People, Trump and co. really could win.Then the fun will be over. — baker

Been there, done that.

It’s uncivilised for sentient beings to undergo involuntary pain and suffering – or any experience below hedonic zero. — David Pearce

Involuntary pain and suffering is most often derived in accidental ways, mistakes and not knowing the potential source, and how to prevent it. I do not think it is possible to eliminate the possibility of such pain and still remain living beings. Nor do I think we ought to attempt to eliminate the possibility of such involuntary pain, as this possibility is what inclines us to think, and develop new epistemological strategies for certainty.

What I think is a far more significant and important issue is the matter of voluntarily inflicting pain and suffering on others. If your goal is to manipulate the human being towards a more civilized existence, then the propensity for human beings to mistreat others is what you ought to focus on, rather than the capacity for pain. See, you appear to be focused on relieving the symptoms, rather than curing the illness itself.

In everyday understanding, when we count, we associate one thing with 1, then the next thing with 2, etc. Literally. We say the numbers, one for each object as we count the objects. Mathematically. this is expressed as a function from the set of things counted to a set of numbers: — TonesInDeepFreeze

We might say the numbers "one for each object as we count the objects", but that does not mean that we associate "2" solely with the object pointed to when "two" is said. In reality we associate "2" with having counted two objects, so the first object is also associated with the spoken "2". It is imperative to the count that the other object counted is remembered, and is an integral part of the meaning of "2'" when it is spoken. If the other object is not remembered as a part of the 2, then we could go back to the first object and say "3", but that's not a valid count.

It is the very point that you can count more than one way.

You can count 'War And Peace as the first, then 'Portnoy's Complaint' as the second. Or you can count 'Portnoy's Complaint' as the first, then 'War And Peace' as the second. In either case, both counts show that there's a first and second, thus there are two. — TonesInDeepFreeze

Right you can count the objects in any order that you want. Therefore "pairing", or bijection, which represents the count as assigning a specific order to the objects is a false representation of counting. In instances when there is a small number of objects we can look at them and see the number of objects, without giving them any order at all. So ordering them, or "pairing" them is accidental to the count, it is not an essential aspect of counting. We simply do it as an aid, to ensure that we are not making a mistake and producing a false count.

You ought to accept and understand this fact, because it is fundamental to many forms of measurement, and how we actually count something in reality. When we weigh something, we do not pair a different part of the object with each gram counted, and when we measure the electrical potential we do not pair each part of it with a volt. This is clear evidence, that in general practice, counting something is not a matter of pairing objects with numbers. In modern practice, we deal with billions, trillions, and numbers so high, that if counting something was a matter of pairing, we'd never get done counting any of these astronomically high numbers which we deal with.

The sequence a,b,c,d,e is a sequence of five letters. e is letter five. — jgill

That's an arbitrary designation, dependent on a stipulation that there is a left to right order to the sequence. "a" could just as easily be letter five, or we could assume an ordering which makes any of the letters number five. The point being that even though we order things when counting, (first, second, third, counted, etc.) because it facilitates distinguishing between what has been counted, and what has not been counted, helping to ensure certainty, ordering is not essential to counting. We can count things without ordering them.

If I'm not mistaken, in another thread, you were using the word 'refer' in the sense of 'denote'. So if not 'denote' what exactly do you mean by 'refer' in this thread? — TonesInDeepFreeze

"Refer" is more general than denote, such that to denote is a specific type of referring. So when we say that a word refers to something, whether that something is a thing, an activity, an idea, a concept, or whatever, it means that we must direct our attention toward whatever it is which is referred to, in order to understand the use of the word.

The numeral '5' has meaning. The number 5 is not the numeral '5'. — TonesInDeepFreeze

The number 5 is a concept, therefore it has meaning, like any other concept.

The fact that 5 is a count doesn't contradict that 5 also is a number no matter what it happens to count. — TonesInDeepFreeze

My point is that 5 must count something, or else we forfeit its meaning. There is no sense to saying that there is a count of five which does not have five things.

5 is the successor of 4. 4 is the successor of 3. 3 is the successor of 2. 2 is the successor of 1. 1 is the successor of 0.

No matter what the numbers count, they exist by virtue of successorship or by being 0. — TonesInDeepFreeze

This is simply not true. Numbers are defined by quantity, not order. If you want to define numbers by order, then you assign temporality as the difference between 1 ,2,3 and 4. But this is not at all how numbers are used. We might assign numbers to units of time, like first second, third, fourth, but it's really not true to say that numbers derive their value from order or succession, rather than from quantity.

of course are different, but nothing is "invalidated". Saying the pairings are "invalidated" is not even sensical. — TonesInDeepFreeze

As I explained, what is invalidated is your representation of the count as a pairing. The pairing you described is not a valid representation of a count, for the reasons explained.

You're doing it again! We do not use '2' to name a book. '2' does not denote a book. — TonesInDeepFreeze

If your count is nothing but a pairing, then that is all you are doing, assigning a number to a book, naming a book, with a number. This is why your representation of a count, as a pairing, or bijection, is incorrect. That is not what a count is.

We can switch them so that we have:

{<'Portnoy's Complaint' 1> <'War And Peace' 2>}

But the greatest number in the range is still 2. — TonesInDeepFreeze

If you switch them, then your original pairing is invalidated. Which pair is the true representation of the count? It can't be both at the same time. But in a true count, neither book is paired with 1 or 2, because a count is not a paring. There are two books, and neither one is number 1 or number 2, they are equivalent as books.

That doesn't contradict that when we see discrete objects then we may count them. — TonesInDeepFreeze

Sure, we can count discrete objects (units), that's what I've been arguing is necessary for a count, to have discrete units which are counted. What is incorrect, for the reasons explained, is your representation of a count, as an act of pairing a discrete unit with a number. Do you understand those reasons given?

How we use the concept of counting is a matter of practical approach, such as putting the water in a beaker with lines and counting the lines in the beaker to the point the water level ends or whatever. Whatever difficulties there may be conceptually with that, they don't negate the more basic notion of counting by bijection. — TonesInDeepFreeze

Again, this is completely untrue. If we want to know what a number is, within a count, then we must produce a true representation of what a count is. To simply produce a false representation of a count, for the sake of supporting your claim of what a number is, is to just beg the question with a false premise.

You present as so confused that I wonder whether you are posting as some kind of stunt or dumb cluck character. — TonesInDeepFreeze

You present yourself as someone who has not yet learned how to count.

The way I see it is that as human beings, we are first and foremost, animals. That's what defines us, although we like to separate ourselves from the other animals, to say that we're somehow a special type of animal. Let's say that specialness as "civilised". If we're already civilised, then what could it even mean to suggest making us more civilised? If civilised is a general category, then all sorts of particular instances qualify as civilised, and what would make one "more" civilised than another? If we are not yet civilised, then what really does "civilised" mean? Distinguishing us from the other animals, is not even justified now. Unless we answer this type of questions, assuming that such and such is "more civilised", is simply an unjustified assumption.

(2) A count is the result of counting. "The count of the books is five."

A number (we're talking about natural numbers in this context) is a count in sense (2). That doesn't preclude that a number is a mathematical object. — TonesInDeepFreeze

That's right, it doesn't preclude that the number is a mathematical object. But the point is that your definition (2) stipulates "the result of counting". So correct use of "5" is dependent on the count of the books, that there are five books. Therefore the number 5 loses its meaning if it does not refer to five of something counted, books in this case. Anytime we use "5" regardless of whether you think it refers to a mathematical object or not, it necessarily refers to five distinct units, or else you are using it incorrectly.

We better dispense with that notion. It's nuts. A number is not a book. — TonesInDeepFreeze

I'm not saying a number is a book, that's nonsense. But when we use "5" it is necessary that there are five distinct units indicated in that usage or else you are using "5" in an unacceptable way. Do you agree?

So the numeral does not denote a book, but rather it denotes the number that is paired to the book in the bijection (or, in everyday terms, in the pairing off procedure we call 'counting'). — TonesInDeepFreeze

Strictly speaking this (bijection in the way you describe it) is not a valid count. Suppose we say that there are two books. "War and Peace" is numbered as 1, and "Portnoy's Complaint" is numbered as 2. The relation between "Portnoy's Complaint" and the number 2 is not a simple pairing. This is evident from the fact that if we remove "War and Peace", there is no longer two books, and the pairing is invalidated. You might still use "2" to name the book, but it is not a valid count of two, because there is only one book.

So we cannot say that "Portnoy's Complaint" is paired with 2. That is a false representation because it does not include the necessary requirement of another book. "Portnoy's Complaint" can only be paired with 2 in a valid count, if there is another book paired with one. Furthermore, neither Portnoy's complaint nor "War and Peace" need to be paired with either 1 or 2, for there to be a valid count of 2. Do you recognize this point? There is no need for a pairing to have a valid count. We can have two objects, and say that there are two, without naming either as one or two, they are simply two.

This latter point is something which is very important to understand, especially when we count things like electrons which are difficult to distinguish from one another. We can have a count of 2 without establishing the principles required to distinguish one from the other. We can say that there are two electrons in the same orbit, without the need of distinguishing one from the other. We have principles which say they are distinguishable, but we need not distinguish them. Likewise, we can talk about 12 volts, without the need to distinguish and label each unit of electrical potential, as 1,2,3, etc..

So it is very clear that your method of representing "a count", as pairing a number with a unit (bijection) is a totally inadequate representation of what a count really is.

We don't say "''1' denotes 'War And Peace' and '2' denotes 'War And Peace' together with 'Portnoy's Complaint'". That's crazy. — TonesInDeepFreeze

You think it's crazy, but it's what's required to have a valid count. If "2" denotes "Portnoy's Complaint", unconditionally, and you have no other books, then obviously your count of 2 books is invalid. If you deny this requirement them you allow for invalid counts. You look at your bookshelf, number "Portnoy's Complaint" as 2, and bring it in to me, telling me you have two books in your hand, because "Portnoy's Complaint" is identified as two books. That's what's really crazy.

Right, but do you agree that it is necessary that there is a thing counted, a book in this case? So as much as the numeral "1" "denotes" what you call the number 1, which is a property of "the count", it must also refer to the one book, or else the count is not a true count. For "the count" to qualify as a true count, there must be something which is counted. If "1" does not refer to the book, as well as what you call the number, then there is nothing being counted, and therefore no count, because if there is nothing being counted, this does not qualify as a count.

Therefore, we cannot dispense with the fact that "1" must refer to the object being counted, a book, as well as what you call the number 1, or else we have annihilated "the count" as false because we cannot have a count with nothing being counted. But we cannot annihilate the count, because that is what gives logical coherency to the numbers.

If this is not clear to you, imagine that you go to count the books, and you count the same book over and over again, 1, 2, 3, 4, etc., such that you could have an infinite number of books, by counting the same book over and over again. That is not a valid or true count. To have a true count, "1" must refer to the first book, "2" refers to the first and second together, "3" refers to those two with a third, etc.. If we remove the need to have distinct objects being counted, then the count is not a valid or true count.

But to return to the earlier example of playing chess, one can fanatically aspire to improve one's game and play to win even though one will invariably lose. — David Pearce

I don't agree. One cannot play to win if the person knows that winning is impossible. In a similar way one cannot get the same enjoyment from winning if the person knows that losing is impossible. So there must be the real possibility of losing (suffering) if winning is to be enjoyable.

Two invincibly happy (trans)humans can play competitive chess against each other and both improve their game. Honestly, I don't see the problem! — David Pearce

The point is that one must lose, and suffer from the loss, if the other is to win and obtain the enjoyment of winning. If we remove the winning and losing from the game, we can't call it a competitive game.

Rather, what needs questioning is the widespread assumption that the "raw feels" of suffering are computationally indispensable. If the indispensability hypothesis were ever demonstrated, then this result would be a revolutionary discovery in computer science: — David Pearce

The issue, in my mind, is not whether suffering is indispensable, but the question of whether we can have gain without the possibility of suffering. If it is the case, as I believe it is, that all actions which could result in a gain, also run some risk of loss, and loss implies suffering, then to avoid suffering requires that we avoid taking any actions which might produce a gain. But if gain is necessary for happiness, and this is inevitable due to biological needs, then the goal of happiness cannot include the elimination of suffering. Therefore the goal of eliminating suffering must have something other than happiness as its final end. What could that final end be? If eliminating suffering is itself the final end, but it can only be brought about at the cost of eliminating happiness, then it's not such a noble goal.

Maybe contemplating the pain of a defeated opponent sharpens the relish of some winners today. Let's hope such ill-will has no long-term future. — David Pearce

It's not the pain of the opponent which I am talking about here, it's the aspect of the pleasure derived by the winner, which is produced by knowing that the pain of losing has been avoided. So the winner does not wish ill-will on the loser, only attempting to avoid the potential of the pain for oneself. That's "sportsmanship", you do not intend ill-will on the opponent, only the best for yourself. But the game is designed such that there is a loser. In the competition, all competitors know that someone (or team) will suffer the pain of lose. In good sportsmanship, it is the goal of the competitors to win and avoid such pain. It is not their intent to inflict pain on others. The joy in winning is intensified not by the thought that others are in pain, but by knowing that the pain of lose, for oneself, has been avoided.

So, competing against earlier iterations of oneself or an insentient AI does not address the issue, because we still must allow for the possibility that one loses, and therefore suffers from the lose. Replacing the opponent with an AI does not remove the necessity for the possibility of lose, and the consequent pain and suffering. The issue here is that much joy and happiness, and the drive, motivation, or ambition for success, comes from the desire to avoid the pain and suffering caused by failure. If we remove that pain and suffering, extinguish the possibility of failure, make the AI always lose no matter what, or whatever is required to negate the possibility of suffering, then there is no drive or ambition to better oneself.

But as I said, emphasizing hedonic uplift and set-point recalibration over traditional environmental reforms can circumvent most – but not all – of the dilemmas posed by human value-systems and preferences that are logically irreconcilable. — David Pearce

So what would be the point to continually inducing the joy and pleasure of winning in a person, without requiring the person to actually compete and win, or even do anything, to receive that pleasure? If it is not required to do the good act, to receive the pleasure of doing a good act, then when is anyone ever going to be doing anything good?

1 is the count at the first member of the set, a particular unity (whatever it is). 2 is the count at the second member of the set. Etc. And '1' and '2' name different individual numbers. And 1 is the count of the members of the set with one unit. And 2 is the count of the members of a unity that is a set with two members. And a set with one member is a different kind of unity from a set with two members. — TonesInDeepFreeze

I do not assume any sets, or numbers, to begin with. Numerals are used fundamentally for counting things, objects like chairs, cars, etc.. There is no such thing as "the count", without things that are counted. So in that situation "1" signifies the existence of one object counted, "2" signifies two, etc..

'2' denotes the number 2. The number 2 is the count of a set with two members. And a set of two members is itself a unity as a set. But '2' does not denote a unity; it does not denote the set that it counts. It denotes the COUNT of a set that is itself a unity. When we say that a set is a unity, we mean that it is one set, while we recognize that the number of members of the set may be greater than one. — TonesInDeepFreeze

The inconsistency arises now, if we say that numerals signify numbers rather than the things being counted. Let's call the number, "the count" which seems acceptable to both of us. Let me look at the difference between a count of one, and a count of two.

To have a count of one, there must be an object which is counted. In order for the count to be a valid count, there must be something which is counted. This is not the number 1 which is counted. It is something independent, an object like a chair, or a car, one of the things which is going to be counted. What validates the count of one, is an independent object, what I call a fundamental unity, which is counted.

Now let's consider a count of two. The count of two is justified by the existence of two such objects. But you want to say that "the count" itself is an object, the number two. So we have two distinct types of objects referred to with "a count of two". We have the two material objects, which have been counted, justifying the count of two as a valid count, and also we have the count itself, as an abstract object, which is called the number.

So, if we assume the reality of abstract objects, numbers, then when we use "2", there is always, if it is a valid use of "2", two distinct types of objects referred to. There is a number, 2, which as a unified object, as "the count", and there is also two of another type of unity, being the things counted, in order that the count is a true and valid count. In the case of "1" however, we can say that the number is the fundamental unity, the thing being counted, and also the abstract unity, represented as "the count", because they are each one simple unity. Therefore we would have consistency saying that the number 1 is both the thing being counted, making a valid count, and an abstract object itself.

To summarize now. Let's say that "1" refers to the number 1, which represents the count, and is also the thing counted, abstract numbers. We cannot use "2" in the same way. "2" might refer to a number, which represents "the count", as an object, or it might refer to the two distinct objects which are counted. It cannot refer to both, due to the inconsistency of one being one object, and the other two. My contention is, that if we use "2" to refer to "the count" itself, as the number 2, an abstract object, and this is what you are doing in your post, then the count itself is rendered false or invalid, because "2" cannot refer to both one object and two objects at the same time without contradiction.

"It's not enough to succeed. Others must fail", said Gore Vidal. “Every time a friend succeeds, I die a little.” Yes, evolution has engineered humans with a predisposition to be competitive, jealous, envious, resentful and other unlovely traits. Their conditional activation has been fitness-enhancing. In the long run, futurists can envisage genetically-rewritten superintelligences without such vices. After all, self-aggrandisement and tribalism reflect primitive cognitive biases, not least the egocentric illusion. Yet what can be done in the meantime? — David Pearce

So this "intensely rewarding experience" which we get from succeeding in competition, you designate as seated in a vice, or vices, This would mean that it is a bad rewarding experience which ought to be eliminated. But on what principles do you designate some rewarding experiences as associated with vices, and some as associated with virtues? I would think that if you want to eliminate some such intensely rewarding experiences, and emphasize others, you would require some objective principles for distinguishing the one category, vice, from the other, virtue.

If society puts as much effort and financial resources into revolutionising hedonic adaptation as it's doing to defeat COVID, then the hedonic treadmill can become a hedonistic treadmill. Globally boosting hedonic range and hedonic set-points by biological-genetic interventions would certainly be a radical departure from the status quo; but a biohappiness revolution is not nearly as genetically ambitious as a complete transformation of human nature. And complications aside, hedonic uplift doesn't involve creating "losers", the bane of traditional utopianism. — David Pearce

I think I've already mentioned the problem with this perspective. That is the divisiveness that such a proposal (which you admitted might be unethical) would induce. Global cooperation is not facilitated without consistent belief. Look at the issue of climate change for example, and even an immediate threat to the lives of many, like COVID, does not obtain unanimous consent to the designated required response. You might find a good example of global cooperation with the issue of CFCs and the ozone layer. That was a serious issue which seemed to obtain global cooperation.

However, it appears to me like such cooperation is more likely to be obtained in the face of serious evil, rather than the effort to obtain some designated good. So I feel like the challenge to you would be to demonstrate that failing to follow your proposed program would be a great threat to humanity. I perceive three levels of attitude toward action, or inaction, in relation to such a proposal. There are those who say "do it", and may start such an action, those who say "do nothing" (status quo), and those openly opposed to doing it. It seems like those who say "do it" have a huge task to persuade the others, and bring them onboard, which must be carried out prior to starting any such action. This would require a huge effort of education and some very strong principles. That is because starting any action without first persuading the others, logically would shift those in the "do nothing" group over to the "openly opposed" group.

Participating at TPF has necessitated that I become an expert at grade school principles, because many people here do not seem to understand these very basic principles, like what "=" signifies. And so, I have to explain over and over again, the same principle, in as many different ways as possible, in an attempt to dispel the misunderstandings which these people hold. It seems to be much easier to teach young children these principles than it is to teach adults who have already developed bad habits of misunderstanding, by accepting contrary principles. So the teacher of adults, must become an expert, rather than just an average teacher, requiring not only to instill good habits of understanding, but first needing to dispel bad habits of misunderstanding.

But neither P nor Q are stated coherently by you. And there's no reason to think anyone wants P or Q anyway. — TonesInDeepFreeze

Then I conclude that what needs to be discussed is clarification of P and Q.

Of course the notion of 'one' is related to that of a unity. But even aside from parsing, I don't know who in particular you think holds that "The "2" represents two of those individuals together, and "3" represents three, etc". It would help if you would cite at least one particular written passage by someone that you think is properly rendered as "the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" and "'2" and "3" represent some kind of unity". — TonesInDeepFreeze

Whenever we count something it is like this. Count the books on the shelf for example. "Book" signifies the type of unity being counted, "1" signifies that a unity called "a book" has been identified, and a first one has been counted , "2" signifies two of these units, etc..

t would help if you would cite at least one particular written passage by someone that you think is properly rendered as "the numeral "1" represents a basic unity. an individual. — TonesInDeepFreeze

I assume you know how to use Google or some other search facility. You could simply search this if you need such a confirmation, instead of asking me to do your research for you. Here is the first paragraph from the Wikipedia entry on "1":

1 (one, also called unit, and unity) is a number and a numerical digit used to represent that number in numerals. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer.[1] It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. — Wikipedia

Also, if you actually are interested (which you don't seem to be by your half-hearted replies, and refusal to do any research yourself, and near complete denial of the relation between one and unity), you could look into number theory, and the reason why 1 is generally determined as not a prime number. Here's the first entry I get when I Google that question, is 1 a prime number: https://blogs.scientificamerican.com/roots-of-unity/why-isnt-1-a-prime-number/
Here's a passage from that article:

In the very most basic example, we can ask whether the number -2 is prime. The question may seem nonsensical, but it can motivate us to put into words the unique role of 1 in the whole numbers. The most unusual aspect of 1 in the whole numbers is that it has a multiplicative inverse that is also an integer. (A multiplicative inverse of the number x is a number that when multiplied by x gives 1. The number 2 has a multiplicative inverse in the set of the rational or real numbers, 1/2: 1/2×2=1, but 1/2 is not an integer.) The number 1 happens to be its own multiplicative inverse. No other positive integer has a multiplicative inverse within the set of integers.* The property of having a multiplicative inverse is called being a unit. The number -1 is also a unit within the set of integers: again, it is its own multiplicative inverse. We don’t consider units to be either prime or composite because you can multiply them by certain other units without changing much. We can then think of the number -2 as not so different from 2; from the point of view of multiplication, -2 is just 2 times a unit. If 2 is prime, -2 should be as well.

*This sentence was edited after publication to clarify that no other positive integer has a multiplicative inverse that is also an integer. — * reference above

What does it mean? — fishfry

"2+2=green" means that whatever is represented by "2+2" is equal with whatever is represented by "green". Isn't that the way we use logic? We learn to apply the rules without regard for what the particular symbols represent.

When I say that 2 + 2 = 4 has meaning, it's because I have defined '2', '4', '=', and '+' according to the standard mathematical conventions, either within the Peano axioms or ZF set theory. In other words from my viewpoint 2 + 2 and 4 and '=' all refer to something. The somethings that they refer to are abstract mathematical objects. And I will stipulate that when you challenged me to define exactly what I mean by those, I was stuck. I admit that! But at least by saying what these expressions refer to (in my mathematical ontology), I can thereby assign meaning and value to them. The meaning and value of these expressions derive from the referents I have assigned to them. — fishfry

You are missing something in your interpretation of "2+2=4". The "+" signifies an operation, not an object. Do you understand that an operation, as an action, is something other than an object?

But you say that 2 + 2 and 4 don't refer to anything. So it is now incumbent on you -- not just for me, but for working out your own thoughts for yourself -- to figure out how to define the meaning and value of syntax tokens that you claim don't refer to anything at all! Do you take my point here? — fishfry

Sure, I see your point. It's not difficult, the task you ask of me; "2" signifies a quantity, "+" signifies an operation of addition, "=" signifies 'has the same quantitative value as', and "4" signifies a quantity. So, "2+2=4" signifies that a quantity of two, added to another quantity of two, through that operation of addition, has the same quantitative value as the quantity of four. See how easy it is? Grade school stuff.

There is nothing simple about your point of view. Nor have you explained "what '=' signifies" in the least. I haven't seen you do it. — fishfry

Come on fishfry I've said over and over again that "=" signifies having the same value. I even quoted Wikipedia in the last post:: "In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value." Now don't come off saying that I haven't explained what "=" signifies. This is how I ended the last reply to you:

Do you accept that there is a difference between "is the same as" and "has the same value as"? The former phrase is the phrase used by the law of identity. The latter phrase is what is signified by "=", as the Wikipedia entry indicates. — Metaphysician Undercover

It's funny. You can't answer the question I put to you: If 2 + 2 has no referent, how does it obtain its meaning or value? — fishfry

That question is simple too. A word can derive its meaning through examples, like "green", without referring to any particular thing. It can derive meaning from a definition, like "square", and "circle" do, without referring to any particular thing. And there is a number of other ways, by which usage hands meaning to a word, which does not refer to any particular thing. In this case, we use "2" to signify a quantity, and "+" to refer to the operation of addition, and the symbols derive their meaning from that usage.

But I have a perfect understanding of what the meaning and value of 2 + 2 are. — fishfry

Clearly you do not have a "perfect understanding of the meaning of "2+2", because your interpretation does not include the operation of addition, which is signified by "+". You cannot simply leave out the meaning of some symbols in the phrase, then claim to have a perfect understanding of the phrase.

I DO have a crystal clear understanding of how the meaning and value of 2 + 2 derive from the mathematical REFERENT of the expression. Whereas you DENY there is a referent, so you are STUCK trying to figure out how to derive the expression's meaning and value. Why don't you work on this and let me know if you have any fresh ideas on the matter. — fishfry

OK, if you're so convince that you are correct in your crystal clear understanding, interpret the expression for me, "2+2", symbol by symbol, and show me how that expression signifies the object signified by "4".

Agreed on this point. But note that I can define what the value of 2 + 2 is, and you can't. Because you deny that 2 + 2 has any referent. — fishfry

Tell me please, in your mind, how is a value an object?

But you deny the expressions have any referents at all, so I don't see how you're in a position to claim that they have the same value, or different values, or any values at all. How can we know their values if they have no referents? — fishfry

A value is not a thing, or object, it is what a mind assigns to a thing, as a property, just like "big", "heavy", "green", etc. So a value is the product of a judgement. There is no referent because we assign the same property to multiple things, due to the abstract nature of properties. And, we assign the same value to multiple things, so there cannot be an object as a referent. "Green" doesn't refer to any particular thing, because many things are green, so there is no referent for "green". It is a judgement we make.

It is a similar situation with "2", we assign that value to many different situations, as the property of them, but it has no particular referent. We can start with, 'what a thing is worth' as a defining feature of "value", and see that a value exists in relation to a purpose. A thing is worth something only to the extent that it is desirable for some purpose, useful toward some goal or something like that. So we know the value of "2" by its usefulness. That is what the judgement is based in.

I, on the other hand, have a perfectly sensible way to define their values, based on the referents I have assigned them in PA or ZF. I can do this from first principles. — fishfry

One big problem here, your interpretation leaves out the operation signified by "+". And, it is by means of these various operations that the numerals obtain their signified values. They are useful for these operations. So your way, is really not at all sensible, because you completely neglect the operations by which the numerals get the values which are associated with them.

Not only that, but your way creates an unnecessary layer of separation between the numeral and the represented value, which is commonly called a number. This medium, or separation obscures the true meaning, and value represented by the numeral, making it much more difficult to understand the nature of quantities.

* You claim 2 + 2 has no referent, and since it has no referent, you can't tell me how to determine its value. — fishfry

You have obviously misunderstood. I have no problem telling you how we determine the value of "2+2". We simply look at how the symbols are used, just like when we determine the meaning of "green". That's why I said it's a matter for grade school, which you took as an insult. We see that in common use 2+2=4, so 2+2 clearly has the same value as 4, that's what the "=" tells us.

What I can't get past is that physicist have used General Relativity to derive a size for the universe, and pretty much agree on the result; in doing so they relied on the relativistic versions of the equations you refer to.

And yet, without showing us the calculations, you insist that they are wrong.

I don't think there is more to say here. That the velocity of light is a constant, fixed for all observers, is fundamental to physics. — Banno

I explained this to you already. What results from the application of general relativity, is the conclusion that space is expanding. This separation of things which is accounted for by the concept of spatial expansion is a type of motion of things relative to each other, which does not qualify as "motion" within the precepts of the general theory of relativity. Therefore we can conclude that there are motions of material things in the universe, to which general relativity is not applicable. This is regardless of whether the principles of relativity theory, special or general, are fundamental to physics.

Now, Gary would prefer not to apply the general theory of relativity, and therefore avoid the conclusion that space is expanding. That's a valid starting point. From this perspective we can take all the observed motions, and class them together, and see that there is good reason not to apply the principles of relativity, as they are inadequate. So we ought to seek a better theory which can account for all the motions in the universe as "motion".

I understood that; I thought you meant that you do want to take '2' and '3' as representing a type of unity, while you think that that is contradicted by 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" so that it needs correction .

Am I not correct that that is your view? — TonesInDeepFreeze

That's pretty close, except I do not necessarily want to take "2" and "3" as representing unities, that's why I said "if" we want to. I see the numeral as representing a group with a specific number of things in that group, but the unity of that group is questionable.

.

More basically, I don't know why one would fret over any of this, since I don't know anyone who claims "the numeral "1" represents a basic unity. an individual. — TonesInDeepFreeze

I find that very strange I hear them used that way all the time. I suppose I didn't explain very well. Isn't this how we count? One represents one unit, two represents two of those, etc.. If you're put off by the terminology, "unity", "represent", etc., that's understandable, but why don't you just relax and enjoy the simplicity of the terms. It seems to me like there's always some people who get really flustered, and then have difficulty understanding simple terms, as soon as you mention any sort of problems within the systems of mathematics.

In sum, I can't make sense of what you're trying to say. — TonesInDeepFreeze

Yes, I can see that. You haven't really ever thought about such fundamental issues as how we use numerals, and you don't really understand why anyone else would. Why did you engage me, if what I was saying appeared so foreign to you?

Suggestion: You could reference some actual piece of mathematical or philosophical writing that you disagree with and show how you think you can correct it. — TonesInDeepFreeze

I've addressed particular pieces of mathematical writing which I disagree with before, in the past, but I cannot think of any way to correct these issues. So people have told me that if I don't have a solution, then don't point out a problem. But I think that's nonsense. I think we have to find the problems, and get a good clear understanding of why and how they are problems, before we can move toward an adequate solution. Solutions don't come easily, they require a thorough understanding of the problems.

Yes, as I thought, you find that there is a problem with the notion (whatever it means) that 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc". — TonesInDeepFreeze

No, I see no problem with that in itself. The problem is when we want to say that, and also that "2" and "3" represent a type of unity.

But (aside from even trying to parse the broken phrases) I don't know who says anything along the lines of 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc". So I don't see why you think it is a problem that needs to be addressed. — TonesInDeepFreeze

I don't know about you, but I always use "1", "2", and "3" in that way. If you don't ever talk about 1 chair, 2 or 3, or any number of other things like that, then I guess you don't use them the same way. But if someone asks you how old you are, do you answer with a number?

I thought you meant that there is a fundamental problem with:

"The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well."

And that your supposed solution to the supposed problem is:

"[...] we have to allow that "1" represents a different type of unity than "2" does [...]" — TonesInDeepFreeze

There is no proposed solution. The issue was stated as a fundamental problem with numbers, without a solution.

Or perhaps you would make clear which parts of your passage are ones you are critiquing and which parts are ones you are claiming. — TonesInDeepFreeze

I am not critiquing anything, the whole thing is what I am claiming. I am claiming that there is a fundamental problem with numbers. If "1", "2", "3", etc. , are used to represent unities, then "2" and "3" must represent a different type of unity from "1", for the reason I explained.

Now here is a proposal for a solution. If "2" and "3" are said to represent numbers, then maybe we ought to say that "1" represents something other than a number.

Perhaps consider the most intensely rewarding experiences of human life. They are experienced as intensely significant by their very nature. — David Pearce

Let's take an example then, competition. Winning a competition is one of the most intensely rewarding experiences for some people. Even just as a spectator of a sport, having your team win provides a very rewarding experience. But we can't always win, and losing is very disappointing. How do you think it's possible to maintain that intensely rewarding experience, which comes from success, without the possibility of disappointment from failure? It seems like a large part of the rewarding feeling is dependent on the possibility of failure. We can't have everyone winning all the time because there must be losers. And there would be no rewarding experience from success, without the possibility of failure. How could there be if success was already guaranteed?

What do you need a link for? If you don't understand what I said, just show me what you do not understand, and I'll explain. If you understand but disagree, just tell me what you disagree with, and maybe we can hash it out.

I think this is a small example of a larger problem - the inability to accept reality.

Reality deniers come in many shapes & sizes: Vaccines, the Holocaust, Flat Earth, climate change, etc.

I wish I knew what causes this. I have close relatives & friends who deny at least one (and typically many) aspects of reality. My amateur psychologist analysis is that this is partly driven by fear. The way they view themselves and how they fit into the world is being challenged. And they are afraid of that change.

And the thing is - they are not stupid people. You can have intelligent conversations with them on any number of issues, you can share laughter & tears, etc. — EricH

Yes, "bad physics" threads are necessary to bring attention to the fact that even highly intelligent people, like physicists, sometimes are amongst those who cannot accept reality.

Where can I actualy read anyone explaining the concept of numbers that way? — TonesInDeepFreeze

Didn't you just read it?

I think that a stable system is not real by the second law of thermodynamics. If "positive feelings" are associated with stability, then we are fighting a losing battle, and won't have any positive feelings until we reach maximum entropy.

Wow, can you imagine the boredom of being in a spaceship flying to another galaxy? To see what? There must better reasons for wanting an extended life than this. But what are they exactly? If we remove all suffering, doesn't the extended life just turn into one long boring flight to nowhere. Might as well be an eternal brain in a vat.

No I don't. Nor should you. But we each choose our paths. You might consider joining forces with Metaphysician Undercover. His concern is the supposed equality between 2+2 and 4. :roll: — jgill

There is a fundamental problem with the concept of numbers. The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well. So we have to allow that "1" represents a different type of unity than "2" does, or else we'd have the contradiction of "2" representing both one and also two of the same type of unity.

I'm sure there a bunch of terms that physicists pull from somebody else's discipline because they keep getting punked by "reality." It's no wonder others feel free to chime in when they see the struggle using familiar terms. — James Riley

What flavour is that quark? I don't know bite it and see. Ha ha ha!

As you have indicated, H2O and water are very different concepts.

If you use "properties" in that way, referring to the function of a thing, then you must respect that functions which the object does not currently have, though the object has the capacity to be used that way if approached by the right mind, are not actually properties of the thing, because it is not being used that way. Otherwise the thing has all sorts of different properties at the very same time, in violation of the law of non-contradiction.

Waves might be substrate-less. That is, they may not be like the waves in the water, which is the substrate for the waves. They are only waves. — spirit-salamander

When you start into basic physics in high school, they'll teach you about waves, and do demonstrations of waves in wave tanks, and you'll learn about sound waves and such. You learn the physical structure of waves. It is nonsense, completely illogical, and fundamentally contrary to good science, for anyone to say that "waves might be substrate-less", regardless of your appeal to authority.

stick can be used to bash over the head, or it can be used as a lever to roll a giant rock down a hill. Or it can be used to scratch symbols in the sand. The same basic physical form can have radically different functionalities. Therefore radically different abilities. So even if beings have the same physical form, they can have radically different 'shapes' with respect to their environments. And hence different properties as reflections of their 'shapes.' Which are different abilities.

If as a result of a purely mental operation otherwise identical physical things can acquire different properties, then these properties are instantiations of the mental. And if these properties enhance survival then they result in progressive physical modifications. So the 'shape' of the mind in the world is a product of its own mental operations (in a physical context) and not merely a physical product. — Pantagruel

I think it is misleading, and therefore incorrect to call this immaterial property "shape". What you describe is that the same physical object can be used for a multitude of purposes. Hence the same "shape", the shape which the object has, can have different functions. "Function" is determined by purpose which is dependent on a goal. So "function" is determined in relation to the goal. It is incorrect to say that the function of a thing is a property of the thing, because it is really a feature of the thing's relation to the goal. So we cannot correctly call it a property or "shape" of the thing.

pecifically, I like the notion of mental shape because shapes have specific properties, and our properties or abilities 'fit' with what I've described as environmental gradients. — Pantagruel

The problem with this perspective is that our capacities always extend beyond our properties. This you describe in the op when you say that the same physical object can be used in multiple ways. "Property", if could by applied to usage, would refer to the current usage, and cannot go beyond that, as it is incorrect to say that something has a property which is not currently existing. But if a creature produces a new intention, has a new goal, then the same physical object might be be used in a new way, and this may become a new property (if property could be applied to usage). But as I explained above, the capacity of the object to be used in all sorts of different ways is not a property of the object itself, because it does not exist within the object, as it is dependent on the mind which views the object with intent toward a goal.

First, it is unlikely that there are exactly two types of stuff, particles and waves, absolutely differentiated. The reality must undoubtedly be so much more complex that duality ceases to have descriptive relevance. Second, all matter thus far experienced has evolved from common antecedents, so it is most likely that if particles ride a more foundational wave substance, the particles evolved out of it. Its not conceptually impossible for eternally distinct particle and "wave" substance to exist, nor is anything else, but the most probable explanation due to their pervasive interactiveness is that they have a common origin with impulsion towards combinatory states. As a fanciful example, if particles ride dark matter waves their behavior is probably mutualized enough with dark matter for whatever reason that this amounts to a synthetic substance in some degree. — Enrique

The existence of waves necessitates the conclusion that there is a substance (commonly referred to as the ether) within which the waves are active. One might deny the reality of the ether, but this leaves the relationship between the waves and the particles as unintelligible. The Michelson-Morley experiments indicate that the ether is not a separate substance, i.e. it is not distinct from physical objects. This implies that particles must be conceived of as a feature of the wave substance (ether), not as something distinct from it, "riding" it.

Hmmm. Excuse my error, then. — Banno

OK, you are excused, but you really do need to pay more attention to subtle differences, something very important in philosophy. Notice the difference between saying "language is a game", and "language is something within which there are numerous games". In the first case we might consider a composite whole, united by one consistent set of rules. In the second, we have numerous distinct sets of rules without any identified source of unity, yet we assume a whole and call it by one name "language". In the latter case we must inquire further to identify the source of unity which enables us to apply one name, assuming one whole, because there is not one complete set of unifying rules to make one game.

This difference, as the difference between a system, and a multitude of systems, is what I spent much time attempting to explain, already in this thread. To which you replied "I do find you verging on the incomprehensible." So, in case you are interested, I'll provide you with a review. Please remember, and adhere to the fundamental idea that there is a difference between a system, and a multitude of distinct systems, and perhaps what I said will be more comprehensible to you.

Now let's position the "system of believe" relative to the true doubt. The doubting person cannot be "within" the system of believe because that would mean that the system is already accepted by that person. The doubt must be aimed at the system as a whole, because as "a system" we must assume that there is consistency between the parts (individual beliefs) of the system, and one cannot reasonably doubt one part of a consistent system. So true doubt must be directed at the system as a whole.

Would you agree with that? If we say doubt can only occur from within a system of belief, that system of belief must be other than the system being doubted. The two systems may not even be remotely related. So the assumption "doubt can occur only within a system of believe", is really an irrelevant point, because that system of belief must be other than the one which contains the belief being doubted.. And if we take the game analogy, true doubt can only come from the person who refuses to play the game, because to play the game is to consent to the rules, and to consent to the rules is to forfeit your right to doubt them. — Metaphysician Undercover

Here's how what I stated above is relevant to this thread. If we assume that any specific language-game is a representation of a system of beliefs (consistency being a necessary requirement of "system"), then true doubt can only be directed at any specific language game from outside that particular game. I.e. the person who refuses to play. I'll call that person the skeptic, is the only one who may cast true doubt. If we assert that the skeptic must pose one's doubt from a position of being within a language-game, within a system of beliefs, then that system providing the skeptic's approach, must be other than the one doubted, and there cannot be consistency between these distinct language-games, or else true doubt would be impossible. This implies that language in general, as a whole, cannot be represented as a single language-game, because of the inconsistency between distinct language-games which makes true doubt a real thing.

The other course we could take, is to allow inconsistency within any specific language-game, and system of belief, thereby allowing for doubt within the system. If there is inconsistency within the game, or system, then doubt from within would be true justified doubt. But that ought to be seen as epistemologically unsound, to allow inconsistency to inhere within a system. It produces a faulty definition of "game" or "system", one in which the rules of the "game" contradict each other, or the "system" has parts which oppose each other, or are not conducive to its function.

So the logical course is to maintain that a language-game, or a system of beliefs, is necessarily consistent, and true doubt must be directed at the system as a whole, from outside that system. This is also the most practical solution, because if inconsistency appears to inhere within a system of beliefs, it is extremely difficult to isolate the defective parts, with the goal of doubting just those parts. So the entire system must be doubted as a whole. This implies that refusal to play the game is required, and we're at the point of doubting the entire system anyway. — Metaphysician Undercover

I explained very clearly why doubting the entire belief system is the only reasonable form of skepticism. Beliefs within a system are necessarily logically consistent and interrelated. That's what makes it a "system". To doubt one belief within a system requires doubting the beliefs it is dependent upon, and it is implied that the beliefs dependent upon the doubted belief are doubted as well. So it's unreasonable to doubt one belief without doubting the entire system within which it is integrated,

This is why the idea that there are hinge propositions which are somehow indubitable is unacceptable epistemology. If the entire system is intrinsically consistent, and valid, which it must be to be a "system", then no part of the system can be doubted without doubting the whole. And this would require doubting the supposed hinge propositions as well.

The preceding result, is the logical conclusion of assuming that beliefs exist as part of a "system". If we remove that premise, and allow that beliefs have individuality, free from the influence of an overall system, then it is reasonable to doubt individual beliefs. But then the whole game analogy, and the idea of hinge propositions is completely inapplicable. . — Metaphysician Undercover

A belief system must be coherent to fulfill the conditions of being a "system". This means that if one belief within the system is dubious, then the entire system is dubious due to all the beliefs being related through coherency. So it makes no sense to say that some beliefs within the system are dubious but the foundational ones, hinge propositions cannot be doubted. This is like taking a deductive argument, and saying that the logic is valid, the conclusion is dubious, but the premises are beyond doubt. If the logic is valid, we cannot doubt the conclusion without doubting the premises. — Metaphysician Undercover

But then it is incorrect to call this a "system", that's the whole point. If we move away from the "system" representation, to the "big, baggy monster of ways that people do things" representation, then the idea of hinge propositions makes no sense at all, because there is no system for them to be supporting. If there are systems, then the systems themselves must be coherent, so to doubt any aspect of the system implies a doubt of the entire system, including any supposed hinge propositions. Either way, the notion of hinge propositions which are beyond doubt is fundamentally incorrect. That's why Kuhnian paradigm shifts are a reality, the entire system along with its foundations must be dismissed. — Metaphysician Undercover

Oh.

What necessity forces you to use language? People can choose not to use language as freely as they can choose not to play chess. — Luke

Hahaha. I assume that's meant as a joke. If not, I feel sorry for you. The need to get what I want, the mother of all necessities.

Can you give us an example of language without grammar? — Fooloso4

This question is not relevant because "grammar" does not necessarily imply "rules", depending on how one defines the terms. So I have no desire to go around in the same circle which Luke leads me around, with you, except with the word "grammar" instead of "rule".

So now you are saying that those rules for language, the ones it doesn't have, also vary from one language to another. — Banno

Obviously, I never said language does not have rules. Read if you're going to comment. I've argued that rules are not prerequisite for language, they emerge from language use.

You started by claiming that language had no rules, but when this was shown to be silly, you have slid to claiming they are an emergent feature. — Banno

Well I don't think so. I seem to remember joining into this thread talking about the rules in a system of beliefs, and the rules of logical systems. That's not exactly a claim that language has no rules. Nine days ago:

I don't deny that there are rules in language, that's what formal logic is all about. — Metaphysician Undercover

I think you haven't been paying attention. You've been making some exceedingly absurd statements about what you think I believe. Now, I've been arguing this point with Luke for a long time, on numerous threads, the relationship between rules and language. As far as I know I've maintained a very similar position, as has Luke. That's why we go around in circles, Luke refuses to adopt a position which would allow us to proceed toward a better understanding of language.

General Relativity is about curved space-time... — Banno

Right, and special relativity is about curved space-time too ... not. Yet they're still both "relativity". I think you're missing something there Banno. General relativity is how the principles of special relativity are adapted to account for gravity.

You are inhabited by some strange mind which thinks it knows what it obviously does not. So you haven't the foggiest clue how to explain anything.

Seems far more likely that you haven't quite grasped relativistic physics. — Banno

What is the case is that separation caused by spatial expansion, is not considered to be properly called spatial "motion". Very large objects like galaxies get further apart without actually moving at all, because spatial expansion does not qualify as "motion". Since this activity of separating from each other, due to spatial expansion, is not a form of "motion", material things can separate at rates which are much faster than the speed of light, without violating principles of relativity, because within the confines of that theoretical structure, this does not qualify as "motion".

You ought to be able to see, that in the effort to maintain general relativity as the applicable theory for motions in the universe, we have now developed a whole new category of motion which does not qualify as "motion", because "motion" is defined by that theory. In other words, if we want all the types of motion which we have observational evidence for in the universe, to be measurable within one consistent theory of motion, we need a different theory. General relativity does not allow that this type of motion which is the result of spatial expansion is "motion".

Luke is doing a fine job of pointing out the mess that Meta has made for himself. — Banno

If you cannot see how Luke's adherence to the game analogy has lead him into a dreadful misunderstanding of the nature of language, as outlined in my last post, then perhaps you'd like to address that issue, which is the inversion of the relation between freedom and necessity, that is evident in the comparison between chess and language.

Does language have no rules or does it have "competing rules"? What "competing rules" does language have? — Luke

I have stated that language does not require rules, that they emerge as a feature of language. So there is obviously rules within language. The point being that there is language outside of rules. The differences in rules are varied. What is legal in some countries is illegal in others. Some philosophies promote violation of the law of excluded middle, some promote violation of the law of noncontradiction. Different languages have developed different grammatical structures.

How is this different to the game of chess? It is not as though people are forced to play chess against their will by the deterministic laws of nature, or that they are physically unable to make illegal moves. Chess is also "shaped...by freely chosen activities of free willing beings", yet it is still a game for all that, and has rules too. — Luke

Right, some never play chess, because they choose not to. But we really do not have such a choice in the case of language, due to the necessities of nature. Do you see how playing chess has an inverted relation to the forces of nature and free will, from that of languages usage? This is the difference between the two.

We freely choose whether or not we want to play chess, and if one decides to play, one must adhere to the rules when making moves. However, in the case of language usage, we are forced by necessity into using language, yet we are free to choose whatever moves we want. The relation between freedom and necessity is inverted between the two. In one case participation is freely chosen while the moves are determined by necessity, while in the other case participation is necessary while the moves are freely chosen.

As I believe in reductive physicalism, in that I believe that the mind and body are ontologically indiscernible, for me, the mind cannot be prior to spatial existence — RussellA

Well, I wouldn't agree with reductive physicalism, because I don't think it gives us an ontology which is capable of making the existence of abstractions, ideas, and conceptions, which are immaterial, intelligible. When we recognize these properties of the mind as immaterial, we apprehend them as having a non-spatial existence. We cannot measure them in any spatial way, such as size, shape, or any dimensional forms.

Yet these immaterial things do seem to have a temporality. This provides us with the premise to give mind, in its relation with time, priority to spatial presence. In Kant we see time as the internal intuition, and space as the external intuition. Strictly speaking, in terms of absolute, the external is not necessary, yet the internal is, or else there is nothing. (We cannot move to an external absolute because the mind cannot go, where by definition, there is no mind.) With the internal as the only acceptable absolute, spatial existence is not necessary, and follows only as contingent on material being.

I believe that happiness is a stable, balanced state of existence which is consistent with true well-being derived from an inner source of contentment. Joy seems to be more euphoric, requiring external stimulus, and therefore unsustainable in the long term. So I see the difference in temporal terms, whereas happiness is a long term passive well-being which is conducive to consistency in actions, joy is a short term, more of a manic type of thing, which may produce extreme good, but being less balanced it could slip the other way.

These are different "standards" to those in the context of norms and normativity. — Luke

There was no equivocation. The first line in the Wikipedia entry on "Normative": "Normative generally means relating to an evaluative standard." Isn't that just what I said about how I used "standard"?

The problem which you seem to have, is accepting that there is a difference between a publicly stated "rule", and a principle which an individual applies in one's mind when making a decision or judgement. In order to have a proper understanding of language use, we need to maintain this distinction. The reality of this difference is what allows one to know the rule, yet act in a way which is inconsistent with the rule. When I explained this reality to you, you insisted that it's contradiction. But that's only because you do not heed the distinction, rather dissolving it and creating confused ambiguity.

How does the analogy fail? Moving pieces wherever you want, irrespective of the rules of the game, is not playing the game. — Luke

Right, in playing a game we must adhere to the rules with all moves. But in language we see competing rules which makes such a thing impossible, so we ought to drop the analogy right there. Instead, a multitude of games is proposed. However, a closer look at language use would reveal that it is shaped not by rules, but by freely chosen activities of free willing beings. Hence, what is basic or fundamental to the form which language takes, is not a rule governed structure, but the very opposite of this, activities which are free from rules. Therefore, if we adhere to the game analogy when trying to describe, or represent language use, our models will be completely backward. The game analogy represents language use evolving from fundamental rules (hinge propositions or whatever), building more and more rules on top of foundational rules, instead of modeling the reality of language, as a fundamentally free and lawless activity, free from foundational rules, from which rule structured activities may emerge.

How we employ an analogy, as a tool, is that we apply it until the point where it fails. Its failure, and how it fails, tells us something new, which we didn't already know, about the thing that it is applied to. We take a well known thing, and compare it to a lesser known thing, something we are trying to understand. Of course the two things will not be exactly the same. So when we get to the point where the comparison fails, and it can be carried no further, we have exposed the aspects of the lesser known thing which we do not understand. Now we can proceed toward understanding these mysterious aspects. But at this point we can no longer apply the analogy, so we must apply other principles.