Professional Brokers, Retail Buyers and Logic

Logic, epistemology, and scientific evidence don't count for much when you're a professional broker, but they should doubly count if you're a retail buyer.

I have been wondering about the logic of how professional investors buy and sell stocks.  If a professional investor, Mr. A., sells stock #1 and buys stock #2, then Mr. A must think stock #1 will (with a high degree of probability) go down, while stock #2 (with high degree of probability) will go up.  Yet some other investor, Mr. B, must think the opposite of the other guy concerning stock #1, since he bought it, and likewise for stock #2, if he sold it.

Suppose I, a retail consumer, want to get advice on which stocks to buy.  Both Mr. A and Mr. B are professionals.  Yet they would advise me in exactly opposite ways concerning stock #1 and #2!  Since there are always professional buyers and sellers of any given stock in The Big Market everyday, at best I might be following the herd -- i.e., going with what the majority of professional investors are doing.  Is that the winning strategy for a retail consumer like me?

Hardly, and here is the problem:  A study of 10,000 brokerage accounts of individual investors over seven years showed that the average investor does better in selling stocks than in buying them. It is also well documented that the most active traders have the worst results, while those who trade least earn the best returns. [1]

So then, as a retail stock buyer, I am in a very precarious postion, since professionals disagree with one another, and since even they do not do well.  They certainly do well enough to convince retail stock buyers to turn over their money, but not well enough to somehow beat the market based on their (alleged) expertise.  This is why some financial advisers say one should merely buy index funds and ride the general wave of a reasonably expanding market.

I read recently that two out every three mutual funds underperform the market in a given year. Furthermore, most of the big funds that do well are, statistically speaking, only getting lucky and not getting insightful about how the market moves. Naturally, when the luck is holding, they advertise their good returns, and promote a correlation cause fallacy: we analyzed and bought this stock; the stock has been performing well.  Therefore, our analysis and timed buying shows we understand what is causing this stock to perform well. No doubt the vast majority of retails buyers are taken-in by this.  But what seems even more wondrous here is that the professionals seem to believe their own B.S.  Many of them are highly confident that they have some deep, profit-wise reliable intuition about how how stock buying and selling works, yet they have no quantifiable evidence to show this -- i.e., no evidence to separate the above correlation from causation issue about how they happened to have made their money from stocks.[2]

I've been considering buying some stocks lately.  Too bad I have no plan.  But I'm in no worse of a position than anyone else, it seems.  Maybe I'll get lucky.  Actually, it's more rational to think that I won't get lucky, and simply earn about 6% return on my money over the course of many years when taking a buy and hold strategy.

O.



REFERENCES

[image] U.S. Dept. of Labor

[1] Terry Odean, Brad Barber "Trading is Hazardous to your Wealth." (.pdf) THE JOURNAL OF FINANCE, VOL. LV, NO. 2, APRIL 2000

[2] Obviously, they know how they make their reliable money -- from trading and management fees.

Pinocchio Paradox Propositionally Debunked

Dear Mr. Supposed Philosopher:


My nephew taunts that were Pinocchio to say me, "Your nose will grow," a paradox would ensue.  I said, "Nuh Uh."  But, secretly, I'm not so sure.  Is he really that smart, or is he just bluffing?


Signed,
Roundly Razzed
Batavia, OH

Dear R:

I'm going with he's bluffing.  Here's why:


P =def. "Pinocchio"
R =def. "Roundly Razzed"


00. P says, "R's nose will grow."


Theorem 1:
01. If P lies, then P's nose grows. (premise)
02. If P doesn't lie, P's nose doesn't grow. (premise)
03. P lies or P doesn't (tautology)
04. So, either P's nose grows, or it don't. (1,2,3 ; CD)


Theorem 2:
05. If R's nose grows, P's does not. (premise of hypothetical effect)
06. If R's nose don't grow, then P's does. (premise of hypothetical effect)
07. R's nose grows or R's nose doesn't. (tautology)
08. So, either P's nose grows or it don't (5,6,7; CD)


Theorem 3:
09. If R is a physically maturing person, R's nose will grow. (premise)
10. If R's nose will grow, then P doesn't lie. (premise)
11. So, If R is still a physically maturing person, then P doesn't lie. (9,10 HS)


Main Argument:
12. R is still a physically maturing person. (premise)
13. Thus, P doesn't lie.  (11,12; MP)
14. Hence, P's nose doesn't grow. (2,13; MP)
15. Therefore, R's nose still does, though.(6,14; MT)

Analysis: No contradiction found. Thus, no paradox detected.

O.

REFERENCES:

Ray Wiseman Logic and Proofs (Accessed 11/29/2010) - gives a summary of the rules of propositional logic.

Narrative, Logic, and Wishful Thinking in Theology

In a new book, with the possibly oxymoronic title of, "Analytic Theology: new Essays in the Philosophy of Theology," Eleonore Stump writes the following:

"To me, it seems that there are things to know which can be known through narrative but which cannot be known as well, if at all, through the methods of analytic philosophy."[1]

My worry here is that such a view is merely a contingent statement about the psychological assent of the individual, not about careful justification or reliable procedures for having trustworthy (even true) beliefs. A story adapted from the well-known 20th century philosopher, Bertrand Russell, is informative:

There is a small town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. The barber, said to be a persnickety man, has a business rule whereby he shaves all and only those men in town who do not shave themselves. One day, a heavily bearded man, feeling the scratchy irritation that only a string of hot summer days can impute on such a fellow, decides to avail himself of this barber's services. As he's walking up to the shop, the thought strikes him, "Does the barber shave himself?" As he's reaching for shop's door handle, he further thinks, "Well, he does or he doesn't; that's for sure." Sadly, however, when he steps into the shop, he notes that the barber's not there. "Should I wait?" ponders the man, yet again scratching his neck.

Now people who love the narrative method for doing theology (or other religious-type thinking) would probably ask questions like, "Does this barber find meaning in having such a special commitment to whom he shaves?" Or, "Does this barber cheat members of the community by partitioning some from others as to whom he will allow into his business?" And, lots of other kinds of "deepity" fishings for Big Questions would, no doubt, also be asked.

Alas, the problem isn't that the story is just fictional, but that it's logically impossible that there is such a barber. (If the barber does not shave himself, he must abide by the rule and shave himself, but if he does shave himself, according to the rule he will not shave himself. Thus, such contradictions show our conceptual barber is nonsense.) So, what people who formulate such questions about this barber fall prey to is mere psychological assent, thinking they are asking meaningful questions. But there is no reference to the very concepts of their questions! They are fooled into asking about purely vacuous entities and events. Yet this is the very problem with much of what passes for standard theologizing. Many of the issues, even when not empirically defeasible, are simply vacuous. Sometimes theologizing fails by making scientifically false claims. Sometimes theologizing fails by making metaphorically hazy claims. But in these types of instances, theologizing would fail by making vacuous claims.

I once heard an aphorism which seems to be a corollary for this problem, at least for the traditional, dogma-based issues within theology. I'll paraphrase it as follows: "Just because a grammatically structured question can be formulated on some topic, doesn't mean there can be an answer to that question."

O.

REFERENCES

[image] william c hutton jr flickriver (Accessed Sept. 11, 2010)

[1] Oliver D. Crips, ed. "Analytic Theology: New Essays in the Philosophy of Theology" (Oxford Univ. Press, 2009), 255.

Jim's Logic Proof for driving as he does.

Jim had studied enough logic to know he must keep going,
but not enough to know he was supposed to drive down the
center of the road.
 
01. L v R     In the past, Jim had noted that either the
              left lane is closed, or the right lane is
              closed.
02. R > Ml    And he knew that if right lane is closed, 
              then one must take the left lane
03. L > Mr    And also he knew that if the left lane is
              closed, then one must take the right lane.
04. L & R     But Jim can now see that both lanes are
              closed ahead.
----------
05. L         Which means, the left one is closed 
              (4, Simplification) 
06. R         And, too, that the right one is closed.
              (4, Simplification) 
07. Mr        So, Jim deduces he must take the right lane.
              (3,5, Modus Ponens) 
08. Ml v Mr   That, or he must take the left one. 
              (7, Addition)

Jim has correctly reasoned that he must take either of 
the two lanes, and so he yells, "Onward!" and punches the 
gas, as the above picture shows. Yet with a bit more study,
Jim would have reasoned as follows:

09. Ml         "But I must likewise take the left lane."
               (2,6 Modus Ponens)
10. Ml & Mr    "Therefore, I must take the left land and the
                right lane!" (7 & 9 Conjunction)

Such contingencies of life show the value of studying logic.

Kurt Cobain Quote

"Wanting to be someone else is a waste of the person you are."
-- Kurt Cobain

Suppose one were already a waste, and subsequently finds s/he wants to be someone else.  What then follows on Cobain's conjecture?

O.

[ * ] "In Bloom" by Nirvana YouTube (Accessed 5/20/2010)
[ * ] "Smells Like Teen Spirit" by Nirvana YouTube (Accessed 5/20/2010)
[ * ] "Heart Shaped Box" by Nirvana YouTube (Accessed 5/20/2010)
[ * ] etc. etc.

The Multiverse is speculative and wasteful

Sometimes I can't help but ponder this whole multiple universe issue. Maybe it's because I'm a philosopher that I'm attracted to this juicy piece of Science bait -- if talk of multiple universes really is Science, which has been at some controversy. There are two things that I often wonder about. The first is the role that multiverses are suppose to play in cosmological theories, which seems problematic to me. The second is the too-explosive range of universes that supposedly spring into subsistence when available quantum states are utilized as ways of mapping the possibilities from the immediate moment forward.

I
At first glance, it seems that were there a multiverse, it would not be observable, since any such other components of the multiverse are being created outside of our big bang light sphere. Indeed, every other component universe of the multiverse would have the same problem, that of not being able to observe anything outside it's own big bang light sphere.

"Look," someone might counter, "direct observation is not needed to establish or give evidence for the multiverse, for there are other, indirect ways to justify it. This theory has survived falsification and there are no other contenders for anything better." The idea here is that if some physics theory predicts an observational consequence of a multiverse, and we don't see that consequence, then the multiverse theory (or that particular type of multiverse theory) would be defeated.

Put differently, with a bit more detail, suppose somebody claims, that some observation set (+O1) entails a theory of an unobservable multiverse (-T2) And this theory of an unobservable multiverse, entails some other set of observational evidence (+O3). We then note that +O1 should always entail an observational correlation to +O3. So the scientific matter would stand as follows:

+O1 --> -T2
-T2 --> +O3
So,
+O1 --> +O3

If one noted the presence of +O1, but the absence of +O3, then that would be good Popperian[1] defeating evidence for -T2. But the harder problem is where we are now: Where we have +O1 and +O3 kinds of phenomena (from quantum theory, apparently) but the status of darling theory -T2 (the multiverse claim) is worrisome.

Suppose there is some other kind of unobservable theory, maybe of another kind of multiverse with vibrating strings, or maybe of super-powerful beings, or even of a supernatural being which holds the order of space and time together in the way we observe it. Indeed, perhaps there are several of these types of theories floating around. Call any one of them -Tn . (By analogy, suppose you had a jar of colored marbles, M. You close your eyes and pull out one of a certain color, which your near-by friend notes to himself as '+M_red'. But for your part, you can only say, '-M_n' to represent a marble whose color you don't know about.)

So the scientific matter would stand as follows:

+O1 --> -Tn
-Tn --> +O3
So,
+O1 --> +O3

If such a theory did not, up to the most recent testing, show any exception of correlation of +O1 to +O3, does that make it a good theory? There are an infinite number of -Tn -type of theories one could posit that are consistent with the noted observations. That's very worrisome. It looks like one is using speculative, metaphysical linkage to build a cosmological, scientific theory. But if intelligent design posits in biology have taught us anything, this all seems the wrong way to go, for whether the linkage is of a personal metaphysical object (God) or an impersonal metaphysical object (a non-observable super-structure), one leaves the realm of science as it's been practiced since Galileo.

Admittedly, I do think advocates of a multiverse theory can get around the above complaint; since posited, apparently unobservable entities sometimes turn out to be observable after all, as the history of the concept of 'gene' has shown. So my real problem is that cosmological positions about about a multiverse are derived from previously held commitments in quantum theory, and quantum theory is probably the most intensely tested, most reliable scientific theory known to science. Thus, what really tempts me to multiverse belief comes from the bottom-up issues of quantum theory, not from the top-down issues of cosmology. So let me now turn to this side of the issue.

II
The first step that seems to draw me in is what has drawn many in: the unrivaled empirical success of quantum mechanics. Many scientists intimately involved in quantum mechanics think it's more than just a handy mathematical model for organizing data; instead, they have the gaul to say it's "true", even if they often admit they don't understand what it all means. As Michio Kaku writes, “It is often stated that of all the theories proposed in this century, the silliest is quantum theory. In fact, some say that the only thing that quantum theory has going for it is that it is unquestionably correct.”

The second step that makes me muse all metaphysical about multiverse claims is the on-going engineering attempts at quantum computing. Whole governments and academic institutions are pumping big dollars into a form of computation that can use peculiar quantum mechanical phenomena like superposition and entanglement as a way of manipulating data, first by representing the data in parallel ways, and then by operating on all of those representations. But to harken back to the first step above, there are quantum mechanical phenomena, because the world itself has a real structure -- namely, a quantum structure. Quantum computing harness a lot of stuff going on in parallel, specifically bit storage and bit operations. But these parallel activities are supposedly not going on "here" -- so just where are they going on?

The third step which pulls at me is where I make a simple deduction from the first two temptations. We talk about our 'Universe', which is supposed to be the One, the Everything. And these quantum phenomena used in quantum computation are happening at some particular place, in somebody's lab. But these computations, beyond the observed phenomenon, are taking account of several different states which are "not" representative of some local lab's state of affairs. So they represent states of affairs that are not local, but removed from the local. What is the ontological status, the nature of the reality of this non-local place?

And now the mind-thrust begins. Apparently, the states represented by these quantum representations are states of 'possibilia', affairs that are possible in terms of what's happening now, but gain something extra -- call it 'subsistence' -- upon being stored as data. This is akin to the celebrated Schrödinger's cat issue, where the cat has no actual status until one looks at it, or until some arbitrary event collapses the cat's dual-subsistence into some non-arbitrary state of affairs plucked from the set of 'possibilia' --i.e., the cat, as both alive and dead, moves from subsistence into existence. So, just as there is an actual cat that enters a non-actual, dual-subsistence cat state for a bit; likewise, there are quantum phenomena that enter a non-actual state for a bit, and then -- well, it's just more than I really want to think about; but, I can't seem to avoid such thoughts. People are always writing about it, bringing it up in conversations, occasionally outright asking me about it -- even though I really wish they wouldn't.

Anyway, to summarize -- there's the way things are, and the way things might be, and the "might be's" are somehow accessible from the way things are in quantum computing. But a moment's thought makes one realize that there are an infinity of the way things 'might be' from the way things 'are.' At this moment I could utter, by voice, any given number. I might say "One!" at the top of my voice. Or I might whisper "Two-thousand eight -hundred and fifty-two to the 39th power." Short of having to just take the few moments to utter the very sounds it takes to identify the arbitrary number in question, there are an infinity of numbers I can select from. I could even partition my arbitrary utterances into a structure: I could resolve beforehand to utter only odd numbers, or only even numbers, or only numbers divisible by five --- it doesn't matter! I still get an infinity of choices within whatever pet basis criteria for utterance I happen to choose beforehand. This must mean that there are an infinity of parallel states of affairs that either could spring off, or do spring off from this very moment, from this tiny choice of what I may utter. Add all the other utterers available, and the possibilities loom ghastly large. What am I supposed to think of this? How am I supposed to think of this?

Maybe the latter question is at least tractable. Take a slightly different angle: why utter elements from infinite, structured sets of numbers? 'Too dang many chickens in that coop! Instead, in order to narrow things down, I could utter collections of formula from algebra: "1< y < 20", "x < y*3 < z." Hell, that's some pretty talk right there! I like this game! Again, how about this one: "Let z=x and x<7; and, x is either 2, 3 or 4; moreover, stipulate that x is not 4." Now I've thrown in some logic operations as well! Call this 'f' for fancy formula utterance. And for good measure let's call the set of answers for f (if there are any answers) by the capital letter 'Z'.

Behold -- my utterance f hangs in the air, held temporarily by my (and by any hearer's) short term memory, or maybe it would hang a bit longer if written on a chalkboard, or stored in a computer, or chiseled in granite -- whatever; it's stored someplace in some physical medium, where I, or somebody, can later retrieve it.

Certain strange ideas can arise here. Suppose you ask me how much I'm going to spend on coffee this morning. On the one hand, I could say, "Why, only as much as I have in my wallet!" But there is an exact amount in my wallet, I just happen to be ignorant of how much that amount is. On the other hand, and here's where the strangeness begins, I could say, "Why, f!" (And then I'd jump up and write the formula for f on the chalkboard so you're not clueless.) You'll grant me that there are different equivalent ways to write f on the chalkboard.

I could write the original locution:

f: "Let z=x and x<7; and, x is either 2, 3 or 4; moreover, stipulate that x is not 4."

Or, maybe this:

f1: "Let z=x+0 and x<7; and, x is either 2, 3 or 4; moreover, stipulate that x is not 4."

Or, though odd and extraneous, this:

f2: " Let z=x+1-1 and x+1-1<7; and, x+1-1 is either 2, 3 or 4; moreover, stipulate that x+1-1 is not 4."

The first, second, and third versions all have different information in them, a different collection of symbols, but they all yield the same list of answers in Z -- namely, { 2 , 3 }. (So, it's turned out that the variable z could be a legitimate answer for f in more than one way. So that's why we need not just 'z', but 'Z' to track the list of all legitimate answers.) When you ask me the coffee question, formula f is somehow identified as the answer, even if (chatty guy that I am) I answer your question in two or three different, but synonymous ways, likeunto f1 and f2 above.

Alas, now I'm forced to introduce yet another capital letter, 'F', to account for all the ways that I could synonymously utter (e.g., speak, or maybe chalk-down) f as an answer to your coffee question. A moment's thought shows there's an infinite number of elements in the set F. (I could also add zero, or two zeros, or three; or, I could add one, and then subtract it, or two, and then subtract it, or three...)

And now for further weirdness. As earlier, the states represented by Z are states of possibilia, affairs that are possible in terms of what's happening now (I might pay $2; I might pay $3 for coffee), but these 'possibilia' have gained subsistence upon being stored as data, the job that f is doing in our conversation. Restated, there's the way things are, and the way things might be, Z, and the "might be's" { 2, 3 } are somehow accessible from the way things are at the moment of conversation. So too are the states represented by F, and its "might be's", affairs that are possible in terms of what's happening now (I might restate f one way, another way, etc.), but these "might be's" { f, f1, f2, f3, ... fn } have likewise gained their own subsistence at the moment of conversation.

But now there's yet a further explosion on the already ghastly number of multiverse possibilia branching out from the moment of conversation. Granted, by uttering any synonymous phrase f within F, I've constrained my money commitment to only one of two expenditures, $2, or $3; but, that does not mean there is only two possibilia branching out in the multiverse. Why? Well, since there are an infinity of ways of communicating f (an infinite number of elements in F), there are a concomitant infinite number of subsisting possibilia too. An infinite number of me's, and an infinite number of you's out there waiting with baited breath for me to grab onto the horn of which dollar commitment I'll take as regards to coffee expenditures. Yet this infinity arises not because there are an infinite number of dollar options, but because there's an infinite number of ways of stating even a limited number of dollar options. Afterall, even if I'd just said "I'll spend two dollars," where Z has now only a single element { 2 }, F would still have it's infinite number of elements.

There's nothing in the laws of physical possibility, much less logical possibility, which constrain me to state f in one way rather than another. But this means there is this infinity of duplicate universes, this grand waste of me's and you's where there would be only a single, syntactic shuffle, a trade-off of a couple of extraneous +1's/-1's for a couple of extraneous +2's/-2's within F that separates whole branches or collections of branches within the multiverse. What's the lesson of that?

I will tell you. The multiverse is wasteful. Occam's razor counsels us not to multiply entities beyond necessity; but Quantum's razor provides us with the ugliest possible corollary to that claim: beyond entities there's the necessity of multiplication.

O.

REFERENCES

[Image] Nature.com (Accessed 1/2/2009)

[1] A quick over-view of Karl Popper's falsification procedure can be found by Ralph E. Kenyon, Jr., "Popper's Philosophy of Science" (Accessed 1/2/2009)

[ * ] I thought my first post of 2009 should be something both philosophically and scientifically oriented, since that's what the blog is supposed to be about. Yes, I'll admit I wander from that ideal now and then. And I can't believe I'm still piling time into this (so-called) little side venture of going on four years. The problem is that Google tells me that people from all over the world drop in on this blog, and about a third of them are returning visitors, so it always feels worth it to write something that people are going to read (or listen to).

Token identity and second-order logic (mash-up comics)

Click the above image for full size.

The purpose and character of the use of comix herein is for nonprofit, educational purposes, as subject to limitations found in sections 107 through 118 of the Copyright Act (title 17, U. S. Code). Character likenesses adapted from http://cobb.typepad.com

O.

Counterfactuals, Possible Worlds, and my Mom

{ Audio this essay @ 11min. @ 2.6MB }

A counterfactual is

a conditional statement whose antecedent is known (or, at least, believed) to be contrary to fact. Thus, for example, "If George W. Bush had been born in Idaho, then he would never have become President." Unlike material implications, counterfactuals are not made true by the falsity of their antecedents. Although they are not truth-functional statements, counterfactuals may be significant for the analysis of scientific hypotheses.[1]

The Philosopher J. L. Mackie, for instance, held that counterfactuals are condensed arguments; therefore, they cannot have truth values.[2] Arguments, it will be recalled, are sound (or not) or valid (or not). Only propositions, which can make up arguments, are assessed as true or false.

However, I have to confess. I believe counterfactuals are truth-functional, since I often accuse others (and get accused by others) for being wrong about my claims of hypothetical states of affairs. Sometimes it's about affairs of the past – e.g., if you had asked her on a date, she would have gone out with you – and sometimes it's about affairs of the future – e.g., if you ask her on a date, she will go out with you. The regular and effortless usage (along with communicative and predictive success) of these kinds of claims in ordinary discourse is what I think justifies my belief that counterfactuals are truth-functional. In this essay, I'll attempt to analyze counterfactuals by first placing them within the context of possible worlds, and then developing a single counterfactual to see what sense I can make of it. In the end, though I'll argue that counterfactuals can rightly be assessed as true or false, I won't be wholly convincing – admittedly, even to myself.

I

David Lewis is considered to have given the first robust account of counterfactuals by analyzing them in terms of the semantics of possible worlds. The truth is, I don't fully understand what this means. But I like what I've seen. Possible worlds are descriptions of the way things might be, and not every description of the various ways things might be (or might have been) can be stated in conjunction. Sometimes, it's "either/or" but not "both/and." (Sometimes this is called the hard "or" -- i.e., the "xor")

For example, it's not possible that I'm both (a) the biological son of Bill and Kay, *and* (b) the biological son of two other people (on the presumption that all sons have but two biological parents). These, (a) and (b), are two possible worlds cases that are not compatible with one another. One among those possible worlds is the so-dubbed actual world, the world in which Bill and Kay are my parents. I'll give this statement a short-hand index label.

(0:) Brint is the son of Bill and Kay.

However, some possible worlds are more similar than others. Intuitively, it seems more accurate to say that a possible world in which

(1:) Brint is the son of Bill and Vennie

has more comparative similarity to the the actual world, than a possible world in which

(2:) Brint is son of Cepheus and Myrtle.

(Let Cepheus and Myrtle be two arbitrary people who are non-relatives of my parents) In comparing the two statements, we would say that (1) is "closer to actuality" (to use the Lewis vocabulary.) To use a short-hand, we could say that (1) is closer to (0) than is (2).

In sum, given the full set of possible worlds, there will be one world in that set which is the actual world – i.e., is the world I am in when uttering the various statements. In a trivial sense, that possible world resembles the actual world more than any other; or, to say the same thing -- the actual world resembles itself more than any other of the worlds in the set of possible worlds. Or again, (0) is closest to (0). Also, there will be various worlds closer or farther away in terms of the attributes they share with the actual world. Indeed, there can be "ties" among this ordering of worlds. Recall (1), Brint is the son of Bill and Vennie, and now consider:

(3:) Brint is the son of Mike and Kay.

These two, (1) and (3), are equally close to the actual state of affairs. (Again, neither are actual states of affairs; Only Bill and Kay are rightly assessed as my parents.)

II

Now after that bit of review about possible worlds, maybe I'm finally in a position to examine a counterfactual. In the early '60s, my mother and father (again, Bill and Kay) met, married; and eventually bore myself and my younger brothers in the natural manner. So to construct a counterfactual, I'll posit this:

(4:) If Bill and Kay had never met, then Brint would not have been the son of Bill and Kay.

The thought behind (4) is that their meeting one another caused me to come into being, caused me to be the biological son of Bill and Kay. Again, they met and initiated a set of causes which eventually make (0) true. (I have to wonder if a chain of causes is a truth maker for a proposition. Is that right? I'm unclear on how truth is assessed for a proposition that represents a chain of causes over a temporal window. I'm guessing that I'm not the only clueless one about such matters.) So (4) presumes no meeting, counter to the historical facts of what happened in the early '60s; and (4) presumes no Brint, counter to the actual facts. (I'm here; I'm their son).

Notice that there is an event, a meeting, tied to (or not tied to) a relational fact, being a son. This tie worries me a bit. A simpler statement would be, “If the petroleum had exploded, then there would have been energy released.” That's two presumed events tied together. Or, “If the city hall were made of granite, then some building in town would be made of stone.” That's two presumed facts tied together. (4) is a bastardized version of event and fact; and even here it's of an event that wasn't, and of a fact that isn't.

III

Oddly enough, though (4) appears to be counterfactual, I suspect it probably isn't so. The antecedent could be true, and yet the consequent could be false – that is, it can be true that “Bill and Kay never met”, and still true that “Brint would have been the (biological) son of Bill and Kay.”

There is a possible state of affairs which barely departs from what actually happened in the early 60s. Suppose my father, being a good Hoosier, stayed to complete his degree at Indiana University. And that my mother, being a crazy-fast typist, stayed working at the newspaper office (also in Indiana). Now as is often the case, my father would have been a cash-strapped college student; and, would have taken that quick shot at earning easy money, as have done many college males: selling DNA at a local sperm bank. My mother, married at the time, would have wanted children, but obtained none from unproductive Mike. Thus, would she have simply made the choice to avail herself of a fertility clinic, the very one which good-ol' possible world Dad too regularly profited from – well, the rest falls out easily. The timing of the ovary release; the happenstance of that one special sperm cell – and here I would be, born even of the same womb, sired even by the same father. Thus, (4) does not seem appropriate as a counterfactual after all, since I could still be their biological son though they never met.

Now all counterfactual statements are hypothetical statements, and hypothetical statements are false just when the antecedent is true and the consequent is false. I was able to posit a true antecedent and false consequent without any contradictions appearing. So that's why I am thinking (4) probably isn't a counterfactual. But this introduces a confusion to me: What exactly am I claiming when I say, “That counterfactual is false.”?

First, suppose someone claims (wrongly) this to be a counterfactual:

(5:) If Bill and Kay had met, then Brint would have been the son of Bill and Kay.

Well, as a matter of history, they did meet (true antecedent) and I am their son (true consequent). Thus, at first glance, I could claim (5) is not counter to fact at all. It is a fact. A rebuttal might be that I've confused two things:

(5a:) Brint would have been the son of Bill and Kay
(5b:) Brint is the son of Bill and Kay

(5b) seems more straightforwardly true or false. But (5a) far less so; it seems to demand a context be filled before it's truth status can be assessed. Indeed, (5) itself could be read with a non-temporal “had” in the antecedent:

(5)* If Bill and Kay would have met, then Brint would have been the son of Bill and Kay.

And in this case the same worry appears for the antecedent of (5)* as it did for the consequent of (5a): a context seems demanded before a truth value can be assessed. Perhaps the undetermined truth status of “would”'s is why it has been claimed that counterfactuals are not truth-functional statements.

Second, somebody could argue more generally that I've misunderstood counterfactuals. (It's possible I've misunderstood them; I'll certainly grant that.) That a counterfactual is affirmed, doesn't exclude it from being possibly true. All I've done is given a consistent state of affairs that shows the antecedent is consistent with the state of affairs identified by the consequent. But the role of a counterfactual, so the argument runs, is to refer to a false state of affairs, not to show inconsistency between states of affairs. Perhaps there's merit to this charge against me; but, I would like to know what the object of such a reference would be – i.e., where are these so-called “false states of affairs”? Are they but abstractions within our own minds? Are they in some platonic realm of forms? Are they (false) ideas in the mind of God? I think there are problems all around here.

At this, then, I must conclude my analysis, for if I were to continue to think of counterfactuals, then it is possible that I would drive myself (and my readers) insane.


REFERENCES

[image] Jennifer Dixon "Best of All Possible Worlds" ICM 2006 Benoit Mandelbrot Fractal Art Contest

[1]Philosophical Dictionary

[2] "Counterfactual Theories of Causation" Standford Encyclopedia of Philosophy