Over the
last week or so several news stories have appeared (e.g. here and
here)
suggesting that it is technologically possible to “hack” the brain and extract
from it PIN numbers, credit card data, and the like. This naturally raises the question whether
such a possibility vindicates materialism.
The short answer is that it does not.
I’ve commented on claims of this sort before (here and here)
but it is worth revisiting the issue in light of what I’ve said in recent posts
about how the Aristotelian-Thomistic (A-T) philosopher understands the
relationship between thought and brain activity.
Tuesday, September 4, 2012
Friday, August 31, 2012
Animals are conscious! In other news, sky is blue, water wet
A reader
calls my attention to a
Discovery News story which breathlessly declares:
A prominent
group of scientists signs a document stating that animals are just as
“conscious and aware” as humans are.
This is a big deal.
Actually, it is not a big deal,
nor in any way news, and the really interesting thing about this story is how
completely uninteresting it is. Animals
are conscious? Anyone who has ever owned
a pet, or been to the zoo, or indeed just knows what an animal is, knows that.
OK, almost anyone. Descartes notoriously denied it, for reasons
tied to his brand of dualism. And
perhaps that is one reason someone might think animal consciousness
remarkable. It might be supposed that if
you regard the human mind as something immaterial, you have to regard animals
as devoid of consciousness, so that evidence of animal consciousness is
evidence against the immateriality of the mind and thus a “big deal.” This is not what the article says, mind you,
but it is one way to make sense of why it presents the evidence of animal consciousness
as if it were noteworthy.
Tuesday, August 28, 2012
Think, McFly, think!
As
Aristotelians and Thomists use the term, intellect
is that faculty by which we grasp abstract concepts (like the concepts man and mortal), put them together into judgments (like the judgment that all men are mortal), and reason logically
from one judgment to another (as when we reason from all men are mortal and Socrates
is a man to the conclusion that Socrates
is mortal). It is to be distinguished
from imagination, the faculty by
which we form mental images (such as a visual mental image of what your mother
looks like, an auditory mental image of what your favorite song sounds like, a
gustatory mental image of what pizza tastes like, and so forth); and from sensation, the faculty by which we
perceive the goings on in the external material world and the internal world of
the body (such as a visual experience of the computer in front of you, the
auditory experience of the cars passing by on the street outside your window,
the awareness you have of the position of your legs, etc.).
Wednesday, August 22, 2012
The metaphysics of bionic implants
Take a look
at the classic title sequence
of The Six Million Dollar Man. Oscar Goldman (the bionic man’s superior in
the Office of Scientific Intelligence) says the following in the famous
voiceover:
Gentlemen, we can rebuild him. We have the technology. We have the capability to make the world's
first bionic man. Steve Austin will be
that man. Better than he was before. Better, stronger, faster.
Now that raises
an interesting philosophical question. Aquinas
holds that:
[T]here exists in everything the
natural desire of preserving its own nature; which would not be preserved were
it to be changed into another nature. Consequently,
no creature of a lower order can ever covet the grade of a higher nature; just
as an ass does not desire to be a horse: for were it to be so upraised, it
would cease to be itself. (Summa Theologiae I.63.3)
Now, Steve
Austin loses an arm, an eye, and his legs.
They are replaced with artificial parts which allow him to surpass his
previous levels of strength, speed, and visual distance perception. Still, they are artificial. His normal human organs are not restored;
instead, he becomes a cyborg. We might even suppose that he likes being one
-- certainly to every teenage boy, and to some of us middle-aged types, the
idea sure seems pretty cool. So, is the bionic man a counterexample to
Aquinas’s claim? For isn’t a cyborg --
being “stronger, faster” than an ordinary human being -- also “better” than an
ordinary human being? And doesn’t the fact
that someone might plausibly desire to be a cyborg show that a thing could
desire to be another kind of thing?
Friday, August 17, 2012
Rediscovering Human Beings
My article
“Rediscovering Human Beings” will appear in two parts over at The
BioLogos Forum. Today you can
read Part
I. Part II will be posted
tomorrow.
UPDATE: Part II has now been posted.
UPDATE: Part II has now been posted.
Philosophy on radio (UPDATED)
I’ll be appearing
once again on Catholic Answers Live this coming
Monday, August 20th, at 4:00 pm (Pacific time). Links to some previous radio interviews can
be found here.
UPDATE: The podcast of the show is now available here.
UPDATE: The podcast of the show is now available here.
Tuesday, August 14, 2012
The road from libertarianism
I have pretty
much always been conservative. For about
a decade -- from the early 90s to the early 00s -- I was also a
libertarian. That is to say, I was a
“fusionist”: someone who combines a conservative moral and social philosophy
with a libertarian political philosophy.
Occasionally I am asked how I came to abandon libertarianism. Having said something recently about how I
came to reject atheism, I might as well say something about the other
transition.
Tuesday, August 7, 2012
Disching it out
One of the
hazards of hagiography is that it virtually begs for debunking. Pile the honors on too thick and too
uncritically, and eventually someone’s going to come along and try to blast
them off. (That’s why the word “hagiography”
is seldom used these days except ironically.
Good hagiography shouldn’t be too hagiographical.)
Consider the
praise heaped upon Ray Bradbury after his recent death -- I provided
a little of it myself -- or indeed, that heaped upon him during his life. Was there anyone who didn’t like Bradbury’s
work? Turns out there was, as I find on
dipping into the late Thomas M. Disch’s essay collection On
SF.
Monday, August 6, 2012
Briggs on TLS and tone
Statistician
William M. Briggs is beginning a series of posts on my book The
Last Superstition. In the first installment he considers
the polemical tone of the book and tells his readers to get any remarks on that
subject out of their systems now so that he can move on to more substantive
matters in future posts. Briggs writes:
Feser gives us a manly Christianity,
in muscular language. His words oft have
the tone of a teacher who is exasperated by students who have, yet again, not
done their homework. The exasperation is
justifiable…
Feser… does not suffer (arrogant)
fools well—or at all. This perplexes
some readers who undoubtedly expect theists to be soft-spoken, meek, and humble
to the point of willing to concede miles to gain an inch. Feser is more of a theological Patton: he is
advancing, always advancing, and is not interested in holding on to anything
except the enemy’s territory. This
stance has startled some reviewers.
Typical is [one reviewer] who ignores the meat of the book and whines
about “ad hominems.”
Thursday, August 2, 2012
Concretizing the abstract
Eric
Voegelin famously (if obscurely) characterized utopian political projects as
attempts to “immanentize the eschaton.”
A related error -- and one that underlies not only political utopianism
but scientism and its offspring -- might be called the tendency to “concretize
the abstract.” Treating abstractions as
if they were concrete realities is something Alfred North Whitehead, in Science and the Modern World, labeled the
“Fallacy of Misplaced Concreteness,” and what has also been called the “Reification
Fallacy.” It has been an occupational
hazard of philosophy and science since the time of the Pre-Socratics. The Aristotelian strain in Western thought formed
a counterpoint to this “concretizing” tendency within the context of ancient
philosophy, and also more or less inoculated Scholasticism against the tendency. But it came roaring back with a vengeance
with Galileo, Descartes, and their modern successors, and has dominated Western
thought ever since. Wittgenstein tried
to put an end to it, but failed; for bad metaphysics can effectively be
counteracted only by good metaphysics, not by no metaphysics. And Aristotelianism is par excellence a metaphysics which keeps abstractions in their
place.
Monday, July 30, 2012
Back from Sydney
And quite
tired from a very busy week (and very long flight!) I want to thank my new friends at the Catholic Adult Education Centre and all the
other fine people who treated me so well during the trip. Regular blogging will resume this week.
Friday, July 20, 2012
Philosophy of Mind on audio
A couple of
months ago I called attention to the recently released audio
version of my book Aquinas. My book Philosophy
of Mind is now also available in an audio
version of its own.
See you in Sydney
I’ll be in
Australia next week for the CAEC speaking tour I announced recently. Blog activity will be sporadic at best until
I return. You can find information about
the tour here, and
a YouTube promo here. The Catholic
Weekly of Sydney has run an interview with me that you can read here,
and a separate radio interview can be heard here.
Thursday, July 19, 2012
The Aquinas Institute
The Aquinas Institute in Wyoming
will, over time, be publishing the works of Thomas Aquinas in an affordable
hardcover format, both in Latin and whenever possible in bilingual Latin/English
editions. Their initial offerings are
the complete Commentaries on Paul’s Letters, the Summa
theologiae, the Commentary on John, and the Commentary
on Matthew. The pre-order period has been extended to August 8th.
Tuesday, July 17, 2012
The road from atheism
As most of
my readers probably know, I was an atheist for about a decade -- roughly the
1990s, give or take. Occasionally I am
asked how I came to reject atheism. I
briefly addressed this in The
Last Superstition. A longer
answer, which I offer here, requires an account of the atheism I came to reject.
I was
brought up Catholic, but lost whatever I had of the Faith by the time I was
about 13 or 14. Hearing, from a
non-Catholic relative, some of the stock anti-Catholic arguments for the first
time -- “That isn’t in the Bible!”, “This came from paganism!”, “Here’s what
they did to people in the Middle Ages!”, etc. -- I was mesmerized, and
convinced, seemingly for good. Sola scriptura-based arguments are
extremely impressive, until you come to realize that their basic premise -- sola scriptura itself -- has absolutely
nothing to be said for it. Unfortunately
it takes some people, like my younger self, a long time to see that. Such arguments can survive even the complete
loss of religious belief, the anti-Catholic ghost that carries on beyond the
death of the Protestant body, haunting the atheist who finds himself sounding
like Martin Luther when debating his papist friends.
Monday, July 16, 2012
Cosmological argument roundup
A year ago
today I put up a post with the title “So
you think you understand the cosmological argument?” It generated quite a bit of discussion, and
has since gotten more page views than any other post in the history of this
blog. To celebrate its first anniversary
-- and because the argument, rightly understood (as it usually isn’t), is the
most important and compelling of arguments for classical theism -- I thought a
roundup of various posts relevant to the subject might be in order.
Classical theism roundup
Classical
theism is the conception of God that has prevailed historically within Judaism,
Christianity, Islam, and Western philosophical theism generally. Its religious roots are biblical, and its philosophical
roots are to be found in the Neoplatonic and Aristotelian traditions. Among philosophers it is represented by the
likes of Augustine, Anselm, Aquinas, Maimonides, and Avicenna. I have emphasized many times that you cannot properly
understand the arguments for God’s existence put forward by classical theists, or
their conception of the relationship between God and the world and between
religion and morality, without an understanding of how radically classical
theism differs from the “theistic personalism” or “neo-theism” that prevails
among some prominent contemporary philosophers of religion. (Brian Davies classifies Richard Swinburne,
Alvin Plantinga, and Charles Hartshorne as theistic personalists. “Open theism” would be another species of the
genus, and I have argued that Paley-style “design arguments” have at least a
tendency in the theistic personalist direction.)
Wednesday, July 11, 2012
Oderberg updated
David
Oderberg has revamped his website and given it a new location. Update your bookmarks accordingly. Take note also of his new Metaphysica article,
“Hume, the Occult, and the Substance of the School.” Here’s the abstract:
I have not been able to locate any
critique of Hume on substance by a Schoolman, at least in English, dating from
Hume's period or shortly thereafter. I
have, therefore, constructed my own critique as an exercise in ‘post facto
history’. This is what a late
eighteenth-century/early nineteenth-century Scholastic could, would, and should
have said in response to Hume's attack on substance should they have been
minded to do so. That no one did is
somewhat mysterious. My critique is
precisely in the language of the period, using solely the conceptual resources
available to a Schoolman at that time. The
arguments, however, are as sound now as they were then, and in this sense the
paper performs a dual role—contributing to the defence of substance contra
Hume, and filling, albeit two hundred years or so too late, a gap in the
historical record.
Tuesday, July 10, 2012
Barr on quantum mechanics
Over at Big
Questions Online, physicist Stephen Barr addresses
the question of the relationship between quantum physics and theology. Take note of the discussion board attached to
the article, to which Barr has contributed.
(And if you haven’t watched Barr’s lecture on “Physics,
the Nature of Time, and Theology” from the Science and Faith Conference at
Franciscan University of Steubenville last December, you should.)
Thursday, July 5, 2012
Atheistic teleology?
There has
been a lot of talk in the blogosphere and elsewhere about former atheist
blogger Leah Libresco’s
recent conversion to Catholicism. It
seems that among the reasons for her conversion is the conviction that the
possibility of objective moral truth presupposes that there is teleology in the
natural order, ends toward which
things are naturally directed. That
there is such teleology is a thesis traditionally defended by Catholic
philosophers, and this is evidently one of the things that attracted Libresco
to Catholicism. A reader calls my
attention to this
post by atheist philosopher and blogger Daniel Fincke. Fincke takes issue with those among his
fellow atheists willing to concede to Libresco that an atheist has to reject
teleology. Like Libresco, he would
ground morality in teleology, but he denies that teleology requires a
theological foundation.
Monday, July 2, 2012
Friday, June 29, 2012
Reply to Steve Fuller
As I noted
in a recent post, the Spring
2012 issue of Theoretical and Applied
Ethics contains a symposium on Ethics, Atheism, and Religion, with a lead
essay by atheist philosopher Colin McGinn.
I wrote one of the responses to McGinn’s piece, and one of the other
contributors, Steve
Fuller, wrote an essay with the title “Defending Theism as if Science
Mattered: Against Both McGinn and Feser.”
What follows is a reply to Fuller.
(Readers who have not already done so are advised to read McGinn's essay, mine,
and Fuller’s before proceeding. They're all fairly brief.)
Monday, June 25, 2012
Sentient plants? Part II
Gene
Callahan responds to my recent
criticisms of his view that plants are sentient. (Some plants or all? Gene seems to think all of them are, though
the evidence he appeals to would show at most only that some of them are.) Recall that I had noted three reasons
Aristotelians deny that any plants possess conscious awareness. The first is that plants lack the specialized
sense organs we find in animals. The
second is that plants lack the variability of response to stimuli that animals
possess. And the third is that sensation
together with appetite and locomotion form a natural package of capacities, so
that since plants lack locomotion they must lack sentience as well.
Friday, June 22, 2012
Sentient plants?
Economist Gene
Callahan (a friend of this blog) calls my attention to this
article, which claims that plants are capable of “sensory” responses to
their environments, and even that they “talk and listen to one another.” Gene
concludes that “contrary to Aristotle, plants are active and communicate to
each other, with sounds among other methods” so that “neo-Aristotelians ought
to drop the idea that plants lack sensations.”
And while Gene allows that “this certainly does not invalidate all of
Aristotle's metaphysics,” it does in his view show that Aristotelians should be
wary of once again “ma[king] the mistake of tying Aristotelian metaphysics to
Aristotelian natural science.”
But (no disrespect to Gene intended) as usual
with these breathless journalistic “Science has shown that…!” stories, the actual
facts are far less exciting than the sensationalistic packaging would suggest.
Wednesday, June 20, 2012
McGinn on atheism
The Spring
2012 issue of Theoretical and Applied
Ethics contains a symposium on Ethics, Atheism, and Religion. The lead essay is by Colin McGinn and is
followed by responses from me, Steve Fuller, Ted Peters, and Robert Sinclair. All the essays can be read online, so go take
a look.
Sunday, June 17, 2012
Philosophy of nature and philosophy of [fill in the blank]
A reader of my
recent post on the philosophy of nature asks some excellent questions:
I wonder, where does the philosophy
of physics and in general the philosophy of science fall in between the scheme
of metaphysics and philosophy of nature?...
Also, where does the discussion on
the topic of the laws of nature belong? Is
that also philosophy of nature?
Let’s start
with the question of how the philosophy of science is related to the philosophy
of nature. Recall from my recent post
that as the middle ground field of the philosophy of nature gradually
disappeared off the radar screen of modern philosophy, the disciplines on
either side of it -- on the one hand, metaphysics and on the other, empirical
science (in the modern rather than Aristotelian sense of “science”) -- came to
seem the only possible avenues of investigation of reality. Recall also that the methodology of metaphysics
came to seem a matter of “conceptual analysis,” while any study with empirical
content came to be identified as part of natural science. The very notion that there could be a middle
ground field of study with empirical foundations but arriving at necessary
truths, thus transcending the contingent world described by physics, chemistry,
etc. and pointing the way to metaphysics -- as Aristotelian philosophy of
nature claims to do -- was largely forgotten.
Sunday, June 10, 2012
Ray Bradbury (1920 - 2012)
When Ray
Bradbury was twelve years old, he went to a carnival and encountered Mr.
Electrico, a performer who sat in an electric chair with current running
through him so that his hair stood up and an electrical sword he held would
glow. Touching the sword to the young
Bradbury’s head, Mr. Electrico exclaimed: “Live forever!” Alas, Mr. Electrico’s command has gone
unheeded, for Bradbury died last Tuesday at 91 -- long-lived, to be sure, but
well short of forever.
Thursday, June 7, 2012
Oerter on motion and the First Mover
George Mason
University physicist Robert Oerter has completed his
series of critical posts on my book The
Last Superstition. I responded
to some of his remarks in some earlier posts of my own (here
and here,
with some further relevant comments here
and here). In this post I want to reply to what he says
in his most recent remarks about the Aristotelian argument from motion to an
Unmoved Mover of the world.
Friday, June 1, 2012
Color holds and quantum theory
When
figuring out how many human beings of average weight can be carried on an
airplane, engineers deal with abstractions.
For one thing, they ignore every aspect of actual, concrete human beings
except their weight; for another, they ignore even their actual weight, since
it could in principle turn out that there is no specific human being who has
exactly whatever the average weight turns out to be. This is perfectly fine for the specific
purposes at hand, though of course it would be ludicrous for those responsible
for planning the flight entertainment or meals to rely solely on the
considerations the engineers are concerned with. It would be even more ludicrous for them to
insist that unless evidence of meal and movie preferences can be gleaned from
the engineers’ data, there just is no fact of the matter about what meals and
movies actual human beings would prefer.
Tuesday, May 29, 2012
Natural theology, natural science, and the philosophy of nature
Physicist
Robert Oerter has added some further installments to his
series of posts on my book The
Last Superstition, including a reply to some of my criticisms of his
criticisms of the book. I will respond
to his latest remarks in a forthcoming post, but before doing so it seemed to
me that it would be useful to make some general remarks about certain
misunderstandings that have not only cropped up in my exchange with Oerter and
in the combox discussions it has generated, but which frequently arise in
disputes about natural theology (and, for that matter, in disputes about
natural law ethics and about the immateriality and immortality of the
soul). In particular, they tend to arise
in disputes about what we might call classical
natural theology -- natural theology grounded in philosophical premises
deriving from the Aristotelian, Neo-Platonic, and/or Scholastic
traditions.
Thursday, May 24, 2012
Cinematic representation
What makes
it the case that a picture of Grandma represents Grandma? That it looks
like her, you might say. But that
can’t be the right answer, or at least not the whole answer. The picture might look like any of several people; still, it represents only Grandma. Or
it might not look much like her at
all -- consider a bad drawing, or even a photograph taken at an odd angle or in
unusual lighting or while the subject is wearing a very unusual expression -- yet
still represent her. Indeed, that resemblance of any sort is neither sufficient nor
necessary for representation is about as settled a philosophical thesis as
there is. (The reasons are many. An object might resemble all sorts of things
without representing them. Resemblance
is a symmetrical relationship, but representation is not: If a certain picture
resembles Grandma, Grandma also resembles the picture; but while the picture
might represent Grandma, Grandma does not represent the picture. There are many things we can represent in
thought or language -- the absence of something, a certain point in time,
conditional statements, disjunctions, conjunctions, etc. -- without these
representations resembling their objects, either pictorially or in any other
way. And so forth. Chapter 1 of Tim Crane’s The
Mechanical Mind provides a useful discussion of the issue.)
Monday, May 21, 2012
John Paul the Great Academy
John Paul the Great Academy in Lafayette,
Louisiana is a fine Catholic college preparatory institution promoting the
classical curriculum, the Thomistic intellectual tradition, and fidelity to the
teaching of the Church. Unfortunately,
the Academy is suddenly facing the prospect of closure and is urgently in need
of the prayers and financial assistance of those sympathetic to its mission. Take a look at the school’s website to find
out more about the Academy, and please consider making a
contribution.
Sunday, May 20, 2012
Oerter contra the principle of causality
The
Scholastic principle of causality states
that any potential, if actualized, must be actualized by something already
actual. (It is also sometimes formulated
as the thesis that whatever is moved is
moved by another or whatever is
changed is changed by another. But
the more technical way of stating it is less potentially misleading for readers
unacquainted with Scholastic thinking, who are bound to read things into terms
like “motion” or “change” that Scholastic writers do not intend.)
In an
earlier post I responded to an objection to the principle raised by
physicist Robert Oerter, who has, at his blog, been writing up a
series of critical posts on my book The
Last Superstition. Oerter has
now posted two further installments in his series, which develop and defend his
criticism of the principle of causality.
Let’s take a look.
Thursday, May 17, 2012
Aquinas on audio
Your print
copy of Aquinas
is dog-eared. You’ve worn out your
Kindle reading the
e-book version. If only you could
give your eyes a rest! And avoid the car accidents you’re
risking by flipping though the book on the way to work! Well, you’re in luck: Aquinas is now available in an audio
version.
Wednesday, May 16, 2012
Review of Krauss
Something of
a latecomer to the ecumenical Lawrence Krauss-bashing that has been taking
place across the Internet, my review of A
Universe from Nothing appears in the latest (June/July) issue of First Things. You can read it online here. More on this unusually awful book anon.
Monday, May 14, 2012
Oerter on universals and causality
George Mason
University physicist (and author of The
Theory of Almost Everything) Robert
Oerter is writing up a
series of posts on my book The
Last Superstition over at his blog.
Oerter is critical but he engages the book seriously and in good
faith. He’s presented a couple of
objections so far, and they merit a response.
So, here’s a response.
Tuesday, May 8, 2012
Kripke contra computationalism
That the
brain is a digital computer and the mind the software run on the computer are
theses that seem to many to be confirmed by our best science, or at least by
our best science fiction. But
we recently looked at some arguments from Karl Popper, John Searle, and
others that expose serious (indeed, I would say fatal) difficulties with the
computer model of the mind. Saul Kripke
presents another such argument. It is
not well known. It was hinted at in a
footnote in his famous book Wittgenstein
on Rules and Private Language (WRPL)
and developed in some unpublished lectures.
But Jeff Buechner’s recent article “Not Even Computing Machines Can
Follow Rules: Kripke’s Critique of Functionalism” offers a very useful
exposition of Kripke’s argument. (You
can find Buechner’s article in Alan Berger’s anthology Saul
Kripke.)
New from Editiones scholasticae
I
called attention some time back to Editiones scholasticae, a new
German publishing venture devoted to publishing works in Scholastic philosophy,
including reprints of works which have long been out of print. Three new reprints are set to appear, which
will be available in the United States this August via Transaction Publishers:
J. Elliot
Ross, Ethics:
From the Standpoint of Scholastic Philosophy
Michael W.
Shallo, Lessons
in Scholastic Philosophy
Maurice de
Wulf, An
Introduction to Scholastic Philosophy: Medieval and Modern
Sunday, May 6, 2012
Contemporary Scholasticism
Ontos
Verlag, the international publisher in philosophy and mathematical logic,
is pleased to present the new book series:
EDITED BY
Edward Feser • Edmund Runggaldier
ADVISORY BOARD
Brian Davies, Fordham University, U.S.A.
Christian Kanzian, University of Innsbruck,
Austria
Gyula Klima, Fordham University, U.S.A.
David S. Oderberg, University of
Reading, U.K.
Eleonore Stump, Saint Louis University,
U.S.A.
Contemporary Scholasticism is a new book
series providing a forum for the growing community of philosophers who are
interested in applying insights drawn from the Aristotelian and Scholastic
traditions to current philosophical debates.
The first volume of this new series, Metaphysics:
Aristotelian, Scholastic, Analytic, has now been published. Edited by Lukáš Novák, Daniel D. Novotný, Prokop
SousedÃk, and David Svoboda, the volume is the fruit of the conference of the same name
held in Prague in 2010, and contains many of the papers there presented.
Wednesday, May 2, 2012
Rosenberg roundup
Having now
completed our ten-part series of posts on Alex Rosenberg’s The
Atheist’s Guide to Reality, it seems a roundup of sorts is in
order. As I have said, Rosenberg’s book
is worthy of attention because he sees more clearly than most other contemporary
atheist writers do the true implications of the scientism on which their
position is founded. And interestingly enough,
the implications he says it has are more or less the very implications I argued scientism has in my own book The
Last Superstition. The
difference between us is this: Rosenberg acknowledges that the implications in
question are utterly bizarre, but maintains that they must be accepted because
the case for the scientism that entails them is ironclad. I maintain that Rosenberg’s case for
scientism is completely worthless, and that the implications of scientism are
not merely bizarre but utterly incoherent and constitute a reductio ad absurdum of the premises that lead to them.
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