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Language, Logic and Understanding


We make many decisions during the course of the day. Sometimes these decisions are guided by emotion, sometimes we just rely on a hunch, sometimes we rely on experience, and sometimes we analyze a situation logically and make a decision according to this logical analysis. But very few things in life are easy to analyze in a completely logical way; in most cases, our actual decisions are based on a combination of emotion, experience, and a little bit of logic.


However, when we want a conclusion that isn’t based on any emotion, or hunch, we want a conclusion that is arrived at purely by means of logical argument. This site is devoted to showing how many results that are commonly accepted as being the result of a completely logical argument are in fact flawed because of the failure to acknowledge the significance of the way language is used in the argument - a seemingly innocuous statement can contain subtle errors which render the statement illogical. Unless every aspect of a statement is very carefully analyzed with regard to the use of language by the statement, an ostensibly logical statement may actually contain subtle errors of logic. Even fairly innocuous looking statements can be difficult to analyze, see Natural Language and Reality.



This site explains how intuitive errors may occur; in most cases it is because insufficient attention has been given to the use of language. If you are visiting this site for the first time, I suggest these pages as suitable starting points:

In principle, a logical argument should never rely on an unstated intuitive assumption. It is well known that intuition can lead to erroneous results, and that there are many examples of this having happened. So it should be the case that every logical argument should be carefully examined to ensure that it contains no intuitive assumptions. But there seems to be a blind spot when it comes to the possibility that the way that language is used in an argument might affect the validity of the argument. This possibility is commonly dismissed without any justification for its dismissal. But everything that is referred to by a logical argument must be referred to by symbols that belong to some language. And since that is the case, the fact that those symbols belong to some language is an inherent part of the argument, and is not something that can simply be ignored.



Much of this website deals with the confusion that occurs when levels of language are not clearly delineated. Kurt Gödel set the ball rolling on this in 1931 with his incompleteness theorem which hides its language confusion under an impressive looking facade of complexity. Amazingly, it has long being accepted as correct even though Gödel never actually proved the crucial step in his proof, and although his proof leads to a blatant contradiction, see Gödel’s contradiction. And over the years since that there seems to be an alarming increase in the willingness of certain academics to forgo the need for clear precise logical Picture: Snake eating itselfproofs of any claim, and now there are numerous people who like to call themselves “logicians”, but who are content to simply make a crucial assumption rather than actually make an attempt to prove it, and proceed to base an entire structure of claims based on that assumption. That assumption is that a completely formal language can actually reference itself - that is, that within a completely formal language there can be a sentence that explicitly refers to that entire sentence itself.


Despite their self-appellation as “logicians”, that isn’t logic, and the inane results of these assumptions aren’t logical - they are worthless. For an example of this sort of nonsense, see Halbach and Zhang: Yablo without Gödel.



Most of this site is, naturally enough, based on logical and factual analysis. To provide some contrast, I decided to include some viewpoint based material here - this is where I get an opportunity to voice my opinion on various matters. Feel free to disagree.



17 Jan 2020    The Mary’s Room fallacy

Some people believe that there is something about consciousness that must be due to some non physical process. Recently I read an article critical of that belief, written by Massimo Pigliucci (How to make up philosophical problems and then “solve” them). In the article he refers to an argument called the Mary’s Room argument. This is an argument that proceeds by a thought experiment and attempts to establish that there is some knowledge that can be discovered only through non physical means.


Reading the article, while I concurred that the Mary’s Room argument is invalid, I did not consider that Pigliucci made a convincing case against it, and he failed to identify the real root of the fallacy of the argument. It also seems to be the case that although many other people have also raised objections to the argument, no-one appears to have been able to identify the fallacy at the heart of the argument, see for example the Wikipedia page Knowledge Argument.


Since the Mary’s Room argument appears to be one of mainstays of the believers in non physical consciousness it is important that it should be properly rebutted, and that rebuttal is given below. The original text of the Mary’s Room argument was set out by Frank Jackson as follows: (Footnote: Frank, Jackson, “Epiphenomenal qualia”, Philosophical Quarterly 32, no. 127 (1982): pp 127-136. doi:10.2307/2960077)


Mary is a brilliant scientist who is, for whatever reason, forced to investigate the world from a black and white room via a black and white television monitor. She specializes in the neurophysiology of vision and acquires, let us suppose, all the physical information there is to obtain about what goes on when we see ripe tomatoes, Black and white roomor the sky, and use terms like “red”, “blue”, and so on. She discovers, for example, just which wavelength combinations from the sky stimulate the retina, and exactly how this produces via the central nervous system the contraction of the vocal cords and expulsion of air from the lungs that results in the uttering of the sentence “The sky is blue”. ...


What will happen when Mary is released from her black and white room or is given a color television monitor? Will she learn anything or not?


It seems just obvious that she will learn something about the world and our visual experience of it. But then it is inescapable that her previous knowledge was incomplete. But she had all the physical information. Ergo there Is more to have than that, and Physicalism is false.


Jackson goes on to claim that the same type of argument could be used for taste, hearing and other bodily sensations and that in each case is that there is knowledge that is “left out of the physicalist story ” and that one can have all of the physical information but not “all the information there is to have”. This type of argument is often referred to as a knowledge argument.


It is rather ironic that logical analysis shows instead that the basis of the argument arises from profound ignorance, as will be demonstrated below.


When Mary is allowed to see colors, she can differentiate them, but she does not know which English word to associate to the sensory impulses that she has when observing a light of a given wavelength. Red Traffic Light That is not a lack of any scientific knowledge about color, it is a lack of an ability to communicate certain things within a language. The simple fact is that humans do not have an innate association of English words to colors (and this applies to other languages and other things also). In the same way I cannot correctly associate a Chinese word for a color with the sensory impulses that I have when observing a light of a given wavelength.


If Mary is allowed to go out into the real world, and observe red traffic lights, red fire engines, red strawberries, etc, she can learn which color to associate with the word red. She has to learn which word to associate with certain sensory impulses that are elicited by various colors. Of course, Mary, being a conscientious scientist, will use scientific equipment to produce light of various wavelengths. She knows which wavelengths are associated with which English words for colors and so, for any wavelength, she can associate the correct English word for that color. Strawberry When she is doing that, she is calibrating her visual sensory system to both wavelengths of light and to English words. (Footnote: Note that for many other senses there may not be any easily measurable reference values, unlike for the case of colors for which there is the readily available wavelength of light.)


So, yes she does learn something new, but the fact that she has complete scientific knowledge of color is an irrelevant red herring, since that has nothing to do with calibrating her own individually unique sensory system. There is no reason whatsoever to suppose that this involves anything other than new neural connections which are entirely physical.


To understand this better, one might suppose that a scientist is developing artificial intelligence machines that have complete scientific knowledge about colors, but which have no environmental sensors. He then attaches to each machine a light sensor that outputs different voltages according to different wavelengths of light. Red Traffic Light However, the sensors are not all the same, and different sensors may output different voltages for the same wavelength. Each machine can observe that different wavelengths of light give different output voltages, but without testing in some way, it has no way of knowing which voltage represents which wavelength. This simply means that the machine does not have total knowledge of the sensor. It could have complete scientific knowledge of such sensors in general, but that would not mean it has complete knowledge of the fine structure and the output characteristics of its own individual sensor. Of course, given the appropriate tools and methods, the machine can calibrate its own sensor (without using any non-physical means).


In the same way, Mary can have complete scientific knowledge of human sensory systems in general, but that would not mean she has complete knowledge of the fine structure and output characteristics of every person’s visual sensory systems, including her own. That would be absurd. In the same way, it is absurd to argue that when Mary is calibrating her own visual sensory system to accord with English words for colors, that she is doing something that cannot be the physical process that is establishing a new set of neuronal connections in the brain - there is no evidence whatsoever to support that assertion.


The same applies to other sensory systems and the Mary’s Room argument can be seen to be a confusion predicated on the false premise that scientific knowledge of a subject, which deals in generalities, implies complete knowledge of every aspect of every individual thing that falls under that subject area.

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Diverse opinions and criticisms are welcome, but messages that are frivolous, irrelevant or devoid of logical basis will be blocked. Difficulties in understanding the site content are usually best addressed by contacting me by e-mail. Note: you will be asked to provide an e-mail address - any address will do, it does not require verification. Your e-mail will only be used to notify you of replies to your comments - it will never be used for any other purpose and will not be displayed. If you cannot see any comments below, see Why isn’t the comment box loading?.

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The Lighter Side


Paper on ‘indefinable’ real numbers

There is now a paper that deals with a common misconception regarding real numbers, see On the Reality of the Continuum and Russell’s Moment of Candour. Also see the associated paper that deals with the matter of language and the diagonal proof, see On Considerations of Language in the Diagonal Proof.

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Other recently added pages

Proof of more Real numbers than Natural numbers


The Myths of Platonism


Goodman’s Paradox


The Platonist Rod paradox


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Lebesgue Measure

There is now a new page on a contradiction in Lebesgue measure theory.

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Easy Footnotes

I found that making, adding or deleting footnotes in the traditional manner proved to be a major pain. So I developed a different system for footnotes which makes inserting or changing footnotes a doddle. You can check it out at Easy Footnotes for Web Pages (Accessibility friendly).

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O’Connor’s “computer checked” proof

I have now added a new section to my paper on Russell O’Connor’s claim of a computer verified incompleteness proof. This shows that the flaw in the proof arises from a reliance on definitions that include unacceptable assumptions - assumptions that are not actually checked by the computer code. See also the new page Representability.

Previous Posts

A Failure to Understand

Random selection of numbers

Moderate Platonism

Descartes’ Platonism

The duplicity of Mark Chu-Carroll

A John Searle Inanity

Man versus Machine

Fake News and Fake Mathematics

Ned Block’s Blockhead

Are we alone in the Universe?

Good Math, Bad Math?

Bishops Dancing with Pixies?

Artificial Intelligence

Cranks and Crackpots

The Chinese Room


For convenience, there are now two pages on this site with links to various material relating to Gödel and the Incompleteness Theorem


– a page with general links:

Gödel Links


– and a page relating specifically to the Gödel mind-machine debate:

Gödel, Minds, and Machines

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Please note that this web site, like any other is a collection of various statements. Not all of this web site is intended to be factual. Some of it is personal opinion or interpretation.


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