of mathematical knowledge.  There may be an argument for this, but since Platonic metaphysics is the result of a long period of contemplation and analysis, there is no obvious move from a feature of momentary perceptions to the results of long, thorough contemplation. 

When reflecting upon the nature of number or goodness, one may be doing little more than staring out of a window, pen and notebook in hand, mulling over arguments of Frege and Russell, or Kant and Aristotle.  The perception of the trees and birds beyond the pane of glass may – though may not – be an essentially entangled mix of what is seen then with memory and anticipation.  It is not at all clear, however, what impact this has on one’s reflection of Frege’s attempts to translate the Peano axioms into axioms of the predicate calculus.  Suppose, as one read The Foundations of Arithmetic, one’s perceptions were consistently temporally mixed in just this way: what is the significance of this fact for reflecting on whether the logical reduction of arithmetic is sound?  It would seem that the inability to separate the temporal components of experience would have no bearing on this.  Further, even if one cannot separate out the components of experience at the time they are happening, it doesn’t follow that one can’t look back on one’s experience with the benefit of additional information and then disentangle the strands, which might lead to a principled way to do so in general.  In short, it is not at all clear how the alleged features of temporal experience would undermine the choice of axioms and rules of inquiry that are required to get any investigation off the ground.  Conversely, if such features do destabilize all such choices, then they would undermine the principles that undergird the deconstructionist inversion.

So this is an example of a theory applied to a text that is supposed to result in something interesting and informative about reality.  However, if the text itself is simply off base, then the move proposed by this theory will not likely tell us anything interesting or informative; at least it gives us no reason to suppose so because it offers no means of correcting the text other than rearranging its parts, which is of not help if the text is fundamentally incomplete.  Moreover, we have to have some reason to believe that the inversion proposed by the theory is a good move: likely to be informative, corrective, truth-conducive, or what have you.  For this, more than a priori reflection on texts is required, because what we want to know is when texts are better or worse at getting things right.  Inverted Plato vs. Regular Plato leaves us in no position to judge.  It is like being told that A believes that P and B believes that not-P.  Without evidence from outside their belief states, we have no way of adjudicating between them.

So, until we can demonstrate that humanistic writing, that isn’t grounded in math and science, can reveal something about reality, then any attempt to reverse, pervert, subvert, or otherwise undermine previous such writing cannot be said to amount to knowledge of anything.  What, then, can it tell us?  I am not sure.  Perhaps something about the mind of Derrida, but I am not sure what that would be without more empirical evidence about him and how human minds work in general; i.e. not without some science. 

Obviously more has to be said to make the case.  In particular, I am, here, relying on a single source about a single aspect of a single author’s work, so it would be illegitimate to generalize from this single case.  It is, however, illustrative of the point I made in the previous post: that a non-scientific theory of texts applied to texts to create other texts does not seem to be the kind of thing that will generate knowledge of the world; at best it would generate knowledge of the applier of the theory, but even that would be suspect without detailed empirical investigation.  So, the question is what the theory – in this case a principled inversion – could possibly teach us about the world.

Let me end with a limited defence of Plato.  It seems to me that his “elevation” of forms had to do primarily with an observation, that Euclidean geometry, which is an a priori and formal axiomatic system, manages to correctly describe space.  He proposed, along Pythagorean lines, that the explanation of this is that reality itself is ultimately mathematical in nature, so that it shares its form with the Euclidean axioms.  If this is correct, then the basic structure of reality is timeless and unchanging, in which case the idea that the world is a place of change and flux must be some kind of mistake or illusion.  This may be wrong, but it is reflection on the basis of a mathematical-physical knowledge and observation.  So, to return to the original point, it is far from obvious why a general “inversion” of the resulting system would be true, interesting, or valuable.