Are symbols meaningless?

In other words, it is not even possible to write anything about the real, physical world. That impossibility is strictly enforced in mathematics. — alcontali

I still find that impossible to reconcile with engineering which relies heavily on the application of mathematics to the physical world. What am I not understanding?

Okay. Point out to me where you have discussed any impact of die Kehre on analysis of 'meaning'.

I still find that impossible to reconcile with engineering which relies heavily on the application of mathematics to the physical world. What am I not understanding? — Wayfarer

Engineering is a semantical and even a very intentional thing.

For example, you want to build a boat. It must be 55 meters long.

By dragging "55" into the fray, which are symbols that have inherently absolutely nothing to do with boats, you have subjected yourself to number theory. You cannot do whatever you want with "55", if you want to do it consistently.

You are now bound by a bureaucracy of formalisms, i.e. rules and regulations that govern the abstract, Platonic world of numbers. It constrains you and reins you in. With every mathematical object that you drag into the fray, you will become increasingly beholden to the formalisms that govern them.

Before you know, you are the prisoner of a web of constraining formalisms that will tightly wrap up your boat project.

It is not that you wanted to do mathematics. No, you just wanted to build a boat.

By dragging "55" into the fray, which are symbols that have inherently absolutely nothing to do with boats, you have subjected yourself to number theory. You cannot do whatever you want with "55", if you want to do it consistently. — alcontali

But so much of what we use every day - every minute! - depends on maths, and without maths it wouldn’t exist. Take the device you’re reading and replying on; computer science and cybernetics is intensely dependent on maths. Without some maths, you couldn’t be a computer scientist.

One point about Platonism is, in my opinion, that it’s an essential ingredient of the scientific revolution, and one of the principle reasons that the West (as distinct from India or China) devised modern science. So declaring that maths exists in some ethereal platonic domain doesn’t do justice to the facts of history.

I myself am intrigued by Platonic realism, but my interpretation of its significance is rather different to your own. To me, it means that mathematical reasoning is an indispensable ingredient of scientific thinking, although I also don’t believe that there is a scientific explanation for the unreasonable effectiveness of mathematics in the natural sciences. But I agree with mathematical Platonists who believe that maths comprises insight into a real, albeit wholly intelligible domain.

Are symbols meaningless? — creativesoul

If a symbol is a nonterminal, then it can be explained in terms of other nonterminals and terminals, using a production rule, which gives it its definition. Terminals are axiomatic starting points. They are not further explained.

That is how it more or less works for formal languages that abide by a context-free grammar.

In natural language, these terminals are the defining vocabulary. If judiciously chosen, the defining vocabulary can be associated with just images.

For example, you do not need words to explain what an apple is. Just show one or more images, and that will do too.

Apparently, the smallest defining vocabulary is 360 words that gets expanded through a layered system to approx. 3000 words. The origins of this hierarchical system are attributed to Samuel Johnson, who argued that:

Words should be defined using terms less abstruse than that which is to be explained.

But so much of what we use every day - every minute! - depends on maths, and without maths it wouldn’t exist. — Wayfarer

Yes, daily life pretty much unavoidably gets trapped into the web of mathematics, simply, by inadvertently using an abstract, Platonic object of mathematical nature. That's indeed it. The enslavement process will unstoppably start, because the formalisms will kick in, if you want to do it consistently.

So declaring that maths exists in some ethereal platonic domain doesn’t do justice to the facts of history. — Wayfarer

Mathematics has interface points everywhere. It is almost impossible to speak for longer than a minute or so, before the speaker has dragged into the fray a regulated language expression, causing him to become subject to an entire regulatory framework that governs the use of these regulated language expressions.

Still, that does not mean that these regulated language expression are real. They are not. Language expressions do not appear as real, physical objects with physical characteristics. They have no size, weight, temperature, or any other physical characteristic. They are mere abstractions.

It is not just mathematics that exists in some ethereal platonic domain. All language does.

that does not mean that these regulated language expression are real. — alcontali

It all depends on what you mean by ‘real’.

Mathematical platonism has considerable philosophical significance. If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects which aren’t part of the causal and spatiotemporal order studied by the physical sciences. Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate. — SEP

Note the implicit presumption in declaring it ‘would be’ an important discovery. :smile:

It is not just mathematics that exists in some ethereal platonic domain. All language does.

No ! All languages, including the metalanguage of mathematics exist ie. are useful concepts in the only 'domain' that matters to humanity i.e actions and interactions connected with prediction (including pattern seeking) and control. That sentence of mine can be behaviorally construed as an attempt to control/elicit future interactions with me.

No ! All languages, including the metalanguage of mathematics exist ie. are useful concepts in the only 'domain' that matters to humanity i.e actions and interactions connected with prediction and control. — fresco

That still does not mean that language would be a physical phenomenon with size, weight, temperature, electromagnetic radiation. Does language have any particular color or smell?

Seriously, language is an abstraction that lives in its own Platonic world. We cannot avoid using such abstractions, simply, because we communicate.

Still, we should not confuse these abstractions with the real, physical world.

The word "cat" is not a cat. It is a word. It is a language expression. It is not the real, physical thing at all.

but the difference with number is that it's predictive. Through maths, I can discover many things I couldn't otherwise know, including the //technology behind the //device you're reading this on. Nothing you've said here seems to be aware of that, or to acknowledge it.

'Realism' has nothing to do with it. 'Reality' a concept denoted by a word like any other. It's 'meaning' resides in its particular contextual usage where consenus as to 'what is the case' is being negotiated. Naive realists attribute 'properties' especially 'physicality' to 'objects' ignoring the fact that 'physicality' denotes expected types of sensory interaction events with 'the world' on the part of observers. As far as 'mathematical entities' are concerned like 'set membership', Lakoff &Nunez have argued that their 'meaningfulness' resides in the metaphorical relationship to the the experience of bodily actions like 'putting an object into a container'.

but the difference with number is that it's predictive. Through maths, I can discover many things I couldn't otherwise know — Wayfarer

Agreed.

In Kant's lingo, mathematics truly is synthetic, i.e. knowledge.

It is, however, "a priori", i.e. divorced from the real, physical world; unlike science, which is a "posteriori".

Kant insists on the existence of synthetic knowledge a priori (purely abstract), "pure reason", which is separate from synthetic knowledge a posteriori (i.e. real-world).

Unfortunately, Kant did not insist on the fact that pure reason, divorced as it is from the real, physical world, is in and of itself, necessarily meaningless, i.e. free of any possible (real-world) semantics. It is its extreme purity that makes this type of knowledge meaningless and also useless, to be understood as: having no real-world semantics and no direct use or direct application.

You fail to get my point because you fail to understand that talking about language is in essence an infinite regress equivalent to pulling yourself up by your own bootstraps.
The only 'given' we can start from is that we are clever primates with a complex set of socially acquired behavioral gestures ,we call 'human language' which segments what we call 'the world'. The abstract persistence of 'words' (internalised gestures) act as place markers for focal aspects of that shifting flux we call 'things' allowing us to attempt to predict and control aspects of our world relative to our lifespans and our pattern seeking. Place markers are not 'representational' of 'things in themselves', they are contextual memory aids within potential action plans. — fresco

What you have ultimately done here is talk about language - about what language is. So where is your infinite regress?

You provide an "only 'given'" yet provide more than just one 'given', and you used language to represent that 'given' for communicating to others that 'given'.

Are we really clever primates, or is that just a use of scribbles on a screen? Does "clever primates" refer to some state-of-affairs, or is it just scribbles on a screen? Is it a fact that these "clever primates" possess "a complex set of socially acquired behavioral gestures that they call "human language" which segments what they call the world?", or are those just scribbles that don't refer to, or represent, or mean anything?

In using language, what are actually doing? Are you doing something different with language when you listen as opposed to speaking? If we are doing different things with language, then how do we communicate? What is the glue that binds the listener and speaker together? Isn't it meaning?

I see, but I don't think I agree, at least not in the context of this forum. I want to try this again. What does "meaning" mean?

Meaning is a mental relationship, connection between a phenomenon (the referent I guess) and a symbol or symbols such that the symbols represent the referent, e.g. the meaning/definition of a word.
Meaning is a mental relationship, connection between a system of related symbols and a system of related phenomena such that the symbols represent the phenomena, e.g. the meaning of Einstein's theory of Special Relativity. This is a bit clunky. Needs work.
Meaning is used metaphorically to refer to a mental connection between two phenomena which is similar to the connection between a symbol and a referent, e.g. the meaning of life. Clunky too.


As Charles Montgomery Burns once said - I don't know art philosophy, but I know what I hate. And I don't hate that. — T Clark

It's really simple. Meaning is the relationship between some cause(s) and some effect(s).

What some word means is the idea in some speaker or writer's head and their intent to communicate that idea(the cause of the words appearing on the screen). When reading other's words, you are trying to get at their meaning, not yours. If you only try to get at your meaning of the words, then how do you expect to understand what the writer intended? You are trying to get at the cause of the words on the screen and part of that is knowing that scribbles on a screen (the effect) is caused by humans submitting their ideas via language (the cause).

Seeing scribbles on a screen means that some human submitted their ideas via a post on an internet forum. What do the scribbles mean? They mean the ideas (that are not just other words BTW) in some human's head. Which causal relationship do you want to talk about - the one between you and the screen with scribbles, or the one between the scribbles and the author of those scribbles? The fact that we can talk about both and still be talking about language use shows that there are multiple causes that precede you reading scribbles on screen (using language).

When you don't understand what someone wrote - is it that there is no meaning to the words, or is it that there is meaning but you haven't been able to discover it yet (the causal relationship between the scribbles and someone's ideas)?

When we ask what something means we are asking about causal relationships - about some cause or purpose.

I want to try this again. What does "meaning" mean?

Meaning is a mental relationship, connection between a phenomenon (the referent I guess) and a symbol or symbols such that the symbols represent the referent, e.g. the meaning/definition of a word.
Meaning is a mental relationship, connection between a system of related symbols and a system of related phenomena such that the symbols represent the phenomena, e.g. the meaning of Einstein's theory of Special Relativity. This is a bit clunky. Needs work.
Meaning is used metaphorically to refer to a mental connection between two phenomena which is similar to the connection between a symbol and a referent, e.g. the meaning of life. Clunky too. — T Clark

There are many words that carry multiple meanings. Many of these carry meanings that can be distinguished easily from the context in which they are used. And some don't; these are the difficult ones. As a designer, I was always a little bit annoyed by the word "design", and how it meant quite a few different things ... but those things were closer in meaning to each other than the easy ones we just mentioned. So they cannot always be distinguished from context.

I think quality (cf. Pirsig's Zen and the art of motorcycle maintenance), and good, are (examples of) such words. The multiple meanings they carry are too close together to separate easily. Maybe this is what gives rise to confusion? These words carry all of the meanings they carry, often simultaneously (or so it seems). So when it comes to defining these terms precisely, we encounter problems.

Thoughts? :chin:

What you have ultimately done here is talk about language - about what language is. So where is your infinite regress?

No, what I have 'done here' is to use 'languing' behavior to elicit languaging behavior from you ! There is no 'ultimate', but It would have been more gratifying if I had also elicited 'research behavior' as well !
http://www.enolagaia.com/M78BoL.html

'Thoughts'..?
I suggest you think about the 'meaning' of that one key word ...'context'.
You might find that discussion of 'meaning' without that is as vacuous as trying to play tennis with no tennis court and no other player.

I suggest you think about the 'meaning' of that one key word ...'context'.
You might find that discussion of 'meaning' without that is as vacuous as trying to play tennis with no tennis court and no other player. — fresco

Yes, of course, but this is a more or less universal truism; it's not confined to this discussion of "meaning". I said as much, and more.

As a designer, I was always a little bit annoyed by the word "design", and how it meant quite a few different things ... but those things were closer in meaning to each other than the easy ones we just mentioned. So they cannot always be distinguished from context. — Pattern-chaser

My point is that there are some words whose meanings are closer together than the easier examples, and that, for this reason, it is much more difficult to distinguish them purely from context. Words like "mean", "good" and "quality", to offer but three good examples.

Thoughts? :chin:

But you havn't analysed 'context' which I suggest always consists of 'an action decision scenario'.
Your examples:
Take the word 'good' for example...look at the action it might promote like 'continue to work like that (teaching scenario)....'to enjoy eating something good' ...to enjoy reading a good book...etclook at verbs !

Take the word 'design'...already a verb implying activity fulfilling overt or covert criteria some of which may not be explicit.

Take the word 'quality' ...implying the mental action of deciding between desireable alternatives.

Without action, or potential action as to 'what happens next', there is no meaning !

Weird context...suppose a stranger puts his head round the door and says 'shark'....what action would you take?...does the word 'shark' mean anything other than to act as though 'this guy is a lunatic' !

I think quality (cf. Pirsig's Zen and the art of motorcycle maintenance), and good, are (examples of) such words. The multiple meanings they carry are too close together to separate easily. Maybe this is what gives rise to confusion? These words carry all of the meanings they carry, often simultaneously (or so it seems). So when it comes to defining these terms precisely, we encounter problems. — Pattern-chaser

Sure. The ambiguity is part of the fun and the power of language. In the context of this discussion, what's important is that the posters make sure we are all talking about the same meaning of "meaning." Otherwise, we get a muddled mixture of comments that don't seem responsive. When I am king of the forum, I'll make everyone define terms in the first paragraph of the OP. Also, I'll ban anyone with a cute username. Don't worry, "Pattern-chaser" is ok.

It's really simple. Meaning is the relationship between some cause(s) and some effect(s). — Harry Hindu

I don't understand the argument you are making. Your definition doesn't match my understanding of what "meaning" means.

Are you familiar with the work that Fresco mentioned above? In case you are not, let me quote a few passages summarizing 'Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being'. Lakoff is a psycholinguist who has developed a cognitive-psychology based explanation of the origin of mathematics that in many respects in comparable to the position I have been arguing.

"In the course of our research, we ran up against a mythology that stood in the way of developing an adequate cognitive science of mathematics. It is a kind of “romance” of mathematics, a mythology that goes something like this:

.•Mathematics is abstract and disembodied—yet it is real.
•Mathematics has an objective existence, providing structure to this universe and any possible universe, independent of and transcending the existence of human beings or any beings at all.
•Human mathematics is just a part of abstract, transcendent mathematics.•Hence, mathematical proof allows us to discover transcendent truths of the universe
.•Mathematics is part of the physical universe and provides rational structure to it. There are Fibonacci series in flowers, logarithmic spirals in snails, fractals in mountain ranges, parabolas in home runs, and pin the spherical shape of stars and planets and bubbles.
•Mathematics even characterizes logic, and hence structures reason it-self—any form of reason by any possible being.
•To learn mathematics is therefore to learn the language of nature, a mode of thought that would have to be shared by any highly intelligent beings anywhere in the universe.
•Because mathematics is disembodied and reason is a form of mathematical logic, reason itself is disembodied. Hence, machines can, in principle, think.It is a beautiful romance—the stuff of movies like 2001, Contact, and Sphere.It initially attracted us to mathematics.

But the more we have applied what we know about cognitive science to understand the cognitive structure of mathematics, the more it has become clear that this romance cannot be true. Human mathematics, the only kind of mathematics that human beings know, cannot be a subspecies of an abstract, transcendent mathematics. Instead, it appears that mathematics as we know it arises from the nature of our brains and our embodied experience. As a consequence, every part of the romance appears to be false, for reasons that we will be discussing. Perhaps most surprising of all, we have discovered that a great many of the most fundamental mathematical ideas are inherently metaphorical in nature:

•The number line, where numbers are conceptualized metaphorically as points on a line.
•Boole’s algebra of classes, where the formation of classes of objects is conceptualized metaphorically in terms of algebraic operations and elements: plus, times, zero, one, and so on
.•Symbolic logic, where reasoning is conceptualized metaphorically as mathematical calculation using symbols.
•Trigonometric functions, where angles are conceptualized metaphorically as numbers.
•The complex plane, where multiplication is conceptualized metaphorically in terms of rotation."

"Metaphor is not a mere embellishment; it is the basic means by which abstract thought is made possible. One of the principal results in cognitive science is that abstract concepts are typically understood, via metaphor, in terms of more concrete concepts."

Do you agree with any of this?

No, what I have 'done here' is to use 'languing' behavior to elicit languaging behavior from you ! There is no 'ultimate', but It would have been more gratifying if I had also elicited 'research behavior' as well ! — fresco

What is "languaging" behavior? Just making scribbles appear on screen because you put scribbles on a screen? or representing some ideas that are not of some "languaging" behavior with "languaging" behavior?

Is the State of Affairs you are languaging about the scribbles on the screen or something else?

I don't understand the argument you are making. Your definition doesn't match my understanding of what "meaning" means. — T Clark

It might do you some good to read the rest of the post. The definition I used is how everyone uses the word "meaning" - to refer to some cause or purpose.

When someone asks, "what do you mean?", they are asking what ideas you intended to convey with your use of words. They are trying to get past the scribbles and the words to the idea in your head which is the cause of the scribbles or a words.

When someone uses words and we don't understand their use, we don't ask "what do the words mean", we ask "what do you mean" which is talking about your idea in your head and your intent to communicate it.

We understand that people may use words differently than the dictionary definition but that isn't to say that they don't mean something when using the words that way.

When someone asks, "what is the meaning of life?", they are asking about the cause or the purpose of life.

'Languaging' is a form of behavior which co-ordinates behavior. Your languaging sample about 'just squiggles on a screen' is your attempt to to elicit a response from me involving the word/concept 'ideas'. But from Maturana's 'languaging' point of view, 'ideas' are merely sequences of 'internal actions/conversations which we call 'thinking'. It is this ability to 'act off line' which gives humanity an evolutionary advantage over most other species. In fact, one definition psychologists use for 'intelligence' is 'the capacity to delay a physical response'.

it appears that mathematics as we know it arises from the nature of our brains — Joshs

Well, what a total shock. Who would have thought.

Unfortunately, Kant did not insist on the fact that pure reason, divorced as it is from the real, physical world, is in and of itself, necessarily meaningless, i.e. free of any possible (real-world) semantics. It is its extreme purity that makes this type of knowledge meaningless and also useless, to be understood as: having no real-world semantics and no direct use or direct application. — alcontali

Perhaps Kant saw things differently. He was after all a polymath, someone who lectured in science and geography as well as philosophy. He well understood the fact that mathematics relates to what you describe as 'the real world'.

Instead, it appears that mathematics as we know it arises from the nature of our brains and our embodied experience. — Joshs

Are not "the nature of our brains" and the "nature of our embodied experience" part of nature? We experience nature as difference and sameness or similarity; because we can differentiate we can count, and counting is the basis of mathematics. It is not our brains alone which originate difference and sameness.

He well understood the fact that mathematics relates to what you describe as 'the real world'. — Wayfarer

I think @alcontali is talking about meta-mathematics. I could be mistaken.

The very thing which got me into philosophy forums was the notion that 'numbers are real but not material'. They are the same for all who can count, but can only be grasped by a rational mind. Therefore, they are 'rational or intelligible objects' the perception of which is key to the operation of reason herself. This is deeply antagonistic to today's evolutionary naturalism, but there it is. 'Darwin doesn't explain Einstein.'

Therefore, they are 'rational or intelligible objects' the perception of which is key to the operation of reason herself. This is deeply antagonistic to today's evolutionary naturalism, but there it is. 'Darwin doesn't explain Einstein.' — Wayfarer

Cool