Against is
In mathematics, the word is seems justified. Two plus two IS four and even God himself cant change that fact; Two plus two is four seems to live in its own pristine, immutable world, entirely beyond the reach of any outside power to change.
But things seem much different in the material world. An obvious illustration: a mirage seems to show the presences of water when no water is present. But the point goes much deeper than that because everything fallible human beings believe about the exterior world is liable to be wrong. For many centuries, Newtons physics seemed not merely a way of calculating observables but rather a fundamental FACT about the world. Force IS equal to mass times acceleration.
The fundamental problem with is seems to be the person using that word seemingly speaks with a god-like authority: force doesnt merely seem to equal mass times acceleration. Rather, force IS equal to mass times acceleration, and theres nothing you or me or God himself can do about it. It just IS.
So, my children ARE wonderful; democracy IS the best form of government; and, the all-purpose, it is what it is. Yes, it is what it is but, I maintain, it seems impossible for a mere human being to be certain of what anything is. So, it seems what it seems (to me) seems more fitting, seems closer to truth.
P.S. These thoughts were inspired by E-Prime.
E-Prime (short for English-Prime or English Prime, sometimes denoted É or E?) is a version of the English language that excludes all forms of the verb to be, including all conjugations, contractions and archaic forms. Some scholars advocate using E-Prime as a device to clarify thinking and strengthen writing. A number of other scholars have criticized E-Prime's utility.https://en.wikipedia.org/wiki/E-Prime
P.S.S. I once wrote a book mostly in E-Prime. Its available for free reading and download at
ScienceAsNaturalTheology.org
But things seem much different in the material world. An obvious illustration: a mirage seems to show the presences of water when no water is present. But the point goes much deeper than that because everything fallible human beings believe about the exterior world is liable to be wrong. For many centuries, Newtons physics seemed not merely a way of calculating observables but rather a fundamental FACT about the world. Force IS equal to mass times acceleration.
The fundamental problem with is seems to be the person using that word seemingly speaks with a god-like authority: force doesnt merely seem to equal mass times acceleration. Rather, force IS equal to mass times acceleration, and theres nothing you or me or God himself can do about it. It just IS.
So, my children ARE wonderful; democracy IS the best form of government; and, the all-purpose, it is what it is. Yes, it is what it is but, I maintain, it seems impossible for a mere human being to be certain of what anything is. So, it seems what it seems (to me) seems more fitting, seems closer to truth.
P.S. These thoughts were inspired by E-Prime.
E-Prime (short for English-Prime or English Prime, sometimes denoted É or E?) is a version of the English language that excludes all forms of the verb to be, including all conjugations, contractions and archaic forms. Some scholars advocate using E-Prime as a device to clarify thinking and strengthen writing. A number of other scholars have criticized E-Prime's utility.https://en.wikipedia.org/wiki/E-Prime
P.S.S. I once wrote a book mostly in E-Prime. Its available for free reading and download at
ScienceAsNaturalTheology.org
Comments (71)
3+1 "is" 4 but 3+1 "is not" 2+2
Added: "is" as used here is short for "is equal to".
Quoting Art48
Even in Math, one cannot state this in a general way. Two centimeters plus two millimeters do not equal four. (Four what?) They are just equal to "two centimeters and two millimeters". You can only add homogeneous things. Even if both centimeters and millimeters are units of distance, they are heterogeneous. In Math, they are called "incommensurable" (being of different kinds, degrees or dimensions).
(BTW, in Math it is always better to use the term "equals" than "is", since the latter has multiple meanings as I describe below.)
One has to differentiate between the different meanings of the word "is" ("be").
"Be" can mean exist, be present, take place, position in space, come from (some place). And of course, "equal", as described above. It can also refer to a condition or state, age, meaning/signification, attribute/characteristic, and more.
So, which of all of the above meanings of "is" are you against? (Re: "Against 'is'")
Quoting Art48
These refer to attributes you assign to persons and things. They are your opinion; part of your reality. They are true for you. How certain you are about them does not matter.
Outside you, things are what they are. (Re: it is what it is.).
This, depending on the context in which it is stated, it may be just an "empty" statement, meaning nothing in particular, or it may mean something like "be realistic", "try to see things as they are", etc. All of which are relative, indicative or figures of speech. Because no one can actually see things "exactly as they are". One can only do that on a scale: from falsifying facts, to being biased about something, to being honest and showing selflessness in one's judgment and behavior regarding something.
A classic example: "Please try to see me as I am".
So, I cannot see anything "against 'is'"! :smile:
Not to any competent language user.
And the problem doesn't go away when using other words instead of "is".
Because the problem isn't in the verb "to be", but primarily in the use of the indicative grammatical mood for making declarative statetments about other people and things.
To avoid the feel of speaking with god-like authority, one would need to speak in I-messages.
Only under the proviso that such a "competent language user" holds certain other beliefs.
Such as, "Whatever a person says is only their own opinion and not necessarily objective truth."
Quoting SophistiCat
I like psychologist George Kellys approach:
If I say "the floor is hard," I employ a language system in which the subject-predicate relationship inheres in the subject itself. It is the floor which is hard, and that is its nature, regardless of who says so. The statement stands, not because the speaker said it, but because the floor
happened to be what it is. The sentence's validity stems from the floor and not from the speaker.
Suppose our verbs could be cast in the invitational mood. This is to say that instead of being used in the popular indicative mood of objective speech, or in one of the other moods recognized by our language conditional, subjunctive, or imperative a verb could be cast in a form which would suggest to the listener that a certain novel interpretation of an object might be entertained. For example, I might say, "Suppose we regard the floor as if it were hard."
If I make such a statement I immediately find myself in an interesting position. The statement leaves both the speaker and the listener, not with a conclusion on their hands, but in a posture of expectancy suppose we do regard the floor as if it were hard, what then? A verb employed in the invitational mood, assuming our language had such a mood, would have the effect of orienting one to the future, not merely to the present or to the past.
Explain yourself. Do you have some special mathematical definition of "is"?
Quoting Alkis Piskas
Why introduce this non sequitur? "2 + 2" has nothing to do with "two centimeters and two millimeters". It's like saying "red and yellow make orange" must be false because "red firetruck and yellow car don't make orange anything". Category error.
If you still want to introduce mysticism into math, then what do you do with the sentence, "two centimeters and two millimeters is four units of length measurement"? Seems OK to me. So "2 + 2 is (still) 4".
(Next we'll have TPF worthies jumping in to claim zero is not a number, and lines are not made of points.)
I was referring to the general statement Two plus two is four, which is presented as if it is a law of the Universe (Re: "seems to live in its own pristine, immutable world, entirely beyond the reach of any outside power to change"). "Two and two" what? If the context of numbers were mentioned or if the statement were "2 plus 2 equals 4", then there wouldn't be a doubt. But it wasn't. Hence my example with centimeters and millimeters just to show why not any "two" can fit to this equation.
Is it more clear now?
There's a term I haven't heard in a good while. But I mentioned Korzybski's General Semantics only a few weeks ago, somewhere here...
"Is" in English has a few senses. Most folk can work it out from context. In logic it's parsed as "f(x)", "x=x" or "p?p" to great clarity.
Getting rid of it altogether is surely an overreaction.
No. It's still a category error. "Two plus two is four" clearly implies numbers. "Two" and "two centimeters" are not the same. Adding units (cm, mm) changes the sentence.
What is your definition of "is"? (asked Bill Clinton).
NIce.
Nothing special. The OP said:
Quoting Art48
This is commonly understood to mean two plus two equals four and not two plus two is the same thing as four. 3+1 "is" 4 in the sense of equals 4 but not that 3+1 and 2+2 are the same thing.
We could do without "is": 2+2=4, 3+1=4, 2+2=3+1.
So you've changed the meaning of "is" within a single sentence. Clearly 3+1 does not look like 2+2, but neither does it look like 4. To say "3+1 is 4" but "3+1 is not 2+2" is incoherent.
Wait. I think I've got it now. You're thinking of "4" as the name of a set whose elements include "3+1", "2+2", etc. So a better sentence would be, "3+1 is a type of 4".
But then is there another set called "2+2"? What belongs to it?
The comment seems irrelevant to this thread.
Quoting Alkis Piskas
I disapprove of statements that use "is" to purportedly make a statement about objective reality that hides the fact that the statement better qualifies as someone's experience of objective reality.
Quoting SophistiCat
There is some truth to your statement. (Notice how "is" makes that sentence about objective reality. I should have said "I partially agree with your statement.) So, if I say "This ice cream tastes good" most people know I mean "This ice cream tastes good to me." But someone might mistake "The floor is hard" as a statement about objective reality. See my next comment.
Quoting Joshs
"The floor is hard" is a statement about objective reality. Compared to a diamond, the floor is soft. Compared to neutron stars the floor isn't much more than a wisp of smoke.
Quoting Banno
Agree. But being aware of how "is" tends to remove the speaker from the statement so the statement appears to be objective reality seems reasonable.
I haven't changed anything. "2+2 is 4" never meant anything other than 2+2=4. The point of saying that 3+1 is not 2+2 was to indicate that "is" means equal and not the same thing
Quoting Babbeus
Exactly, only we don't even need to expressly qualify statements as uncertain - we only do that occasionally for emphasis. Otherwise, language norms, context and tone do the job for us.
(Not all languages even employ "to be" the way English does. In Russian, for example, you would say something like "Floor - hard.")
The thread is about the use of the term "is". You start with a mathematica example, but "is" as it is used here simply means equal to.
Rather than:
Quoting Art48
you could say: force equals mass times acceleration.
Or are you objecting to this as well because it seems to confer godlike authority?
Object is too strong a work. Certainly, the world will continue using "is" as it has in the past. But, yes, "force equals mass times acceleration" is a statement about objective reality when in actuality it is what we believed before Einstein.
You are aware that 2+2 = 3+1 ?
Agreed that "2+2" is not the same thing as "4" - one requires three keystrokes, and the other just one. So if "is" means equals (as you say), how can you claim "3+1 is not 2+2"?
You want to find mysticism here. I stand by my claim : you are playing fast and loose with your definitions.
Let me see if I understand this. Youre making a distinction between the legitimate use of the word is to make a statement about objective reality vs the use of the word is to state a subjective preference, and your only concern here is with confusions between the two contexts that result in a subjective use of is appearing to be an objective use?
Of course!
Quoting Real Gone Cat
If we are given 4 donuts and I take 3 and give you one, you might complain that is not fair. Would you be satisfied if I defended this by saying that since 2+2 is 4 and 3+1 is 4 then 3+1 is 2+2? Or would you say, as I did above that:
Quoting Fooloso4
Wow. I encounter so many people on TPF who do not know basic math, it's striking.
By your logic, if you kept all 4 donuts, that would be different from sharing them out 3 for you and 1 for me. So I guess 3+1 is NOT 4 after all!!!
You are right about rejecting objective reality, because it doesn't exist.
@Bartricks?
Quoting Art48
What I would say is
1. Not that force is mass times acceleration (metaphysics)
2. But that force is equal to mass times acceleration (mathematics)
As a mathematician I must object to your example though. Saying 'two plus two is four' rather than the more formal 'two plus two equals four' will often lead to confusion. We just don't need 'is' in that context and it causes trouble if we do use it. The word 'equals' in mathematics conveys a relationship with a precise meaning that differs from that usually attributed to the dreaded verb 'is'.
I have worked on minimising my use of the the verb 'to be' over the past few years and find it a really helpful discipline, with profound benefits. It keeps you humble because you have to speak in terms of how things look to you, rather than making godlike pronouncements about the nature of the world.
It also encourages the use of active voice over passive, a very popular theme in the plain english movement that I really like.
Some uses do no harm, such as a prefix to the present participle - "I am thinking" - and even allow nuances not achievable in strict e-prime. Using it to express category membership (attributing properties) also seems harmless to me, and shorter than the e-prime alternative. Only the 'identity' and 'existence' uses cause serious trouble. I have seen and participated in several different lively debates on here over whether saying 'the cup is in the cupboard' means anything more than that if I look in the cupboard I'll probably see a cup.
And while I use the active voice, e-prime version in most cases, sometimes it seems wiser to use the passive. Unless one especially wants to chastise Niruba, one can get a better outcome from the diplomatic "Oh dear the door was left open and a cold draft is coming in" than "Niruba why did you leave the door open?" [again! you dolt!]
Some ontologists won't like you if you spruik e-prime, since it presents a direct threat to their favourite activity.
I find some parallels between an e-prime way of thinking and American Pragmatism - a philosophy that I also like.
As a mathematician, I have to know : why do you think that saying two plus two is four will lead to confusion? How might one misconstrue is?
There appear to be two uses of is in mathematics
What else is there?
I breathlessly await your reply.
Correct.But I'll add that I consider many apparently objective statements to be subjective.
Example: "The cat is on the table" -> "I see the cat on the table"
Quoting andrewk
Good point and good response overall. Do you have a better example of a truly objective statement?
What about "There is no largest prime number"?
I consider that as a genuine objective statement (that is true).
Quoting andrewk
I think attributing properties can be problematic, too, as in "That is a good movie"
But maybe attributing to myself is OK. "I am feeling happy"
Quoting andrewk
Yes. I think the book I wrote in mostly E-Prime is a better book than it would have been otherwise.
But sometimes E-Prime seems awkward. For instance, the last sentence could have been
Yes. I regard the book I wrote in mostly E-Prime as superior to what I might have written otherwise.
Open question: Does the E-Prime attitude better accord with quantum mechanics in that, under the Copenhagen Interpretation, QM tells us what we will see if we measure rather than what IS happening when we aren't measuring. (On the other hand, Bohmian Mechanics does tell us what is happening.)
You have completely missed the point. It is not about the math. It is about the word 'is'. The sum of 2+2 is 4, the sum of 3+1 is 4, but 2+2 is not 3+1.
If 2+2 is not 3+1 simply because they represent different partitions of 4, then 2+2 is not 4 either.
If 2+2 is 4 because they have the same numeric value, then 2+2 is 3+1.
The only way I can make any sense of what you're saying is to assume that you are thinking of "4" as the name of a set to which distinct elements 2+2 and 3+1 belong. But does 4 belong to "4"? Then 2+2 is distinct from 4 and clearly 2+2 is not 4.
You are catching on. The sum of 2+2 is (equal to ) 4.
Quoting Real Gone Cat
Here we get into the question of number theory. The most important contemporary work on this is Jacob Klein's "Greek Mathematical Thought and the Origins of Algebra". Numbers are often treated as abstract entities, but for the Greeks a number tells us how many. It is always a number of something, of some unit, the unit of the count.
Klein worked with Husserl on this. It is not simply a historical study of an outmoded way of thinking about numbers. The claim is that something is lost when we treat numbers symbolically.
When you shift from thinking about numbers as abstract entities to counting then it becomes clear why 2+2 and 3+1 are not the same. Any child who learns math using manipulatives knows this. If I have 3 units, donuts or dollars and you have 1, that is not the same as each of us having 2. If I have 10 dollars and you have 10 cents, we each have 10 of something but not the same thing. The numerical value is the same but 10 dollars is not 10 cents.
You have stated, over and over, that "2+2 is 4" and "3+1 is 4". Without qualifying the "is". Go back and check.
Now it's some great revelation that 2+2 is NOT 4 ?
In math, we call what you're referring to partitions. But unless you and your audience already know that you are talking about partitions, no one - NO ONE - would say "2+2 is not 3+1". Especially after having claimed "3+1 is 4".
Except the mystics on TPF. You're always searching for the woo.
So from now on, when discussing numbers, we know that "is" refers to partitions. Got it.
Oh, and your last paragraph? A total non sequitur.
At the risk of sounding like Bill Clinton, the question is what is is. It is the OP that stated 2+2 is 4. What I said in my first response was:
Quoting Fooloso4
and in the next:
Quoting Fooloso4
Quoting Real Gone Cat
It is not a revelation, it is a clarification on what it means to say that 2+2 is 4. The OP contrasts mathematics and "the material world". But this is to treat numbers or arithmetic (Greek ??????? - arithmós, meaning number) as an abstraction. While there are certainly advantages to this, we should not lose sight of the fact that a number still retains its original meaning, that is, it tells us how many of something. And what that something is is not first or foremost abstract units.
Quoting Real Gone Cat
You seem to have no idea what I am referring to. Let me try one more time. If I ask how many, in order to answer you will have to know how many of what. You have to know what it is that is being counted. If you are to count how many apples, the oranges do not count. If you are counting pieces of fruit the fruit flies do not count.
Once again, the division the OP makes is problematic. Our concern is not simply with numbers as abstractions, but with the question of how many of something. Knowing that 2+2=4 is of limited interest unless we are talking about 2+2 of something or other, that is, we are still within the material world. You cannot make an apple pie with oranges. Although two plus two equal four, two apples plus two apples do not equal four oranges
So you want to take math back to pebble counting. Okay, let's try a thought experiment. If you hold a donut and someone hands you another donut, do you have 1+1 or 2 donuts? Does holding them in one hand or in separate hands matter?
You're using "is" to refer to the partitioning of sets. And now that I know, I'm fine with it. But we could have avoided any confusion if you had said from the beginning, "2+2 and 3+1 are different because they break up the number 4 in two distinct ways".
Nope.
It is a matter of ontology.
Quoting Real Gone Cat
Can you count? Maybe you do need pebbles or some other manipulative.
Okay, let's try a thought experiment. If you hold a donut and someone hands you a dollar do you have 1+1 or 2?
Quoting Real Gone Cat
Do we need to go over this again? I am using "is" as it is typically used, short for is equal to.
Quoting Real Gone Cat
That is one way of looking at it, but you are still treating numbers as abstractions, as symbolic entities. If I have 3 of something and you have 1 this is not breaking up the number, it is breaking up whatever it is we are counting.
This might help you see what is at issue: It is a review of Klein and Husserl's work on mathematics: https://ndpr.nd.edu/reviews/the-origin-of-the-logic-of-symbolic-mathematics-edmund-husserl-and-jacob-klein/
It begins:
A bit further on:
[quote]Specifically at issue is Husserl's expressed concern over the loss of an "original intuition" to ground symbolic mathematical science, and the consequent breakdown of meaning in that science. For the Husserl of Crisis, the history of this breakdown consists of two stages. First is the geometrical idealization of the world via what he terms "Galilean science" (taken as a kind of collective noun). Second is the formalization of that science by means of symbolic algebra, which latter surreptitiously substitutes symbolic mathematical abstractions for the directly intuited realities of the real world ("life-world"). In the face of such loss of meaning, which fundamentally determines (and threatens) modern western civilization in the modern scientific age, the urgent task of philosophy is to bring to light or to "desediment" (so Hopkins) the historically accreted, and by now almost entirely occluded, original meaning constituents of the concepts of modern mathematical science, so as to recover and reactivate the authentic sense of these concepts./quote]
Husserl and Klein want to take math back to pebble counting. And you have apparently joined in. Good for you. I'm not an intuitionist and have no interest.
You object to my 1+1 vs. 2 example. I assume you think you're holding 2 donuts. But why does handing me one turn it into 1+1? What if we are holding the donuts so that they are touching?
If 4 people each hold a donut, you would say that that is different from 1 person holding all four (1+1+1+1 is not 4). But what if 2 of to them live in Paris an 2 in New York? Isn't that 2+2?
If I'm holding a donut and a dollar, the cardinality of the set of objects I'm holding is 2. You seem incapable of accepting a set made up of disparate objects.
You clearly have not understood them or more likely did not even take the time to read the review.
Instead of snide remarks that make you feel superior because you can like any competent school child, look up who Husserl and Klein are and the importance of their contributions.
This is a philosophy forum. Ontology is of central concern. Adding is not.
From the blurb you provided
and
What are "directly intuited realities"? Could it include pebble counting? Apparently, abstraction is the devil's work (and thus Kronecker hounds poor Cantor into depression).
If you're not too furious, please check out the next post.
I have been giving this some thought. Our debate has nothing to do with the word "is", it's with the word "plus".
I realized I have no idea what you mean by the + symbol. It could indicate the addition of numbers as in arithmetic (this seems unlikely given your rejection of "is" meaning "equal to"). It could indicate the cardinalities involved in the union of disjoint subsets (although you seem to recoil at the notion of partitions). What is your definiton of "plus"?
Then questions follow
Let me know. Hope you're not too angry.
A math joke to lighten the mood ...
A biologist, a physicist, and a mathematician are sitting on a bench across from an apartment building. They observe two people enter the building. Five minutes later, three walk out. How does each react?
It is more far reaching. A count it related to the idea of giving an account as well as the question of what is to count, that is, not what it is to count but what counts. There is also a connection with logos in its original sense of gathering together. There is also the question of the 'one' and the 'one and the many', which plays out in various ways in Plato and Aristotle.
Aristotle says that two is the first number. One is not a number, it is the unit (the one) of the count. We count "ones". This is why the question of how many must address the question of how many of what. We can still see this in that when we say that there is a number of things we don't mean one thing.
Plato says that the Forms are each one. Each is distinct and unique.
Well, it started with "is", but in order to see why I would say the 3+1 is not 2+2 I raised the question of what a number is. As abstract entities 3+1 and 2+2 might be regarded as the same since both equal 4, but when we shift to the "material world" other things come into consideration.
Quoting Real Gone Cat
No, just the opposite. What I said, several times and from the beginning is that:
Quoting Fooloso4
Is means equal to.
Quoting Real Gone Cat
Not at all.
Your joke kind of points to what I am getting at.
Gotcha. But we've moved on from the ancient Greeks' weird take on numbers. Now we accept that one is a number, and so is zero. So are negatives, and irrationals, and imaginaries, and transcendentals. (By the way, "number of things" is a metaphor.)
Math left the Greeks behind a long time ago. Their contributions were incredibly important but eulogizing their achievements sometimes led to misunderstandings or wrong turnings. Look at how clinging to Euclid's fifth postulate held back geometry.
Not every pronouncement by Plato and Aristotle should be held up as exalted. Aristotle thought women had fewer teeth than men.
Finally, I believe very few mathematicians today belong to the intuitionist school of thought.
So "is" means equal to. Unless it doesn't. I'm sorry, but that's incoherent. If "is" means equal to, then 3+1 is 2+2. If "is" doesn't mean equal to then you need to define it as more than "looks like".
And I ask again, what is your definition of "plus"? Is it commutative? Does it have an identity element? Does it allow for inverses (i.e., negatives)? Is it mathematical at all?
You've evaded many of my questions (or shrugged them off with a "that's obvious!" argument). I want to go back to an earlier question. If you are holding a donut in each hand, is it 1+1 or 2? Why does handing me a donut matter?
Right.
Quoting Real Gone Cat
The sum of 2+2 is equal to the sum of 3+1. This much we agree on. But sum totals are not the only thing at issue.
If I have 3 dollars and you have 1 dollar that is not equal to me having 2 dollars and you having 2 dollars. In that case we do not each have an equal amount of dollars. In that case 3+1 is not 2+2.
This is so basic I am surprised you do not understand it. Most children would immediately recognize that one person having more and the other less is not an equal amount.
The problem is your definition of "plus", and you won't answer me. To be generous, I think you mean something like "3 things over here and 1 thing over there" when you say "3+1". But that's called partitioning in math.
What we've arrived at is this: sometimes "is" means "is equal to", and other times "is" means "is the same partition as". When you say "3+1 is 4", you mean "3+1 is equal to 4". When you say "3+1 is not 2+2", you mean "3+1 is not the same partition of 4 as 2+2".
My contention - stated in an earlier comment - is you can't switch between meanings in the same sentence. You can't say, "3+1 is 4, but 3+1 is not 2+2", without sowing confusion. No one will understand you. I don't know why you can't see this. It's like saying, "Bill cans peas, but Sally cannot peas". It's nonsense.
You still don't get it. Time for me to move on.
There's yet another issue with taking "is" as something like "is the same as" in the most general sense.
"3 + 1" and "4" are obviously different expressions. So, to say that "3 + 1" is "4" must not mean they're the same expression, only that they have the same value. You'll agree with that, I assume. So our equals sign doesn't mean "is the same as" but only "has the same value as".
The reason that's interesting, to some philosophers, is because it means that "3 + 1 = 4" can be informative. "4 = 4" might also be informative, but what "4 = 4" tells you, that 4 is equal to itself, is different from what "3 + 1 = 4" tells you. But in mathematics we are authorized to substitute equals for equals anywhere and always: "3 + 1 = 4" is also a substitution rule, so anywhere you see "3 + 1" you can substitute "4" without changing the truth-value of your equations.
But even though you're not changing the truth value of the equation, you're changing something, else "3 + 1 = 4" would say the same thing as "4 = 4", and there's clearly a sense in which it doesn't. Frege's solution to this little puzzle was, roughly, that "3 + 1" and "4", seen as expressions rather than as values, have a sense as well as a reference: they both refer to the same value, 4, but in different ways. On such a scheme, "3 + 1 = 4" informs you that these two different expressions have the same value, and you have to be told that because expressions have a sense as well as a reference, and the sense of "3 + 1" is different from the sense of "4".
If you don't have some such scheme, you have to have some other explanation for what we're doing when we teach someone mathematics. How is that someone could know that "3233 = 3233" but not know that "53 * 61 = 3233"?
Again, the problem I have with Foolos4 is switching between meanings of "is" in a single sentence. You shouldn't say, "3+1 is 4" AND "3+1 is not 2+2" in the same sentence. Either they're both "is" or they're both "is not".
Taking it a bit further : I concede that 3+1 and 2+2 can have different meanings. We teach children that 3+1 and 2+2 are different ways to arrive at 4 (called partitions when we get to advanced math). But once you're above the age of 8 (or so), to hear someone say "3+1 is not 2+2" is going to be problematic. The speaker is then going to have to explain, "Oh, I meant splitting 4 things into 3 and 1 is different from 2 and 2". The speaker can't just say, "Come on, it's obvious!" (or assume the listener will have Frege's notions of sense and reference instantly leap to mind). And the reason is we learn to associate "plus" with addition, and "is" with equal-to when numbers are being used. A better sentence would be, "3 and 1 is not the same partitioning as 2 and 2".
This looks like an interesting read. I will give it a go. Thank you for the link, and the effort it must have taken to put this together.
The point is that it should not be taught that 2+2 "is" 4. That is the point of my seemingly contradictory or paradoxical statement. 3+1 "is" 4 is generally unproblematic when it is understood that what is meant is "is equal to", but when it is taken to mean something like "the same as" or "one and the same" confusion can arise. 3+1 is not the same as 2+2.
My second post, which was a response to you:
Quoting Fooloso4
Quoting Real Gone Cat
You mean like when I said?:
Quoting Fooloso4
I suspect that what is really at issue can be found in remarks such as the following:
Quoting Real Gone Cat
And:
Quoting Real Gone Cat
And again to someone else:
Quoting Real Gone Cat
And yet again:
Quoting Real Gone Cat
At least with regard to this discussion you seem to see what is not there and fail to see what "is".
Only to someone in a position of power.
For everyone else, might makes right, and one must hold as true whatever the person says who holds more power than oneself. Or else, face socioeconomic consequences.
1. The predicative sense is of the form "x is F" where F is a property that x bears.
Example: The apple is red.
Logical form: Ra
2. The identity sense is of the form "x is y" where x and y are identical, they're the same thing.
Example: Superman is Clark.
Logical form: s=c
This also means that when counting, we'd not count Superman & Clark as two different people, for they're one and the same, and that they have the same properties.
3. The existential sense is of the form "There is x" which we just assert the existence of something.
Example: There exists an apple.
Logical form: \Existential-quantifier x x=a
This is philosophically controversial: certain Meinongians as well as proponents of free logic alternatively propose an existence predicate, though this comes with its own set of nasty problems.
It is interesting to consider why. It appears that one of the senses of to be tells us the WORD 4 is sufficient to tell us about 3+1 and 3 plus 1 things are sufficient to give you 4 things. Perhaps thats all one of the uses of to be is.
Aristotle would equate this to the formal cause (Ive written about this elsewhere). I suspect the four causes of Aristotle are a relationship between the WORD for something and then the thing in the world, rather than just between two things. In this case 4 is the cause and 3+1 is the effect.
There appear to be four permutations that words can map onto things in a sufficient/not sufficient way and I think thats all the four causes are.
Two are to be in English,
One is to mean in English.
One is to cause in English.
Its a bit of a pet theory, theres more in that other thread: https://thephilosophyforum.com/discussion/13583/is-causation-linguistic-rather-than-in-the-world
b) 4 is even
The Temperature Paradox
1. The temperature is 90
2. The temperature is rising
Ergo,
3. 90 is rising
:snicker:
90 is sufficient to tell us about the temperature, but the temperature is not sufficient (but can potentially) give us 90 (temperature)
rising is sufficient to tell us about the temperature, but the temperature is not sufficient (but can potentially) give us rising (temperature)
So thats not the same as the 3+1 is 4 which is the word 4 is sufficient to tell us about 3+1 and 3+1 ARE sufficient to give you 4.
Theyre both two of the four permutations but theyre quite different.
Quoting Art48Apart from liable being too strong an word, there is also the implicit assumption that if it is true that we are fallible, it does not necessarily follow that we should quasi-assert things in all cases.
Quoting Art48
Do they seem that way? Does seeming count for seeming? Maybe this is one of those fallible ideas?
We often think that seem makes less of a claim than an is statement. But it is and is statement. It claims that something appears to be the case, but we don't know. That's also an is claim, while a subjective one. It's a claim about a subjective experience - and we can be wrong about those. It also universalizes that claim about appearances. (I did notice that you qualified some of the 'seems' statements with 'to me' )Quoting Art48I don't think this is true. I don't think it seems that way. Though sometimes when I here 'is' statements it does.
Further 'the fundamental problem' part of the sentence has an implicit is. What the fundamental problem is seems to be...that there is a fundamental problem and certainly that there is a problem is presumed. Yes, one could further amend this statement....What seems to be a problem and further seems to be the fundamental one ....' But I think we end up with a kind of infinite regression, especially given my argument about 'seems' being a kind of is claim. This may be handled elegantly in Eprime, I don't know.
Also this seems to be viewing language as a container for truth period. My sentences will contain truth and convey this to others. I think that is a very limited view of language and it reminds me of Reddy's Conduit Metaphor essay.....
https://www.reddyworks.com/the-conduit-metaphor/original-conduit-metaphor-article
Further, what is the clearest sign we are dedicated to an 'is'?: how we live, I think. If one shifts one's use of language to Eprime and is critical of the use of English, one is living as if 'is' is a problem. And one is communicating to others and perhaps, if one gets what one wants, changing how they live. In the end, I can't really see how it matters. Is is getting affected by my choices.
Last, when we act in the world, it is often beneficial to act like something is. Not to act like it merely seems. It could be is but we act like it seems. It's not a good strategy for taking shots in golf. It might be ok leading up to the swing, but not for the swing itself. You don't want some qualifier in the air during that swing.
And I suppose as a side note, I am not sure amending language changes our basic is attitude. I imagine some arguments degenerating into 'well, you certainly seem to me to be being a real a______.' 'That seems typical of you.' Eprime merely lacking is may get around this somehow but my guess is that the implicit is will still be there.
Telling a kid he is behaving 'unharmoniously' may seem to avoid the kinds or moral judgment that he is naughty includes. But I suspect that the kid called the former feels pretty much the same. (this was not an example of replacing is with seems, but rather using a different kind of language shift that (in my opinion) fails because the humans means, in the end, the same thing at root, despite the surface change.
I'd say we cannot be wrong about subjective experience but we can be wrong about how we interpret it. For example, "I see water" may be an erroneous interpretation of a mirage. We can be certain of our experience (phenomena) but we cannot be certain as to its cause (noumena).
Quoting Bylaw
I believe we habitually use "is" language. Changing language and the way we think about "is" may or may not have any practical benefit but I find more accurate language desirable in any case.
And if that seems strange, I think it is important to remember that we are not monads. We are complicated and thinking of us as having parts, cognitive,subjective parts, can be a very useful model. That something seems like X to part of us but Y to another part or yet another now in control would rather not accept what it seems like to that first part of us.
3) there's the brute ontological issue deciding that seeming is always what we think it is. That may seem obvious, but seeming is a part of reality also. So, what we are claiming is that there are these perceptions about what are outside us, and these can be fallible but what is inside us, our subjective experiencing, that we can be sure of. And we can be sure that we are not fallible introspectors, that we are not interpreting incorrectly our perceptions of our internal reactions and so on.
I think that's an extremely strong claim. Think about all the motives for not noticed how we actually are experiencing ourselves our internal states our perceptions.
And from there you get an infinite regress. Where we must express ourselves that it seems like it seemed like......
Quoting Art48Desirable to whom? How do you find it this way? What was your process for determining it is more desirable and cannot this process also be fallible?
Agree. As optical illusions demonstrate, for instance, the Adelson's Checker-Shadow Illusion.
Bylaw: So, what we are claiming is that there are these perceptions about what are outside us, and these can be fallible but what is inside us, our subjective experiencing, that we can be sure of. And we can be sure that we are not fallible introspectors, that we are not interpreting incorrectly our perceptions of our internal reactions and so on.
Id say we are fallible as to interpretation but infallible as to our input sensations: I may wrongly think I see water but if I am experiencing light then I am experiencing light. Even if I am hallucinating the light, I am still experiencing and cant be wrong about the fact that I am experiencing. Its like if I say my arm hurts (and Im not lying) then I cant be wrong about the fact that I am experiencing sensations of pain that seem to be originating in my arm. Ive read that amputees sometimes have phantom pain in lost limbs. So I may be wrong that my ARM hurts (if, for example, Ive lost that arm) but I can be wrong about the experience of pain I feel.
Bylaw: Desirable to whom? How do you find it this way? What was your process for determining it is more desirable and cannot this process also be fallible?
If it is agreed that changing our language more accurately represents the world (an idea you may reject), then changing language is desirable if we are concerned about accuracy. However, I dont mean to claim that we become infallible if we change our language.
I didn't take it that way. What I meant is that it can be beneficial to be blunt and certain in many situations, rather than more cautious formulations, EVEN IF we are fallible. So, how do know that even if it is more accurate it is better to have a language that no longer includes this kind of ontological certainty.
As far as the rest, I understood or assumed that you thought our assessments of our subjective experience must be accurate. But I address my skepticism about that in my previous post. Could you respond to those`objections`?
"90" is only sufficient to tell us about 90 of something, something yet unclarified.
90 degrees celcius or 90 degrees kelvin, now that tells us about temperature. Both very different temperatures at that.
Quoting invizzy
"Rising" is sufficient to tell us that something is rising: an idea is rising in my awareness, a boy is rising from bed, a loaf of bread is rising in the oven, the cost of living is rising.
"Rising" alone like "90" - not qualified, means very little informationally.
3 and 4 on the other hand are discrete in meaning as numbers. They don't require further qualification when used exclusively for maths. When using concepts outside of maths on the otherhand we must qualify what those numbers pertain to.
So maths and semantic languages are not the same. One (maths) is objective, the other (spoken language) is open to interpretation unless qualified exactingly.
Thus should dissolve the contradiction you're inquiring about.
And that we are. If not in potential alone then act. Error must exist in some format/manner so that truth may exist by proxy.
I think that "sufficiency" and "neccesity" can be synonyms for one another.
They need not be two things but rather one thing.
What is "true" for example is sufficient for it to be true, and neccesary for it to be "true".
For example it is sufficent for one to pee after drinking water - to meet a requirement, that the body's fluid intake and fluid loss are equal, and it is neccesary - to meet that requirement, hence it is sufficient for the purpose.
Is what? Wait for it...
Quoting Art48
Nice punchline. N-Prime is what we call the version that excludes all proper names. Your turn.