CreateDebate is a social debate community built around ideas, discussion and democracy.
If this is your first time checking out a debate, here are some quick tips to help get you started:
Arguments with the highest score are displayed first.
Argument replies (both in favor and in opposition) are displayed below the original argument.
To follow along, you may find it helpful to show and hide the replies displayed below each argument.
To vote for an argument, use these icons:
You have the power to cast exactly one vote (either up or down) for each argument.
Once you vote, the icon will become grayed out and the argument's score will change.
Yes, you can change your vote.
Debate scores, side scores and tag scores are automatically calculated by an algorithm that primarily takes argument scores into account.
All scores are updated in real-time.
To learn more about the CreateDebate scoring system, check out the FAQ.
When you are ready to voice your opinion, use the Add Argument button to create an argument.
If you would like to address an existing argument, use the Support and Dispute link within that argument to create a new reply.
Sorry, the correct quote is "things which are equal to the same thing, are equal to each other", just to clarify a bit. Please ignore the "all" in the initial quote, it is inaccurate to the original quote.
That changes everything. You would have a tough time convincing me that all things are equal to each other without using very specific definitions. But the idea presented in the revised quote seems acceptable and mathematically accurate.
That doesn't actually work. In math we can switch the numbers on either side of the "=" and it doesn't matter. In this instance it makes a huge difference how you read the statement.
A is B, B is C, so A is C works just fine.
Apples are fruit works.
Fruit are cherries doesn't even make sense. It would read something like "all fruits are cherries."
So there's an obvious logical contradiction in saying "Apples are a fruit" and then "All fruits are cherries," which is basically what "Apples=fruit; Fruit=Cherries" means when not read like a math equation
The contention that "all fruits are cherries" is incorrect is true. This is because there are other types of fruits besides cherries. Oranges and kiwi are examples. The claim that "all fruits are cherries" is false. As a result, the proposed example involving apples, fruits, and cherries is not a valid one to illustrate the truthfulness of the quote in the physical world.
I think the following is a valid example that shows the truthfulness of the quote in the physical world:
Mario Brothers is a game.
Tetris is a game.
Pokemon is a game.
Therefore, Mario Brothers is the same as Tetris and Tetris is the same as Pokemon insofar as they are all games. In other words, these objects are the same thing when we only consider their identity as games or not-games (excluding all of their other characteristics).
False. Determinations of equality are always disproven when tested with adequately precise instruments. I find the concept of equality (the assumption that there are equal things) to be an unacceptable axiom or first principle and more or less illusory.
Determinations of equality are always disproven when tested with adequately precise instruments.
The question, sir, was not "are measurably distinct quantities equal to one another?"; the actual question addressed Euclid's first common notion. It is pointless to bring measured data to a discussion that lies within the realms of Platonic Idealism.
I am attacking the notion of equality itself. I have no reason to believe that any two things are truly equal in value. How else should I illustrate that equality is an illusion?
And then, sir? Did you fall through the floor also?
I can describe a difference wherever none are supposed
I suppose there to be no difference between the lengths of two consecutive wavelengths of a single ray (or, to satisfy the corpuscular theory, one oscillating photon) of monochrome light, passing through an unoccupied region of space, and subject to no unbalanced forces. I also suppose that, if two such rays were to be emitted simultaneously from a single source, the energy of their waveforms would be equal.
And then, sir? Did you fall through the floor also?
On occasion
I suppose there to be no difference between the lengths of two consecutive wavelengths of a single ray (or, to satisfy the corpuscular theory, one oscillating photon) of monochrome light, passing through an unoccupied region of space, and subject to no unbalanced forces.
One difference between what you suppose and what occurs in "non-imaginary" scenarios is that the sources of the radiance are in flux, affecting the wavelength.
I also suppose that, if two such rays were to be emitted simultaneously from a single source, the energy of their waveforms would be equal.
Your imagination assumes "a discrete unit" you refer to as "a single source", with which objective conditions do not comport
And was either the position of the floor or chair affected by these evolutions?
One difference between what you suppose and what occurs in "non-imaginary" scenarios is that the sources of the radiance are in flux, affecting the wavelength.
But at any instant along its plane of motion, or planes of motion, the wavelengths of a ray of monochromatic electromagnetic radiation, will be the same, if they occupy the same medium.
Now, if you must have something which does not vary with time (much as I hate the concept of time), then I shall refer you to the energy levels which electron must occupy, as they orbit (not that we can certainly say that they do orbit - Heis.) a nucleus. It is known, that any two electrons, occupying the same energy level (and, if you like, the same orbital) must be imbued with identical energies for as long as they are so positioned.
Your imagination assumes "a discrete unit" you refer to as "a single source", with which objective conditions do not comport
If a transverse wave is generated by the excitement of any source (but, for the sake of simplicity, let us say a hydrogen discharge tube), then It is counted as a single source. Obviously, a minute inspection reveals that there are in one source of light, immense numbers of individual sources (in this case, hydrogen atoms, or more accurately the electrons about them), but the former is the traditional nomenclature.
Incidentally, the electric charges of the electron and the proton about and within, respectively the nuclei of those atoms, are equal in magnitude.
And was either the position of the floor or chair affected by these evolutions?
I suppose the paths of the components of the chair and floor were affected less by these events than others
But at any instant along its plane of motion, or planes of motion, the wavelengths of a ray of monochromatic electromagnetic radiation, will be the same, if they occupy the same medium.
Your idea of an instant is based on an imperfectly precise estimation, just like in any instance where equality is asserted. The equality you suppose is entirely subject to your estimates inaccuracies.
It is known, that any two electrons, occupying the same energy level (and, if you like, the same orbital) must be imbued with identical energies for as long as they are so positioned.
Concepts of adequate balance can allow for yet to be quantified differences. If you presuppose the absence of such differences it is due to excessive trust in your imprecise instruments of measurement.
If a transverse wave is generated by the excitement of any source (but, for the sake of simplicity, let us say a hydrogen discharge tube), then It is counted as a single source. Obviously, a minute inspection reveals that there are in one source of light, immense numbers of individual sources (in this case, hydrogen atoms, or more accurately the electrons about them), but the former is the traditional nomenclature.
That's just a fancy way of saying it's ok to take things out of context :)
Incidentally, the electric charges of the electron and the proton about and within, respectively the nuclei of those atoms, are equal in magnitude.
You seem to suppose (sans evidence) that currently immeasurable differences are wisely hid behind the symbol "=".
I suppose the paths of the components of the chair and floor were affected less by these events than others
But they were affected, yes? I only ask, because I am intrigued at the prospect of having discovered a material object which allows matter to pass through it, without generating a normal force.
Your idea of an instant is based on an imperfectly precise estimation, just like in any instance where equality is asserted.
I find it difficult to discern, what the phrase emboldened above imports. Indeed, I shall quote Boswell: "The learned society, under whose sanction this gabble is ushered into the world, would do well to offer a premium to any one who will discover its meaning". I am tempted to call him Cronus, whose conception of time, though not expressed, is so vastly more advanced that mine own.
Now that I have given the phrase the ridicule it so thoroughly deserves, I shall give it "a wholesome answer". Rather than address the issue, which is that monochromatic waveforms can be observed to move, and that their wavelengths are instantaneously identical, you have, to support your pseudoscientific hypothesis, decided to mutter some nonsense about the imprecision of my estimates. I have made no estimate; for I have made no attempt to quantify an instant. Indeed, as I hold an instant to be a circumstance in which time does not apply at all (being suspended), your argument is invalid.
The point, which it seems has eluded you (or, perhaps, which you have eluded), is that, notwithstanding the evolutions of time, the wavelengths within a ray of monochromatic light, instantaneously, within one medium, et cetera, are equal.
Or, to satisfy the corpuscular model, the energies of the photons within a ray of monochromatic light, are equal to one another.
Concepts of adequate balance can allow for yet to be quantified differences.
This is unscientific drivel. It equates to "I have not yet measured a difference, but contrary to what I have observed, I shall believe a model which allows for them".
If you presuppose the absence of such differences it is due to excessive trust in your imprecise instruments of measurement.
The basis of your entire argument, is that "imprecise instruments" have measured differences between quantities which had been supposed to be equal. I do not deny, that our instrumentation is imperfect, but I do demand that you hold yourself to the same standards to which you would have me adhere.
That's just a fancy way of saying it's ok to take things out of context :)
No, sir, it was merely intended to dismiss a semantic argument which had not place in this dispute.
You seem to suppose (sans evidence) that currently immeasurable differences are wisely hid behind the symbol "=".
What evidence do you present, which suggests that the two are unequal? All of the evidence which does exist (most saliently, the predictability of ionic bonding, the neutrality of atoms, the decay of radioactive isotopes et alia), proves that the proton and electron have charges of equal magnitude.
And I suppose no such thing. I do not suspect, that there are any differences hidden behind the symbol of equality. Such an opinion would be contrary to the one which I have expressed.
But they were affected, yes? I only ask, because I am intrigued at the prospect of having discovered a material object which allows matter to pass through it, without generating a normal force.
Have you considered that there could be no generation of energy going on in such situations, only transfer of energy.
I find it difficult to discern, what the phrase emboldened above imports.
So then show your class by attempting to ridicule what you don't understand why don't you
Indeed, I shall quote Boswell: "The learned society, under whose sanction this gabble is ushered into the world, would do well to offer a premium to any one who will discover its meaning".
I shall quote myself: "Parroting intelligentsia does not make you a member, merely a tool"
I am tempted to call him Cronus, whose conception of time, though not expressed, is so vastly more advanced that mine own.
If one cannot handle having it -rather simply- pointed out that they deal in estimations without making a disingenuous pseudo-intellectual sarcastic reference, they just might be a little too concerned with the level of advancement of one their fantasy RPG characters
Now that I have given the phrase the ridicule it so thoroughly deserves, I shall give it "a wholesome answer".
Says the bloke who feigns to understand the complex while still struggling to understand the simple.
Rather than address the issue, which is that monochromatic waveforms can be observed to move, and that their wavelengths are instantaneously identical, you have, to support your pseudoscientific hypothesis, decided to mutter some nonsense about the imprecision of my estimates.
I find it funny that you act like an authority on what's scientific and whats pseudo-scientific, and don't seem to be able to tell the difference between informal argumentation and hypothesis! You side-step the fact that there is no steady source, and never mind the fact that the all the prerequisite conditions of these supposedly perfectly identical waveforms exist only theoretically, that no measurements have been ever made by anyone under such conditions, you nevertheless won't let that stop you from talking like they have.
I have made no estimate; for I have made no attempt to quantify an instant. Indeed, as I hold an instant to be a circumstance in which time does not apply at all (being suspended), your argument is invalid.
Now you suppose there are circumstances where time does not apply, how very scientific of you. Now I see why you hate time, it proves your ass wrong. Scientists are supposed to crave being proven wrong.
The point, which it seems has eluded you (or, perhaps, which you have eluded), is that, notwithstanding the evolutions of time, the wavelengths within a ray of monochromatic light, instantaneously, within one medium, et cetera, are equal.
So who has observed and made measurements of monochromatic light under such conditions. Fail to cite the research and it will be as if one of my arrows was a nuclear warhead.
Or, to satisfy the corpuscular model, the energies of the photons within a ray of monochromatic light, are equal to one another.
This still supposes conditions which are known to exist only hypothetically, and only speaks of what the theory predicts the measured results would be if there were such a thing as an isolated system.
This is unscientific drivel. It equates to "I have not yet measured a difference, but contrary to what I have observed, I shall believe a model which allows for them".
This is a crafty dodge on your part. I explained my point in simple terms that aren't field specific. I need not even address the quality of your counterargument, because I trust that anyone who reads them both will see which is the better formed statement.
The basis of your entire argument, is that "imprecise instruments" have measured differences between quantities which had been supposed to be equal.
You really don't get it do you? The way that portion of my argument works is that the instruments we use to measure, however precise they may be, still only give us approximations. If equal is defined as without difference, we would need a perfectly precise way of measuring in order to verify the equality of two things. (be they monochromatic light waves or anything else)
I suppose I forgot to specifically mention that only theoretical light waves
1. pass through an unoccupied region of space
2. move unimpeded by interfering phenomena
3. emit simultaneously from a single source
I did mention however that non-imaginary light sources are in flux and then you backtracked and wanted to discuss the energy levels of orbiting electrons. You were even goofy enough to suggest that somehow this was a process "which does not vary with time"...which seems kinda like your own flavor of "unscientific drivel" to me.
You went on to say:It is known, that any two electrons, occupying the same energy level (and, if you like, the same orbital) must be imbued with identical energies for as long as they are so positioned., which seems to assume that they can't be ever so slightly out of balance, and merely have energy levels that are not different enough to immediately affect coherence.
I do not deny, that our instrumentation is imperfect, but I do demand that you hold yourself to the same standards to which you would have me adhere.
Ok I promise not to presume that since I cannot yet measure a difference that there is no difference.
No, sir, it was merely intended to dismiss a semantic argument which had not place in this dispute.
Calling what you even admit to be multiple sources, a single source ala: Obviously, a minute inspection reveals that there are in one source of light, immense numbers of individual sources an out of place matter of semantics is just sidestepping the issue because you don't find it convenient.
What evidence do you present, which suggests that the two are unequal?
I, like you, am only arguing based on my interpretation of the evidence I've had access to.
You supposed equality under conditions that exist only theoretically. You did not bring to bear measurements made under laboratory conditions, because readings from laboratory instrumentation are sensitive enough to quantify variance. Even barring interference from the medium, there is still the issue of non-steady state of the source. Keep sidestepping it and I will keep putting it in your face.
All of the evidence which does exist (most saliently, the predictability of ionic bonding, the neutrality of atoms, the decay of radioactive isotopes et alia), proves that the proton and electron have charges of equal magnitude.
To the contrary, the evidence shows that decay due to imbalance (inequality) is everywhere.
And I suppose no such thing.
You certainly don't see it that way but anyone can tell by what's emboldened below that essentially you are.
I do not suspect, that there are any differences hidden behind the symbol of equality. Such an opinion would be contrary to the one which I have expressed.
Have you considered that there could be no generation of energy going on in such situations, only transfer of energy.
I shall, in the interest of brevity, abandon the Socratic method. Whether through misdirection, or insensibility, it appears that I have failed to communicate the point of the inquiry.
I shall assume as first principles that you are composed of matter, and that you are subject to the ordinary laws which govern the interaction of matter. Now, suppose that you were sitting on a chair (as you are likely doing), preferably one which is capable of supporting your weight without disintegration. Now, I say that, instantaneously, the force of gravitation, acting upon your body, and the normal force generated (no energy is generated, was purported to have been generated, or could possibly be generated) would be equal; or that, if there be a vibration in the bodies, that the average of the two forces would be equal.
I further posit that, due to circumstances implicitly demonstrated in the scenarios above, that the total quantity of matter-energy in any closed system, or in any open system when inputs and outputs are accounted accounted for, shall remain the same.
So then show your class by attempting to ridicule what you don't understand why don't you
I do not entirely understand why you would cite what is obviously ironic, to demonstrate one's idiocy, but I am certain that you have your reasons.
I shall quote myself: "Parroting intelligentsia does not make you a member, merely a tool"
I would not count James Boswell amongst the intelligentsia. Here is a man who contrived at every turn to make himself appear ridiculous, to whom (to quote somebody truly illustrious) "everything, the publication of which would have made another man hang himself, was matter of gay and clamorous exultation".
If one cannot handle having it -rather simply- pointed out that they deal in estimations
An instant is not a quantity of time, or of anything at all. It therefore cannot be dealt with in estimations. This is the premise upon which I have ridiculed your efforts against me.
without making a disingenuous pseudo-intellectual sarcastic reference
I'll concede the latter charge. The first, I suspect, was included to augment the prose, the second made to insult the opponent. I am therefore not inclined to treat them as serious accusations.
they just might be a little too concerned with the level of advancement of one their fantasy RPG characters
I'll have you know that Vokun is a level 81 mage!
Says the bloke who feigns to understand the complex while still struggling to understand the simple.
I am simply extending to you the courtesy, of assuming that you understand what a Platonic Ideal is, and why they are relevant. I could end the empirical debate quite easily, I suspect, by proposing, that the fluctuations of time notwithstanding, the sum of all quantities in the universe remains the same. To remain the same, should be impossible, if the Platonic Ideal of equality were fictional.
No single observation or measurement can verify this, of course. However, the whole sum of observations and measurements that have ever been taken, anywhere, under scientific conditions supports the notion. You could, if you were so inclined, suggest that such a finite number of observations is insufficient, but then such would constitute an attack on empiricism itself, which would not avail you.
I find it funny that you act like an authority on what's scientific and whats pseudo-scientific, and don't seem to be able to tell the difference between informal argumentation and hypothesis!
I am glad that you have profited in some way from this exchange.
You side-step the fact that there is no steady source
I had supposed that fact (for here we agree) to be irrelevant. The very fact that there are intelligible laws which govern waveforms, suggests that there is a Platonic Ideal of equality, and that identical wavelengths are possible.
and never mind the fact that the all the prerequisite conditions of these supposedly perfectly identical waveforms exist only theoretically, that no measurements have been ever made by anyone under such conditions, you nevertheless won't let that stop you from talking like they have.
I don't believe that I suggested that they had been. Obviously, you are attempting to defeat my arguments (and you are at liberty to question whether they constitute arguments) by asking for empirically obtained data which cannot be provided. I find this itself to be disingenuous, for you have yourself agreed that no instrumentation is precise enough to determine equality.
The greater deficiency of your line of inquiry, however, is that it is entirely inefficacious. Obviously, I am arguing on a Platonic plane. The quotation from Euclid, a section of which forms the title of this debate, also dealt with the Platonic plane; I had supposed this to be obvious. The reason for which I am sullying my hands, by the presentation of scenarios which exist within the imperfect world, and to which we must ascribe a degree of uncertainty, owing to the imperfection of our instruments and faculties, is because you give all the indications of being entirely ignorant of what a Platonic Ideal is. You may, indeed, have read of them, or have studied them, but you appear to have been unable to recognise them, when they were the topic of debate.
I write, content in the suspicion that you will likely declare the above to be pseudo-intellectual (though, if Plato and Euclid were pseudo-intellectuals...) or an attempt to change the topic. For this reason, I shall iterate, in unequivocal language, what are my opinions upon the matter of equality. As a footnote, you may take magnitude for quantity, in most cases.
Of the Platonic Equality
I. Forms exist, as do properties and quantities.
II. The same properties may be measured, and expressed in equal units of quantity.
III. To measure, therefore, requires a concept of equality.
IV To measure a quantity or its effects, is the only empirical means of assessing quantity.
V. Therefore empirical measurement, by III and IV, admits discourse of Platonic equality.
Of empirical equality
I. Instrumentation, though marvellously advanced, remains imperfect.
II. Therefore measurements made by instrumentation shall be imperfect.
III. Equality of quantity can only be ascertained with certainty by perfect measurement.
IV. By II and III, equality cannot be empirically, viz, by measurement, proved to exist.
Corollary I. Equality cannot, by the same principle, be empirically proven not to exist.
Of geometry
I. Mathematical tautologies are always true.
II. Geometry is a branch of mathematics.
III. Geometry represents the relationships between real objects and quantities.
IV. Geometry may be and has been used to demonstrate equality in such relationships. See Philosophiæ Naturalis Principia Mathematica, Book I, section II, for a choice example.
III. Equality exists in reality.
Of divisibility of quantity
I. Quantities may be measured.
II. Quantities so measured are implicitly divided.
III. The units into which a measured quantity is divided, are equal to one another.
IV. By II and III, every empirical measurement supposes equality to exist, to ensure its own efficacy.
Grand conclusion
Equality exists, and empiricism cannot, without destroying itself, disprove its existence.
As I see it, sir, the nature of our dispute is thus:
A history
Finding contention with Euclid's first common notion, which is the premise of debate, you argued that empirical data renders dubious the concept of equality. Perceiving this, I argued first that empirical imperfection cannot disprove a Platonic Ideal; for, it is the nature of the empirical world to be only an imperfect manifestation of the same.
I, not having properly adhered to a classical structure of argument, foolishly fought upon the Platonic field with weapons more suited to mundane combat. Videlicet, I couched Platonic argument in empirical terms, which confused the issue. This gave you occasion to call into question the authority with which I pronounced upon these matters.
Finding that my line of argument was provoking hostility, I reverted to First Principles, which if my notions be correct, ought to be unassailable.
A summary
By the history above, the nature of our dispute has been obfuscated. In essence, therefore, I shall declare it: I maintain that equality is a real Platonic Ideal which is essential to empirical measurement, whereas you maintain that empirical measurement disproves the concept of equality.
I maintain that equality is a real Platonic Ideal which is essential to empirical measurement, whereas you maintain that empirical measurement disproves the concept of equality.
I do not dispute that equality is "a real Platonic Ideal which is essential to empirical measurement", however, that empirical measurement "renders dubious the concept of equality" remains my position. I do not hold the position that it disproves it. I'm starting to doubt that either of us stand to gain an improved understanding as a result of this exchange, I think perhaps we are standing over the body of a clearly deceased horse.
I do not dispute that equality is "a real Platonic Ideal which is essential to empirical measurement", however, that empirical measurement "renders dubious the concept of equality" remains my position.
Well, I can easily reconcile the one statement with the other. It is essential to Plato's theory of Ideas, that Ideals are only imperfectly manifested. As the Idea of consciousness is but dimly incorporated in humans, so is equality but temporarily, and, infrequently manifested in quantities and magnitudes.
It is to avoid miscommunication such as this, that I prefer a classical structure of argument.
So then would you still dismiss the possibility that the concept I introduced as "adequate balance", or as I will word here as "adequate similarity", could be superior to that of "equality" which connotes "no difference" as opposed to admitting the extreme likelihood of differences that may very well just remain to be quantified?
Is your position that no improvements can be made to the platonic ideal of equality?
Then this sir, I am convinced, is the crux of our disagreement.
I cannot, though I endeavour to do so, conceive how it may be supposed, that an ideal is a dynamic thing, susceptible of improvement. The ideal of equality, being the possession of common and identical qualities between diverse matters, cannot be altered. If it were, then it would cease to be equality, and would become some other ideal. It is, surely, the same for all ideals, as beauty, intelligence, matter, light, dark and even "horseness" (upon which theme Plato had much fun).
They are, by definition, beyond the power of men, and thus beyond our alteration. We may only improve our understanding of ideals; we may not alter their nature.