Easy
It is true that all men are mortal. It is also true that 2 + 3 = 5. Yet it is not “true” that all men are mortal, nor is it “true” that 2 + 3 = 5.
True means true. We learn from David Stove (and by experience) that by supplying scare-quotes “true” means “not true, but believed by so-and-so to be true”; which is to say, “true” means false, or, at best, unknown. Waving your fingers around truth is like becoming the assassin who puts his arm around his victim and calls him friend—as he knifes him in the back.
Yet scare-quotes are not the only, or even the best, way to sabotage logical expressions.
A slier method is to embed a truth conditionally. This example comes from Michael Voris (drop the S.T.B. Mikey, and learn to crack a smile!): “Jesus has risen from the dead, we Catholics believe.” (Voris recognized the mistake.)
This way of phrasing gives comfort to those who don’t want to acknowledge the truth—it is only the curious “belief” of some religious sect—while also releasing the teller from his duty of proclaiming a truth. So much less confrontational, you see.
Saying a truth conditionally is to kill with slow poison, not violence. “P is true, so-and-so believes”, “I believe P”, and “My professor said that P” no more imply P is true than does saying “P is ‘true’.” In other words, it is not an argument for P to say “I believe P”. It is the mere announcement of your mental state at some particular time. Since it is not an argument, there is nothing to refute, for there is no definitive way for me to know your mental state (no, not even with an electric phrenology device, i.e. an fMRI). And then all history suggests there is no point in arguing over somebody beliefs.
Update The main and obvious disadvantage of speaking this way is that it sets you back on your heels, puts you on the defensive immediately, when truth is always an offensive weapon.
Not easy
So much for the easy stuff. Let’s now talk about scientists and academic philosophers and their love of talking about conditional truths (i.e. theories) as if conditional truths were truths Stove (from his Rationality of Induction, p. 117), where he gives us three arguments:
(a) “Hume is a father, therefore Hume is a male parent”,
(b) “All male fathers are parents & Hume is a father, therefore Hume is a male parent”,
(c) “If Hume is a male parent then Hume is a father & Hume is a father, therefore Hume is a male parent”.
The first, (a), is a valid argument, which is to say that its conclusions follows from the accepted premise. Since the conclusion of (a) follows from its premise, we can augment that premise, which is why (b) and (c) are also valid (rule of logic: “if p entails q, then p-and-r entails q, for any r“).
But (b) is an example of the formal fallacy ‘undistributed middle term,’ and (c) is an example of the formal fallacy ‘affirming the consequent’ (look them up). Even so, (b) and (c) are still valid. This means that something is wrong with the formality, i.e. the theory, which declares them invalid. Yet philosophers, like scientists, are loathe to abandon a beautiful theory. This creates a severe difficulty, and even psychic pain, for those who cherish the formality (theory):
[T]he formal logician cannot call (a), (b), or (c) valid, consistently with his professional creed: hence his disapproval of them. But he dares not call them invalid either: hence his unease.
A situation so painful as this one is bound to produce distress signals, even if only half-conscious ones. Some of the commonest of these signals sound as follows. ‘Argument (c) is invalid in propositional logic‘; (b) is not valid in predicate calculus‘; ‘(a) is neither quantificationally valid nor truth-functionally valid.’ You can easily see how suitable such phraseology is to the distressed logician’s situation. A phrase like ‘invalid in propositional logic’, for example, by including the word ‘invalid’, has the effect of setting the desired tone, the tone of disapproval; while at the same time it is admirably non-committal, because after all—as the formal logician himself will hasten to assure you—‘invalid in propositional logic’ no more entails ‘invalid’, than (say) ‘suspected murderer’ entails ‘murderer.’ [p. 122]
The gist: “Arguments are not ‘in’ predicate logic, or ‘in’ any other artefact that logicians may happen to make. Still less is their invalidity or validity ‘in’ anything at all, except the arguments themselves.”
In other words, all arguments have to be evaluated individually.
I don’t quite follow your argument since male parent is just a synonym (or possibly definition) of father. It is not like the usual argument involving Socrates and mortality.
Also, as a side note: Did you ever notice that a Google search works as a better spell check than most programs designed as such?
William,
It’s not stated in the form of a syllogism, that’s all.
And I’m guessing you mean “artefact”, which is the British spelling (Stove was Australian).
Now “artefact” has just thrown me for a loop. What are you referring to? Also, I use american spelling most of the time, even though I am Canadian (i.e. Nova Scotian).
Nice illo. In Russian, pravda means truth. The other newspaper, izvestia means news. The old joke ran, “There is no izvestia in pravda and no pravda in izvestia.”
“Jesus has risen from the dead” is the report of a number of observations made by a small number of people, a long time ago. The problem with that report is that it is impossible to verify it now. The persons reporting it are all long dead and cannot be questioned. Jesus himself is unavailable for questioning too. Hence, there is no way to check the report.
People are well-known to be unreliable witnesses, and even to lie. Therefore, to assume this particular report is reliable is not wise. Proper scientists for example never assume people are reporting observations faithfully. Hence the requirements for a description of the experiment so it is possible to do the experiment again.
With one-off events (like people rising from the grave, or stones falling from the sky), one tries to examine the physical evidence after the event occurred. Questioning all witnesses, and examining the person, or objects, in question.
Without evidence, one can choose to believe the witnesses have indeed seen what they have reported, choose to believe they are mistaken, lying, etc, or withhold judgement until more evidence becomes available.
Clearly, Catholics, and other Christians too, believe that the report was reliable, and think Jesus rising from the dead is a fact. They do not believe that Jesus has risen from the dead, as it is technically impossible to believe in facts.
Really don’t like example (b) here – isn’t “male parent” literally the basic dictionary definition of father?
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“All male parents = fathers” = correct.
“Hume is a father” = correct.
“All fathers are male parents” = unstated premise… but correct.
.
“Therefore Hume is a male parent” = follows from premises, unless you cheat by including other meanings of father (eg as a religious title). The use of other meanings of “father” isn’t backed up in (a) etc, so whilst example (b) may strictly speaking be a logical fallacy (ie there is an unstated premise etc), in this particular case the unstated premise works fine. So yeah… bad example.
.
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Wikipedia has, I think, a better example:
.
“All students carry a backpack” = correct.
“My grandfather carries a backpack” = correct.
“Everyone who carries a backpack is a student” = unstated, may not be correct.
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“Therefore my grandfather is a student” = does not follow, due to unstated premise above.
The problem with that report is that it is impossible to verify it now. The persons reporting it are all long dead and cannot be questioned.
So is the report that J. Caesar hesitated a long time on the bank of the Rubicon, then quoted a Greek line from a play that “the die is cast” before crossing. So is the report that a Carthaginian general named Hannibal existed and made war on Rome, with elephants, no less. So is the report that Grant told Lee at Appomattox that surrendering Confederates could keep their horses and mules for the spring plowing.
People are well-known to be unreliable witnesses, and even to lie.
Obscurantism is not the best position for a rationalist to adhere to. Are you saying that Darwin was an unreliable observer of wildlife or that he lied? Did Eddington lie about the transit of Mercury? How is it rational to conclude that because some people have been mistaken that “people” are unreliable simplicitur? Jan Vansina’s book Oral Tradition as History discusses the circumstances as to when and under what conditions people are reliable witnesses, and gives examples from Amerindian and African legends.
With one-off events…, one tries to examine the physical evidence after the event occurred. Questioning all witnesses, and examining the person, or objects, in question.
So like if someone arose from the dead, you would want to know that they entered the tomb and found it empty and the gravecloths folded up, that they would question the women who had discovered it, that they would collate the testimony of maybe 200 people who had reported seeing the resurectee, and even that they had examined the resurectee by, say, sticking their fingers into the nail holes? Maybe they should have tried it that way, hey?
Obscurantism is not the best position for a rationalist to adhere to. Are you saying that Darwin was an unreliable observer of wildlife or that he lied?
Lying and not speaking the truth are not necessarily the same things.
So like if someone arose from the dead, … question the women who had discovered it, that they would collate the testimony of maybe 200 people. Maybe they should have tried it that way, hey?
You are confusing probably true with True.
1) In resurrection, maybe the “dead” person wasn’t dead. I remember a Latin text discussing how to tell when a crucified person was dead. Could it be that the diagnosis was incorrect?
2) People DO lie and they also make-up reality. Once behind a bar, I stumbled across a shooting victim and a person holding a gun (and a badge). There were only three people present yet many that were IN the bar later claimed they saw the shooting.
The problem with Truth (NB: the absence of scary quotes) is no one really has it. “All men are mortal” is a reliance on past observations along with the assumption that the future will reflect the past. For a blog that delves into the fuzziness of certainty, it’s surprising to see such certainty.
b) and c) contain redundancy. Can’t do much about that but what about getting rid of the word belief from the language?
Obscurantism is not the best position for a rationalist to adhere to. Are you saying that Darwin was an unreliable observer of wildlife or that he lied?
DAV: Lying and not speaking the truth are not necessarily the same things.
YOS: Sander van der Wal’s original comment to which the above reply was made was: “People are well-known to be unreliable witnesses, and even to lie.” Darwin was a people. Therefore, he was well-known to be unreliable and even to lie. But somehow, people who moot the unreliability of people seldom apply it to the people they like. They only make blanket statements with no effort to show that it applies in the actual case.
DAV: You are confusing probably true with True.
So it’s only probably true that Caesar said “the die is cast” in Greek before he crossed the Rubicon, and only probably true that Hannibal invaded Italy.
Actually, you are confusing true with factual.
DAV: People DO lie and they also make-up reality.
See the Jan Vansina book referenced elsewhere for discussion of when such an overly broad generality might actually be true and when it is unlikely to be true. (Hint: being a casual witness to events not directly affecting oneself will likely result in no memory or faulty memory. OTOH, oral cultures have mechanisms for transmitting and rehearsing (lit. re-hearing) a received story, and there are certain kinds of alterations that might happen over time.
My grandfather transmitted to me an oral tradition regarding his own grandfather, whom he had never known. He had gotten the story from his father, who had been ten at the time of the accident. When I later found an account of the incident in microfilm archives of a local newspaper, I found his recollection to have been correct in each remembered detail. So as far as unreliability are concerned, it seems to depend on who has remembered what.
So it’s only probably true that Caesar said “the die is cast†in Greek before he crossed the Rubicon
Yes. How would you know otherwise? Even if he dragged along someone to transcribe his every word, there’s the possibility of transcription error and Roman historians seemed to take liberties when telling their stories. Sounds more like something made-up after the fact and those “remembering” it could be “remembering” it like the bar patrons in the shooting incident.
My grandfather transmitted to me an oral tradition… it seems to depend on who has remembered what.
Or maybe more the what. People do back-fill memories and can be completely unaware of surroundings when preoccupied. In the bar shooting incident, you would think people would KNOW whether or not they witnessed an event. I doubt that most of those making the claim of witnessing the shooting were actually lying. I didn’t see them there but of course maybe they saw it happened then went back to drinking and dancing before I arrived.
While the probability of an event may approach one, it’s still a leap to say it’s one.
you are confusing true with factual
No I’m not. They are synonymous but then maybe you know of something factual that you don’t believe is true.
Ye Olde Statistician,
Unless I am totally missing your point, which is possible, you seem to be arguing for an all or nothing approach to historical events. Are you claiming that either all history is up for grabs or we must accept everything recorded by everyone, even many years after the event in question, as absolutely valid. I don’t really believe that you are saying this so maybe you could clarify your position. Asimov, when writing his autobiography, found that his own excellent memory lead him astray when he checked it against a journal (diary) that he had kept from a young age. Without a diary the stories become more fanciful with time. As to history, complete accuracy is difficult or even impossible. We do the best we can and accept the occasional revisions or even discovery of outright fraud.
@William Sears:
I am sure Ye Olde Statistician will clarify, but if I may butt in, that is definitely not what he said. It is of course possible that people misremember, lie, etc. But whether that is indeed what they did can only be decided on a case by case basis, sifting through the evidence available. If you make a blanket statement like the ones who were produced in the thread, universally quantified statements, then you undermine all history and you cannot believe literally anything, whether it is the Gospel accounts, Thucydides or Gibbon. If on the other hand you want to add some qualification to the quantified statement, then you must justify your qualification, and that, once again, can only be done on a case by case basis.
you are confusing true with factual
DAV: No I’m not. They are synonymous but then maybe you know of something factual that you don’t believe is true.
YOS
They are not synonymous. Fact comes from factum est, “something that has been made.” It was cognate with feat at least down to Jane Austen’s time, and still is explicitly so in French, Magyar, German, etc. (The German word for “fact” is Tatsache, lit. “deed-matter.”)
True is an Anglo-Saxon monosyllable, and therefore regarded with disfavor and avoided whenever possible. It comes from triewe (W.Saxon), treowe (Mercian) “faithful, trustworthy,” from P.Gmc. *trewwjaz, “having or characterized by good faith.” It is thus related to the Latinate word “faith” and is cognate with “trust.” Thus, the Beach Boys taught “be true to your school” and when a man and woman are betrothed (be-truth-ed) they promise to be faithful to each other.
Now, just as all probabilities are conditional to the model used, there is no truth in general, only truth in particular. One must be true to something. Scientific theories must be “true to the facts,” a phrase which immediately highlights that they are not synonymous. Fiction must be “true to life.” A mathematical theorem must be “true to the postulates,” i.e. deducible from them.
For a fact to be true, it must be true to something; but to what is a fact faithful? Tycho Brahe measured the diameters of stars and found Procyon was about as large and as bright as Saturn, and so could not be much farther off than 100x the distance of Saturn without being absurdly gigantic. But at that distance a revolving earth would result in obvious parallax and no such parallax was observed. Therefore, geocentrism was true to the facts. However, the measured diameter was an optical illusion due to atmospheric aberration (the Airy disk), not the actual diameter of the star. So this is an example of a fact that was not true in some sense.
Any scientific theory is an example of something that is true without being a fact.
Hope this helps.
@Ye Olde Statistican
Indeed. The reports about Julius Ceasar, Hannibal and Grant & Lee are like that too. Apart from the kind of claims being made. Waiting a bit before crossing the Rubicon is not very important. Claiming to have seen somebody alive who was dead is very important. Extraordinary claims need extraordinary evidence.
If being mistaken, or lying happens often enough, then it is perfectly rational to test all claims that one considers to be important enough to test. If you buy a house, and the seller tells you the foundation is sound, do you believe him, or pay somebody knowledgable to check?
Darwin’s and Eddington’s observations were repeateble by other people. Everybody can go and look at wildlive behaving as it does. Everybody can go and look at Mercury transiting across the Sun, and take the same (or even beter) as measurements as Eddington. Nobody has to believe them at their word. Everybody can go and check for themselves.
Lots of witnesses both testifying that the person was dead (because they checked the pulse, heartbeat, breathing) and lots of people seeing the deceased walk around after three days would help a lot, yes. The prodding, not so much. Nowadays, with better technology, brain scans amd DNA samples.
And why not. The Bile does mention there are witnesses. So having some kind of evidence was deemed necessary. Unfortunately it is the kind of evidence that doesn’t proof very much. I would not buy a house from somebody even if all his friends say the foundations are sound.
Believing that somebody rose from the dead, because his friends said so? Yeah, right.
@William Sears:
Are you claiming that either all history is up for grabs or we must accept everything recorded by everyone, even many years after the event in question, as absolutely valid.
No. But the claim was made that a narrative is unreliable when:
1) a number of observations were made by a small number of people,
2) a long time ago,
3) impossible to verify now; and
4) the persons reporting it are all long dead and cannot be questioned.
Example: Socrates Scholasticus wrote an account of the death of an Alexandrian mystic and philosopher, Hypatia. His is the only account that is near-contemporary, within 20 years. This was:
1) a one-off event, observed only by the members of the lynch mob itself.
2) a long time ago; viz., 1600+ years ago.
3) impossible to verify now; the original city was obliterated by the Arabs in the revolt against the conquest.
4) Socrates Scholasticus is long dead.
(Furthermore, Socrates was either a Novatian or sympathetic to the Novatians and consequently hostile to Cyril, the bishop who allowed the situation to get out of control. Should whatever he says to the discredit of Cyril be taken with a grain of salt?)
+ + +
So now prove to me that Hannibal existed and made war or Rome.
+ + +
The solution to the dilemma is that historians have worked out methods for assessing ancient texts, and the knee-jerk reaction that “people are unreliable” is known by professionals in history and anthropology to be not true without qualification.
For example: In his “Life of Antony,” Plutarch reports that Antony plundered the Library of Pergamon and gave its books to Cleopatra to restock the Royal Library of Alexandria, which had been accidentally burned by Caesar’s auxiliaries during the First Alexandrian War. But Plutarch includes this in a list of other accusations made against Antony and considering the source concludes that they were fabrications by an enemy of Antony.
A joke for you:
3 logicians walk into a bar. The bartender asks ‘Would you all like a drink?’. The first says ‘I’m not sure’. The second says ‘I’m not sure’. The third says ‘Yes’.
YOS,
you are confusing true with factual
and
Scientific theories must be “true to the facts,â€
Sorry but I was assuming we were using English when (again, it seems) you were not. I take it then that facts aren’t true and if something is factual it isn’t true — just factual — and a scientific theory must be true to non-truth. Am I getting that right?
Any scientific theory is an example of something that is true without being a fact.
Yet you can’t prove that truth or at least any theory in particular. Lacking definite proof, you are expressing belief regardless of how well founded you think it may be.
In any case, I asked if you could name a fact that wasn’t true.
DAV: Sorry but I was assuming we were using English when (again, it seems) you were not.
Those are in fact the English meanings, at least insofar as they developed during the scientific revolution. As Oscar Wilde archly observed: “The English are always degrading truths into facts. When a truth becomes a fact it loses all its intellectual value.”
But not to be too Anglocentric about matters, I noted also that French, Magyar, German make the same distinction. Neither truth nor fact is solely the possession of Anglophones.
DAV: I take it then that facts aren’t true and if something is factual it isn’t true — just factual — and a scientific theory must be true to non-truth. Am I getting that right?
No.
Facts are not truth-bearers. Propositions are. A statement about a set of facts may be true — “to the facts,” at least so far as they are known. What are the facts supposed to be true to?
DAV: Yet you can’t prove that truth or at least any theory in particular. Lacking definite proof, you are expressing belief regardless of how well founded you think it may be.
Perhaps, although I suspect Popperian skepticism of science is overstated. (It was Popper who pioneered the used of scare quotes around “truth”.*) I’d say the theory that the Moon is a sphere is definitely true.
re: Popper: (*)’One such method, Stove claimed, was the “neutralizing of success words”. Stove argued that in the philosophies of these authors [Popper, Kuhn, et al.] such things as progress, discovery, evidence and knowledge do not exist and that if this position were stated openly and consistently maintained then few would ever have taken these philosophies seriously. Stove contended that these authors got around this problem by using these success words, but in scare quotes, e.g., “knowledge”. The fact that these words were used regularly, even if in scare quotes, gave the impression that the view being put forward was somehow not rejecting these concepts.
Another method Stove attributed to Popper, Kuhn, Lakatos and Feyerabend was what he called the “sabotaging of logical expressions”. This was the practice of robbing logical statements of their logical force by placing them in epistemic contexts; for example, instead of saying “P is a proof for Q” one would say “It is generally believed by scientists that P is a proof for Q”. This produces what Stove calls a “ghost logical statement”: it gives the impression that serious statements of logic are being made when they are not – all that is really being made are sociological or historical claims which are immune to criticism on logical grounds.
See: http://www.scribd.com/doc/40665939/Popper-and-After-Four-Modern-Irrationalists-David-Stove
DAV: In any case, I asked if you could name a fact that wasn’t true.
I did: the measured diameters of stars as seen by eye or by early telescopes were not true to the actual physical sizes of the stars. However, facts may be more precisely characterized as accurate/inaccurate rather than as true/false. Unless we make a distinction between physical empirical reality and measurements. But this goes deeper than we are drilling.
In mathematics the class of true statements is larger than the class of provable statements. (Provable in math is kinda like factual in science or history.)
Those are in fact the English meanings,
and
Facts are not truth-bearers.
Perhaps so but they don’t follow the general usage of truth in everyday English. “Is it true that the Sun rose this morning?” would be a non-nonsensical question but most people would likely say “Yes” instead of “huh?”. If you must call it a proposition then by all means do so but it’s a fine distinction that amounts to quibbling the way I see it.
I suspect Popperian skepticism of science is overstated.
I think Popper got it right regardless of his intentions. What we get out of Science are the Most Probable Explanations given what we think we know. Jumping from Highly Probable to Certainly True is often an OK shortcut but it should depend upon the cost of being wrong. That it is only a MPE should not be forgotten.
Most times things like Evolution don’t really matter. The worst that would happen if it were wrong would be wasted time. Even more so is “Julius Caesar said ‘X’ before crossing the Rubicon”. It escapes me why anyone would really care.
Given the high cost of being wrong, it would be silly to act as if “All men are mortal” does not applying to me. At least there’s plenty of evidence to support it so I give it high probability. “God exists” not so much. The same for its opposite.
“non-nonsensical” should of course have been “nonsensical”. *&^! spell checker.
Jesus was the avatar of the Age of Pisces sent by Helios to guide us from the rule of law to the rule of grace. He probably didn’t do a very good job.
@Sander van der Wal, et al:
–“Jesus has risen from the dead†is the report of a number of observations made by a small number of people, a long time ago.–
Oh no, no, no. The Lord manifests, in your hippie-language, as an omnipresent telepath (read&send).
Devils also exist, which complicates matters a lot.
You can go look, and you will find. While a search does not present an absolutely crystal-clear answer, it does eliminate everything except biblical (KJV) Christianity. After that, well, you have to struggle: its the way He seems to want things to be, and so they are.
This specific search, for the true God, has been done by many people. With the same result. As long as you do it TRUTHFULLY, the result is the same. Every time.
And that is why so many Christians despise hippies: you lie. We know it. You know it. Yet you try and justify being pathetic by… lying. Lying very well, mind you, but lying nonetheless.
@YOS
Jesus wasn’t he only person declared to be god. Emperor Augustus was thought to be a god too. And so were a number of other Roman Emperors. And the historical evidence for the existence of those people is much better than the historical evidence for the existence of Jesus.
Nevertheless, nobody alive today believes that Augustus was really a god. Despite the evidence. Why should things be different for the evidence regarding Jesus being god?
The distraction is to talk about “proof” as though it some sort of independent entity out there in the world though it’s a useful abbreviation a lot of the time. Really there’s is only that which persuades which varies from person to person.
Sometimes, too, talk of “proof” is like talking about “the science”. It’s a rhetorical trick to purge what we are trying to say of all that messy subjectivity that might cast doubt on what we say. But the messy subjectivity never really goes away. At least that what I think.
DAV:
[The distinction between fact and truth] don’t follow the general usage of truth in everyday English.
YOS
Duh? That’s the whole problem: people using technical terms in non-technical ways. It is precisely this sloppy thinking, this conflation of concepts, that leads to muddy conclusions. You should see what “everyday English” does to “evolution” or “relativity”, or the hash “general usage” makes of the Big Bang.
DAV:
Most times things like Evolution don’t really matter. The worst that would happen if it were wrong would be wasted time. Even more so is “Julius Caesar said ‘X’ before crossing the Rubiconâ€. It escapes me why anyone would really care.
YOS
I suppose it would.
DAV:
At least there’s plenty of evidence to support it so I give it high probability. “God exists[,]†not so much.
YOS
1. an objective universe exists.
2. there are natural causes of natural things.
3. those natural causes will work “always or for the most part” to the same ends.
4. the universe is rationally
5. the laws of nature are knowable to human reason
6. the laws of nature are knowable by numbering, weighing, and measuring.
7. the study of nature is a fit occupation for grown-ups
Thus, by Carnap’s procedure for scientific induction, the hypothesis (God exists) is held more probable if many of these consequences are later confirmed, if there is a rationally-ordered, objective universe, operating according to immanent natural laws knowable to human reason; etc. etc. We can only hope that these will be later confirmed.
+ + +
Sander:
Jesus wasn’t he only person declared to be god. Emperor Augustus was thought to be a god too. … Why should things be different for the evidence regarding Jesus being god?
X-rays were not the only rays declared to exist. There were also N-rays. Why should things be different for the evidence regarding X-rays?
1. What evidence was presented for Augustus being a god? (Hint: have you actually read Suetonius or Plutarch?)
2. What distinction might you suppose existed between the Greco-Roman practice of apotheosis and the Judaeo-Christian concept of God? Is the divinity of Christ really the same kind of thing as the government approved apotheosis of the “father of his country”? How does this compare to the treatment of George Washington or Abraham Lincoln? Or for that matter, what of references to Bette Midler as “the divine Miss M”?
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” there is no definitive way for me to know your mental state (no, not even with an electric phrenology device, i.e. an fMRI).”
There now seem to be some grownups getting involved in MRI based neuro studies.
http://www.theregister.co.uk/2013/04/12/brain_science_low_power_junk/