Uncommon Descent Serving The Intelligent Design Community

Now, draw me one — of square circles and contradictions in terms (being a challenge to those who play rhetorical games with contradictions and confusions in order to reject the design inference)

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The Online Dictionary’s Thesaurus tells us:

contradiction in terms – (logic) a statement that is necessarily false; “the statement `he is brave and he is not brave’ is a contradiction”

As a capital, classic example, say the following words:

“Square Circle”

Now, riddle me this, riddle me that, guess me this riddle and perhaps not:


I confidently assert [HT: Peter Cech], this cannot be done:

One and the same object cannot be circular and square in the same sense and place at the same time, that is “square circle” is a contradiction in terms

You will observe that the square and the circle show how a circle and a square can by degrees be transformed or mapped into each other, but that the one and the same object in the same place and time cannot have the essential properties of squareness and circularity.

In short, we here see how identity and non-contradiction are mutually reinforcing first principles of right reason (with also excluded middle involved).  As Wikipedia, speaking against known general ideological interest affirmed as at c. Feb 2012, in an article on the laws of thought tracing to Dec 2004:

The law of non-contradiction and the law of excluded middle are not separate laws per se, but correlates of the law of identity. That is to say, they are two interdependent and complementary principles that inhere naturally (implicitly) within the law of identity, as its essential nature . . .   whenever we ‘identify’ a thing as belonging to a certain class or instance of a class, we intellectually set that thing apart from all the other things in existence which are ‘not’ of that same class or instance of a class. In other words, the proposition, “A is A and A is not ~A” (law of identity) intellectually partitions a universe of discourse (the domain of all things) into exactly two subsets, A and ~A, and thus gives rise to a dichotomy. As with all dichotomies, A and ~A must then be ‘mutually exclusive’ and ‘jointly exhaustive’ with respect to that universe of discourse. In other words, ‘no one thing can simultaneously be a member of both A and ~A’ (law of non-contradiction), whilst ‘every single thing must be a member of either A or ~A’ (law of excluded middle).

What’s more . . .  thinking entails the manipulation and amalgamation of simpler concepts in order to form more complex ones, and therefore, we must have a means of distinguishing these different concepts. It follows then that the first principle of language (law of identity) is also rightfully called the first principle of thought, and by extension, the first principle [of right] reason (rational thought) . . .

Why am I pounding away on such an obvious point?

Because it keeps cropping up in attempts to evade or dismiss the design inference, whether in the guise of denying non-contradiction [Cf. UD WAC here], or insisting on some imagined ambiguity or attempting to undermine some otherwise clear distinction.

So, let me raise again a fairly simple diagram:

The laws of logic, showing the way in which distinct identity leads straightaway to the first principles of right reason

If at a given moment we distinctly identify and label some thing, A — say, a bright red ball on a table — we mark a mental border-line and also necessarily identify NOT-A as “the rest of the World.” We thus have a definite separation of the World into two parts, and it immediately and undeniably holds that:

(a) the part labelled A will be A (symbolically, [A => A] = 1),
(b) A will not be the same as NOT-A ( [A AND NOT-A] = 0); and
(c) there is no third option to being A or NOT-A ( [A OR NOT-A] = 1).

So, we see how naturally the laws of (a) identity, (b) non-contradiction (or, non-confusion!), and (c) the excluded middle swing into action. This naturalness also extends to the world of statements that assert that something is true or false, as we may see from Aristotle’s classic remark in his Metaphysics 1011b (loading the 1933 English translation):

. . .   if it is impossible at the same time to affirm and deny a thing truly, it is also impossible for contraries to apply to a thing at the same time; either both must apply in a modified sense, or one in a modified sense and the other absolutely.

Nor indeed can there be any intermediate between contrary statements, but of one thing we must either assert or deny one thing, whatever it may be. This will be plain if we first define truth and falsehood. To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true; and therefore also he who says that a thing is or is not will say either what is true or what is false. [Emphases added]

So, we can state the laws in more or less traditional terms:

[a] A thing, A, is what it is (the law of identity);
[b] A thing, A, cannot at once be and not-be (the law of non-contradiction);
[c] A thing, A, is or it is not, but not both or neither (the law of the excluded middle).

In short, the diagram helps take the “mystery” out of the laws, showing us why they make sense. [Cf. responses to objections  here.]  In 1011b, too, Ari gives us a bonus, by aptly defining truth:  to say that what is is, and what is not is not, is true.(As a note for logicians: we are here specifically speaking with reference to the experienced world of credibly real things, so extensions to empty-set contexts in which questions over contrasted empty sets — that is, quite literally: no-thing —  arise, are irrelevant for the moment. That is, we deal here with the classic square of opposition. Then, once we see what follows from dealing with a world of real categories with at least one member each, we may then extend to the case of empty sets and see how much of a difference this possibility makes.)

As a consequence of this, if we say something that directly asserts a contradiction in terms, or that implies a contradiction, that thing we have said is nonsense. We can make mouth noises or string glyphs that reduce to such, but we cannot instantiate what we think we have said on the ground, physically or even in some cases, logically.

The square circle — despite many valiant attempts — is such an entity.

Similarly, there is a classic (probably apocryphal) story of Abraham Lincoln:

A favorite riddle: “How many legs will a sheep have if you call the tail a leg?” Most people answered, “five.” Lincoln then replied that the answer was four, because calling a tail a leg doesn’t make it a leg. His moral was that you can’t solve a problem by simply changing a word or name.

In short, merely saying X does not make X true. “Saying does not make it so.”

I first heard of this in connexion with an aide, but here is a case (probably just as apocryphal) suggested, with a congressman:

The Great Emancipator, Abraham Lincoln, was asked by a congressman why he hadn’t freed the slaves earlier in his term of office.

Lincoln replied that the time had not been right; he wouldn’t have been able to enforce the proclamation.  The congressman was puzzles and didn’t understand what the president meant.

Lincoln explained with a question, “How many legs will a sheep have, if you call the tail a leg?”

“Five,” responded the congressman.

“Not so,” said Lincoln wisely.  “Calling a tail a leg doesn’t make it so.”

But in today’s age of radical relativism and spin tactics, we have a challenge to deal with the nihilism that imagines that might and manipulation make ‘right,’  ‘knowledge,’ and ‘truth.’

Which is outright nonsense.

Just so, and with all due respect, for one instance that has spilled more bits than it is worth here at UD recently, playing games on suggesting that there is a distinction between Intelligent Design and intelligent design, such that the former represents a grand conspiracy that is a hidden agenda theocratic wedge while the latter (it is hard to be sure) seems to suggest that recognising design on empirically observable reliable signs is not possible, does not answer to the question of the existence of and grounds for design inference and its proper grounding, as can be seen again in the per aspect design filter summary:

The per aspect explanatory filter that shows how design may be inferred on empirically tested, reliable sign

I recently (again) summarised the fundamental question that design theory as a scientific project addresses here, in a comment:

1 –> Yes, we can find objects that credibly exhibit traces of the remote past of origins, a far or deep past that we cannot DIRECTLY observe to know by that, the actual deep past as empirical fact.

2 –> However, this is not unique to this case, there are many objects, such as astronomical ones, that we study be observing traces, e,g. light from the sun and remote stars.

4 –> In this general context, Newton put forth his well known rules of reasoning c 1688 — 1704, and it is the context in which, generally, we infer through cause-effect reasoning and characteristic consequences of particular causes. Such can be identified as signs.

5 –> We then provisionally but confidently infer on signs, per like causes like. For simple example, we see that certain elements, when hot enough, give off certain spectral lines, and that when white light passes through layers of such, there are absorption lines in the relevant positions. From these, we examine the spectra of stars and infer composition from Fraunhoffer lines. (Sometimes this has led to interesting results, e,g. discovery of Helium as causing unexpected lines in the sun’s spectrum.)

6 –> This basic pattern is commonly applied to origins of life and of forms, though this is often marred by a want of observational evidence that certain claimed causes are adequate to claimed effects, especially on OOL and OO body plans. Johnson, whom you deride, has aptly pointed out the injection of an ideological materialist a priori, in the guise of mere “reasonable” methodological constraints. Lewontin’s case is most notorious and explicit, but cf here on for much more.

7 –> In the case of functionally specific, complex information and irreducible complexity, these are commonly observed phenomena. In comparing causes dominated by mechanical necessity manifest in lawlike regularities like F = m*a, chance processes yielding statistical variability, and design as known causal factors, it is seen first that necessity does not explain high contingency under similar initial conditions. Indeed, that lack is the sign of a law at work.

8 –> Similarly, high contingency tracing to blind chance, per the results of sampling theory, is at a loss to explain results coming from specific and separately describable UN-representative zones in the field of possibilities. That is, a sample that is necessarily a small grab of a very large space, we can only expect to reflect the BULK of the possibilities. This is how, for instance, we infer to the general pattern of the blood from a small sample.

9 –> We can also show that where we have specific function depending on many well matched, properly arranged and interfaced parts, the zone of functional configs will be a very small fraction of the space of possibilities for the parts. Not only do tornadoes predictably fail to assemble 747′s from junkyard parts, but they will fail to do so for something so deceptively simple as a moving coil meter based indicating instrument in its cockpit.

10 –> This is the context in which on empirical and analytical grounds — once ideological blinkers are removed — it is clear that functionally specific, complex organisation and/or associated information [FSCO/I] are a strong sign of design as best causal explanation.

11 –> To set a conservative threshold for sufficient complexity, note that 500 bits of explicit or implied information implies 3.27*10^150 possibilities. The 10^57 atoms of our solar system, on its conventionally estimated age, if used to search at one search per 10^-14 s [comparable to the fastest chemical reaction rates] would only be able to sample what we can compare as taking a one straw sized sample to a cubical hay bale as thick as our galaxy, about 1,000 light years. (Light from that far away reaching us now, set out sometime about the time of the Norman Conquest of England.)

12 –> So, we have strong reason indeed to accept that if Chi_500 is at least 1, the object with that much specific info in it, was designed:

Chi_500 = I*S – 500, bits beyond the solar system threshold.

So, motive mongering and games with words are not relevant. The pivotal issue is, as always, the matter on the merits. Let us therefore [re-]turn to that. END

Has the site "owners" considered using a different blogging framework from WordPress? ciphertext
Andre: Nice joke. KF kairosfocus
Yes, but they always take sides! Mung
Let me try one more time, squares and triangles all agree that circles are pointless..... Andre
CT: This particular blog has some oddities with codes. I tend to simply use the old fashioned caret to indicate exponentiation, it is safe. KF kairosfocus
RE: Post #13 It would appear that only certain entity codes are being processed differently. Notice the difference in the Logical Not and the Super Script 2 both typed as entity codes. The Super Script 2 is not rendered properly, and yet the Logical Not was rendered correctly. I shall inquire with the site owner of such discrepancies. Perhaps it is due to a plugin being used by Wordpress. If this is NOT what you (fellow posters) see then there is an issue with my particular instance of the Wordpress blog. Note: The entity codes begin with an ampersand "&" and end in a semi-colon ";". ciphertext
Test Post: I'm testing the application of HTML entity codes. They appear to work in the "preview" but when posted, do not render what the are supposed to render. Which leads me to believe that the site will "encode" the text prior to posting, possibly to prevent errors with javascript or other processors being used. Would someone validate for me that this is also the case with their posts? Here are some HTML entity codes you can use. When typing them out, view their "preview" and then post to see the final state. Super Script 2 = ² Super Script 2 (not as entity code) = &sup2 Logical Not = ¬ Logical Not (not as entity code) = &not ciphertext
RE: Andre post #9 Circles are pointless! Or, you could say that circles have an infinite number of points a fixed distance (radius) from its center. If you have a point, you can draw a circle using the Equation of a Circle (x-h)² + (y-k)² = r² h and k are the x and y coordinates for its center and r is the radius of the circle. ciphertext
Circles are pointless!
Points are pointless!
Circles are pointless!
You mean it is not true that a circle has a radius? Mung
Mung: Scan it and send it! (Use some photo site and link.) Otherwise, it's an evasive bluff of a very familiar type commonly encountered with certain objectors to the design inference. (As in, ever played the old shell game where there is no pea under ANY shell, but you don't know that?) JDH: Physicists of the world, unite! I observe:
KN: >> (1) a contradictory object cannot be conceived (though we may be deceived into thinking that it can be conceived, if we have not noticed that its properties are contradictory). >>
This is of course the case of the village barber. And, it does seem to be the case with materialism, as it destroys the possibility of a self-moved, rational first cause. Andre: Indeed, no corners or edges allowed. Which is the very defining essence of a square, being a quadrilateral with equal sides, thence a rhombus, and also a rectangle. That is exactly why a square circle is impossible, it is asking for edges and corners on the one hand and for none of sane on the other. However, in transforming the first to the second, the way to do it is to keep on forming more edges until one has infinitely many, leading to a curve. and of course one has to kick in corners and flatten out curves to go the other way. KF kairosfocus
Circles are pointless! Andre
Has anyone else noticed that KN's proposition #1 perfectly describes the position of 'advocacy for materialism'. Many are deceived into thinking that it is possible to be a true advocate for a materialistic viewpoint. The only problem is that these fools have not yet seen that any advocacy for materialism is inherently contradictory. Mostly because if materialism is true, free will is excluded. JDH
I have drawn a square circle, but since I am here and you are not here, you'll just have to imagine it. Mung
KN & CT: The diagram above gives a clue. We find ourselves moving from one pole to the next and back, but find ourselves unable to fuse the two into one entity that can be stably conceived or expressed in any description feasible in a possible world. This bears more than a passing resemblance to the race hazard oscillations that in principle obtain with an RS latch set to its forbidden state. In physical terms, noise, accidents of circumstance will drive it to settle, and certain devices are deliberately set up so the race is predictably won. That is, we see ourselves facing an impossible object. The other classical case that is visually striking is Lord Russell's village Barber who ends up sweeping the floor with his beard (strictly forbidden!) as he can neither exclusively shave himself nor be shaved by the Barber. (There is an implicit assumption that Barbers are men!) And yet, up to the moment when the exclusivity bites, it seems so plausible that the men should shave themselves or be shaved by the Barber. If the Village is willing to have a lady as Barber, indeed, no problem arises; though of course, that too is liable to lead to problems. (Do we understand the social impacts of the safety razor?) But even so, it has long since been fatal for naive set theory. It turns out that what makes a definable collection is not so simple after all. And therefore, we find that it is not whether it SEEMS conceivable or not, but whether the thing can be instantiated in a possible world. (And this indeed brings up the issues on cause, effect and the like -- is the thing feasible? Is it contingent? Are there on/off switch conditions, and the like.) Once that oscillatory identity hazard appears, game over. KF PS: Notice, superpositions of squares and circles ARE possible, as can be seen along the diagram or as can be done with some plasticine. We must not confuse superposition with excluded middle. A function that superposes by taking in the two is quite feasible, 25% square, 75% circle -- nearly a circle but with four corners. PPS: I am not at all sure that a logically impossible world is not in the same boat as square circles, in terms of something existing in such. kairosfocus
RE: Kantian Naturalist - #4 Would you define your use of the terms "conceive" and "imagine"? I want to make sure I understand your use. For the purposes of my post I will assume "conceived" and "imagined" are a separation in degree of abstraction. That is to say that to conceive is to render an idea in thought only. Where as, to imagine, is to take what was first conceived in thought only and then conceive a method of actualizing the object into the physical world. I've wondered myself about logical contradictions. If we think of objects as having intrinsic properties that are unique to each type of object, then those identifying properties are what prevent the translation of "types" (maybe you could even substitute "kinds") between objects. So, in my thinking, the identifying properties do two things: they establish the identity of the object type; they prevent the transmutation of objects of one type into objects of another type (i.e. "squaring" the circle). I think this mode of thought, when coupled with my definition of conceive and imagine, is described in your second point. However, I think you may be "on to something" with your your first point. Specifically, you indicate that it would be impossible to conceive (render in thought per my definition) of a contradictory object. You indicate "...though we may be deceived into thinking that it can be conceived, if we have not noticed that its properties are contradictory"[sic]. However, I would even go so far as to include that we could also be confused about the object's actual type, and therefore also be deceived into believing a logical contradiction exists when one does not. The reason I say this, is because to me, the "conception" of a contradictory object would first necessitate a comparison between two objects' identifying properties. In the example of the "square circle", in order for us to conceive of such a contradictory object we must first analyze the identifying properties of both a circle and a square. In this sense, the contradictory object of which we are attempting to conceive wouldn't even exist in thought. The closest we can come is an approximation of a contradictory object based upon the comparison of two objects' identifying properties. Which, I don't believe is the actual conception of such an entity, since there wouldn't be a set of properties that we could develop in our mind to identify this contradictory object. We couldn't say for instance that a square circle is an object whose area can be reliably calculated as both S² and Π × r². That is merely the result of comparing the properties of two objects. Note: That in the above example, I am assuming that the mathematical formulas which are for calculating the area of a circle and the area of a square are sufficient as identifying properties. Perhaps another example would have been to identify a circle as any entity that can be reliably "described" by the following equation (x-h)² + (y-k)² = r² Even when we conceive of a logical contradiction such as a "square circle" we have not actually conceived of a logical contradiction. Rather, we are saying what each property being compared either is or is not. We are simply reinforcing the identities of the respective objects, in this case both the square and the circle. We could use the same formulation using two different objects (e.g. a "married bachelor"). We again are simply referencing the properties of the two "objects" being compared. One being a "married" man, and the other being a "single" man. We don't have the ability to synthesize the properties that identify a "married bachelor" (I posit those properties do not exist), rather we compare the properties of the two objects "married man" and "bachelor". ciphertext
I hope my views won't be a casualty of your work on causality. I've been trying to figure out just how to think about "contradictory objects," e.g. square circles. Here are some options: (1) a contradictory object cannot be conceived (though we may be deceived into thinking that it can be conceived, if we have not noticed that its properties are contradictory). (2) a contradictory object can be conceived but it cannot be imagined. (3) a contradictory object can be conceived but it is not logically possible, i.e. does not exist in any logically possible world. (4) a contradictory object is that which exists in a logically impossible world. These are neither exclusive nor exhaustive. (3) and (4) imply each other, for example. (2) is more restrictive than one might like, if imaginable worlds are a class of possible worlds. Suggestions? Kantian Naturalist
Not interested. kairosfocus
KF, I wonder if this article, with further work and development, could be published somewhere. Like a scholarly journal, I mean. Collin
F/N: Hopefully this issue on how saying does not make it so, will help Gregory et al rethink. I hope to get on to causality soon. KF kairosfocus

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