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 International Skeptics Forum Pressure Gradient in a Box?

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 13th August 2019, 02:24 PM #1 PhantomWolf Penultimate Amazing     Join Date: Mar 2007 Posts: 18,548 Pressure Gradient in a Box? Okay so I have a quandary. We usually assume that if we have a container with a gas in it, then the gas pressure will be equalized inside the container, right? However, what happens if I make that container 100 km high? Gravity is still acting on the air inside the box, just as it does on the air outside of it, so why shouldn't it form a graduated pressure differential inside the box just as the atmosphere does? If the box was open at the top there there is no question that it would have a graduated pressure inside, but why would this go away merely because the top was closed? Am I missing something, or does the idea of a gas equalizing the pressure in a container start to break down when the container is tall enough that gravitation forces can start to play a part? __________________ It must be fun to lead a life completely unburdened by reality. -- JayUtah I am not able to rightly apprehend the kind of confusion of ideas that could provoke such a question. -- Charles Babbage (1791-1871)
 13th August 2019, 02:30 PM #2 theprestige Penultimate Amazing   Join Date: Aug 2007 Posts: 36,892 Seems to me that there'd even be a pressure gradient in a 1 cubic meter box at sea level. It would probably be too small to measure, though. Also, I'm not sure we do "usually assume" this in any meaningful way. We assume that's the default behavior of gases, absent any other significant forces. Thought experiments involving Maxwell's Demon and spherical cows come to mind. I think mostly in practice we assume equalized pressure in scenarios where it is a reasonable and more than sufficient approximation. It's not like mechanically the gravity differential is going to play a noticeable part in a fuel injector or a jet engine.
 13th August 2019, 02:33 PM #3 RecoveringYuppy Philosopher   Join Date: Nov 2006 Posts: 8,983 The air in the box will have a pressure gradient. So will the material the box is made of. __________________ REJ (Robert E Jones) posting anonymously under my real name for 30 years. Make a fire for a man and you keep him warm for a day. Set him on fire and you keep him warm for the rest of his life.
 13th August 2019, 03:40 PM #4 Robin Philosopher   Join Date: Apr 2004 Posts: 9,943 Originally Posted by PhantomWolf Okay so I have a quandary. We usually assume that if we have a container with a gas in it, then the gas pressure will be equalized inside the container, right? It depends who "we" is. I don't assume that. Any container of gas, whatever the size, in a gravitational field or undergoing acceleration will have a pressure gradient in it. Sometimes the gradient is small enough for it to be disregarded for most purposes. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" Last edited by Robin; 13th August 2019 at 03:48 PM.
 13th August 2019, 04:03 PM #5 JimOfAllTrades Muse   Join Date: Aug 2011 Posts: 511 Originally Posted by PhantomWolf Okay so I have a quandary. We usually assume that if we have a container with a gas in it, then the gas pressure will be equalized inside the container, right? The way I learned it was that a gas exerts equal pressure on all sides of a container absent any other force to the contrary. Gravity is a force to the contrary, pulling the gas (and the container) toward the center of gravity. Across small distances this is negligible for practical purposes. But in a gravitational field (or in any other accelerating frame) there will be a gradient inside the box even though in small containers it might be too small to measure. Added after preview: Ninja'd by pretty much everyone else.
 13th August 2019, 04:03 PM #6 Robin Philosopher   Join Date: Apr 2004 Posts: 9,943 I would suggest that most people don't usually assume that, because if we knew a sealed container had two types of gas in it, one heavier than the other, then we would assume that the heavier one would settle to the bottom, wouldn't we? So we usually assume there is a pressure gradient in a sealed container of gas. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 13th August 2019, 04:08 PM #7 Thor 2 Philosopher     Join Date: May 2016 Location: Brisbane, Aust. Posts: 5,322 Originally Posted by Robin It depends who "we" is. I don't assume that. Any container of gas, whatever the size, in a gravitational field or undergoing acceleration will have a pressure gradient in it. Sometimes the gradient is small enough for it to be disregarded for most purposes. Don't count me among the we's either. The pressure gradient in the box will depend on the gas, and depth also. Hydrogen being lighter will have a lesser gradient than say nitrogen, and the deeper the gas the higher the rate of change of pressure. __________________ Thinking is a faith hazard. Last edited by Thor 2; 13th August 2019 at 04:11 PM.
 13th August 2019, 05:08 PM #9 BillC Bazooka Joe     Join Date: Jul 2004 Posts: 3,791 I'm pretty sure pressure differences can be readily measured between the ground and top floors inside tall buildings. Also: the pressure can be measured to increase at the rear of an accelerating, sealed car. The helium balloon experiment shows this: https://www.youtube.com/watch?v=2-UzBitLmf8 Last edited by BillC; 13th August 2019 at 05:10 PM.
 13th August 2019, 05:11 PM #10 Myriad Hyperthetical     Join Date: Nov 2006 Location: A pocket paradise between the sewage treatment plant and the railroad Posts: 15,140 Accelerations of less than a full G can produce noticeable (as well as measurable) changes within a closed container of gas as well. One example you might have experienced is carrying helium party balloons in a car or other vehicle. When the vehicle accelerates, the balloons move forward (despite inertia), because the acceleration increases the air pressure toward the rear of the vehicle. __________________ A zømbie once bit my sister...
 13th August 2019, 06:31 PM #11 DevilsAdvocate Philosopher     Join Date: Nov 2004 Posts: 5,188 Until the box is opened, there both is and is not a pressure gradient. __________________ "Nothing scarier than piled up adirondack chairs." - AvE
 13th August 2019, 09:30 PM #12 smartcooky Penultimate Amazing     Join Date: Oct 2012 Location: Nelson, New Zealand Posts: 12,222 Originally Posted by DevilsAdvocate Until the box is opened, there both is and is not a pressure gradient. Schrödinger's Gas Law? __________________ “Give me your tired, your poor, your huddled masses yearning to breathe free, the wretched refuse of your teeming shore - if they're white!" If you don't like my posts, my opinions, or my directness then put me on your ignore list. This will be of benefit to both of us; you won't have to take umbrage at my posts, and I won't have to waste my time talking to you... simples! !
 13th August 2019, 10:26 PM #13 Skeptic Ginger Nasty Woman     Join Date: Feb 2005 Posts: 75,107 I haven't read the thread and of course I should have. Gravity is one of the forces acting on the gas molecules. So if the container is tall enough, of course there will be a density gradient. __________________ That new avatar is cuteness overload. Restore checks and balances no matter your party affiliation.
 14th August 2019, 12:22 AM #14 GnaGnaMan Graduate Poster   Join Date: Sep 2008 Posts: 1,707 Originally Posted by PhantomWolf Am I missing something, or does the idea of a gas equalizing the pressure in a container start to break down when the container is tall enough that gravitation forces can start to play a part? Unfortunately, below university level, it is often not made clear what (or even that!) simplifications are made. Ignoring the effects of gravity is one, as has been pointed out. Another simplification is that pressure travels instantly. Small disturbances in the pressure travel as waves, which we call sound. Changes in pressure travel at the speed of sound. There's also the issue of density changes. __________________ It makes no difference whatever whether they laugh at us or revile us, whether they represent us as clowns or criminals; the main thing is that they mention us, that they concern themselves with us again and again. -Hitler
 18th August 2019, 08:15 PM #16 Molinaro Illuminator     Join Date: Dec 2005 Posts: 4,413 Originally Posted by BillC I'm pretty sure pressure differences can be readily measured between the ground and top floors inside tall buildings. Also: the pressure can be measured to increase at the rear of an accelerating, sealed car. The helium balloon experiment shows this: https://www.youtube.com/watch?v=2-UzBitLmf8 Absolutely. When I worked as a bike courier in Toronto, I had a watch with a built in altimeter function. It calculated it by measuring air pressure. You don't even need to go very high for a small device like that to measure the change. It would update every 2m change in my altitude. Interestingly it also allowed me to clearly see what elevators were airtight as the altitude reading would not change while the elevator rose. But when the doors would open it would suddenly jump to the new reading. __________________ 100% Cannuck!
 19th August 2019, 03:01 AM #17 BillC Bazooka Joe     Join Date: Jul 2004 Posts: 3,791 Originally Posted by theprestige Seems to me that there'd even be a pressure gradient in a 1 cubic meter box at sea level. It would probably be too small to measure, though. Also, I'm not sure we do "usually assume" this in any meaningful way. We assume that's the default behavior of gases, absent any other significant forces. Thought experiments involving Maxwell's Demon and spherical cows come to mind. I think mostly in practice we assume equalized pressure in scenarios where it is a reasonable and more than sufficient approximation. It's not like mechanically the gravity differential is going to play a noticeable part in a fuel injector or a jet engine. According to U.S. Standard Atmosphere 1976, atmospheric density varies from 1.225g/cm3 at 0m altitude to 1.112g/cm3 at 1000m, so I would expect the density at the top of the 1m cube box to be 1.225 - (1.225-1.112)/1000 = 1.224887 g/cm3, assuming it entrapped the same mass of air as an imaginary cube of the same size at sea level.
 19th August 2019, 05:05 AM #18 Robin Philosopher   Join Date: Apr 2004 Posts: 9,943 Originally Posted by BillC According to U.S. Standard Atmosphere 1976, atmospheric density varies from 1.225g/cm3 at 0m altitude to 1.112g/cm3 at 1000m, so I would expect the density at the top of the 1m cube box to be 1.225 - (1.225-1.112)/1000 = 1.224887 g/cm3, assuming it entrapped the same mass of air as an imaginary cube of the same size at sea level. Although I think the situation would be different with a sealed box. There would still be a pressure gradient, but much smaller. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 19th August 2019, 06:29 AM #19 Dr.Sid Graduate Poster   Join Date: Sep 2009 Location: Olomouc, Czech Republic Posts: 1,965 Originally Posted by Robin Although I think the situation would be different with a sealed box. There would still be a pressure gradient, but much smaller. No, the pressure gradient will be the same in both sealed and unsealed box. The gradient is caused basically by the air on top of the box pushing down on the air on the bottom of the box. The difference in pressure will always be height difference * density of air * 1g.
 19th August 2019, 07:25 AM #20 Jack by the hedge Safely Ignored     Join Date: Oct 2009 Posts: 9,657 Originally Posted by Dr.Sid No, the pressure gradient will be the same in both sealed and unsealed box. The gradient is caused basically by the air on top of the box pushing down on the air on the bottom of the box. The difference in pressure will always be height difference * density of air * 1g. Agreed. If you carefully slid a lid onto the top of the box, the air inside would not suddenly reorder itself into some not-so-affected-by-gravity arrangement.
 19th August 2019, 07:29 AM #21 Pope130 Illuminator     Join Date: Sep 2005 Location: Oregon Posts: 3,064 Originally Posted by Robin Although I think the situation would be different with a sealed box. There would still be a pressure gradient, but much smaller. Perhaps it will be clearer if, instead of imagining pumping air into a sealed box, you picture it this way: Build a box around an existing mass of air. Let's go to the extreme and make it a cube 200 miles on a side. Floor first, no effect on air pressure. One side, the top now sticks up into space, sea level pressure at the bottom, no pressure at the top. Two more sides, still no effect. Last side, you have now cut off a block of air from contact with the rest of the atmosphere, still sea level at the bottom, vacuum on the top. Now put the top on. The top does not interact with the air in the box at all, since it is at the vacuum elevation and doesn't touch any air. Perfect pressure gradient from top to bottom.
 19th August 2019, 07:42 AM #22 Robin Philosopher   Join Date: Apr 2004 Posts: 9,943 Originally Posted by Jack by the hedge Agreed. If you carefully slid a lid onto the top of the box, I didn't say slide a lid onto it. I said a sealed box. Quote: the air inside would not suddenly reorder itself into some not-so-affected-by-gravity arrangement. Still affected by gravity. Not so affected by all the air above it. Yes, it would reorder itself, having that weight above removed. I didn't say there would be no pressure gradient. I said the situation would be different. If you seal something then the top of the container is now taking the weight of all the atmosphere above. The pressure gradient inside is now a function only of the weight of the air in the container. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 19th August 2019, 07:48 AM #23 Robin Philosopher   Join Date: Apr 2004 Posts: 9,943 Originally Posted by Pope130 Perhaps it will be clearer if, instead of imagining pumping air into a sealed box, you picture it this way: Build a box around an existing mass of air. Let's go to the extreme and make it a cube 200 miles on a side. Floor first, no effect on air pressure. One side, the top now sticks up into space, sea level pressure at the bottom, no pressure at the top. Two more sides, still no effect. Last side, you have now cut off a block of air from contact with the rest of the atmosphere, still sea level at the bottom, vacuum on the top. Now put the top on. The top does not interact with the air in the box at all, since it is at the vacuum elevation and doesn't touch any air. Perfect pressure gradient from top to bottom. Remember, this is a sealed box. It is air tight. Is the air in that box going to be affected by the weight of all the air above it? __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 19th August 2019, 07:50 AM #24 Robin Philosopher   Join Date: Apr 2004 Posts: 9,943 Originally Posted by Dr.Sid No, the pressure gradient will be the same in both sealed and unsealed box. The gradient is caused basically by the air on top of the box pushing down on the air on the bottom of the box. The difference in pressure will always be height difference * density of air * 1g. OK. So it would have the same gradient. It just wouldn't have sea level pressure. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 19th August 2019, 08:04 AM #25 Dr.Sid Graduate Poster   Join Date: Sep 2009 Location: Olomouc, Czech Republic Posts: 1,965 Originally Posted by Robin OK. So it would have the same gradient. It just wouldn't have sea level pressure. It would. Unless you change amount of gas inside, or change the volume, the pressure will be the same. Imagine air in the box on the top plane, where the lid would be (but it's not at the moment). The air bellow the plane pushes against the air above the plane. Now you just push the lid between them. The pressure from both sides of the lid remains the same. Pressure inside container really doesn't drop by simply sealing it:-) Last edited by Dr.Sid; 19th August 2019 at 08:05 AM.
 19th August 2019, 08:12 AM #26 Jack by the hedge Safely Ignored     Join Date: Oct 2009 Posts: 9,657 Originally Posted by Robin I didn't say slide a lid onto it. I said a sealed box... If you slide an (airtight) lid onto a box, it becomes a sealed box. The air pressure is in equilibrium as the lid slides closed and nothing changes at the moment the lid seals shut. The air pressure immediately next to the lid is the same all over (assuming the lid is thin). The presence of the lid does not take pressure off the molecules in the top of the box.
 19th August 2019, 08:14 AM #27 Pope130 Illuminator     Join Date: Sep 2005 Location: Oregon Posts: 3,064 Originally Posted by Robin Remember, this is a sealed box. It is air tight. Is the air in that box going to be affected by the weight of all the air above it? There is no weight of air above it. There is no air above it.
 19th August 2019, 08:17 AM #28 Jack by the hedge Safely Ignored     Join Date: Oct 2009 Posts: 9,657 Originally Posted by Robin Remember, this is a sealed box. It is air tight. Is the air in that box going to be affected by the weight of all the air above it? While the lid is open, obviously yes; the weight of all that air above it presses a certain amount of air into the box, with a very small pressure gradient increasing the pressure deeper into the box. When the lid seals, that amount of air is now fixed. The pressure is stabilised and the gradient is stabilised. Changes in air pressure outside the box now have no effect on the pressure inside (presuming the box is rigid).
 19th August 2019, 08:34 AM #29 RecoveringYuppy Philosopher   Join Date: Nov 2006 Posts: 8,983 To resolve the latest question of whether the lid changes anything you need to specify how rigid the box is. If it's rigid enough to resist the pressure difference (which is likely to be minor in the cases being discussed) then the air inside becomes independent of the weight of the air above the box. __________________ REJ (Robert E Jones) posting anonymously under my real name for 30 years. Make a fire for a man and you keep him warm for a day. Set him on fire and you keep him warm for the rest of his life.
 19th August 2019, 08:38 AM #30 Dr.Sid Graduate Poster   Join Date: Sep 2009 Location: Olomouc, Czech Republic Posts: 1,965 Originally Posted by RecoveringYuppy To resolve the latest question of whether the lid changes anything you need to specify how rigid the box is. If it's rigid enough to resist the pressure difference (which is likely to be minor in the cases being discussed) then the air inside becomes independent of the weight of the air above the box. It will become independent, or in other words, isolated. But the pressure will not change just by closing the lid.
 19th August 2019, 08:47 AM #31 theprestige Penultimate Amazing   Join Date: Aug 2007 Posts: 36,892 Originally Posted by PhantomWolf This is pretty much what I had determined, I just wanted to make sure that my thinking wasn't in error. The reason I brought it up was that often I see Flat Earth debunkers use the fact that we have a pressure gradient to "prove" that there is no container, because if the Flat Earthers were right then there'd be no pressure gradient. I was thinking about this, and I came to the conclusion that there would be a pressure gradient either way, so we can't use it as a proof of there being no container. Of course that it is caused by gravity, and so proves that we have gravity, which flat earthers deny, still means that it destroys their stupid flat model (if they ever come up with a consistent one) but it also means we need to be better in our arguments because the "gradient equals proof of no container" is not actually valid and as debunkers we should avoid using incorrect debunks. I liked this thread better when it wasn't about a slapfight between flat-earth strawmen.
 19th August 2019, 08:49 AM #32 Pope130 Illuminator     Join Date: Sep 2005 Location: Oregon Posts: 3,064 If it were correct that pressure equalized inside a sealed container then you could use it as a pump. Put the lid on your hypothetical box, the pressure equalizes inside the box, the pressure at the top of box is higher inside than outside. You can now open a valve and air will blow out. Use the air flow to drive a generator. Free Energy!
 19th August 2019, 09:24 AM #33 theprestige Penultimate Amazing   Join Date: Aug 2007 Posts: 36,892 Originally Posted by Pope130 If it were correct that pressure equalized inside a sealed container then you could use it as a pump. Put the lid on your hypothetical box, the pressure equalizes inside the box, the pressure at the top of box is higher inside than outside. You can now open a valve and air will blow out. Use the air flow to drive a generator. Free Energy! Opening and closing the valves costs energy. The real question is whether the box-pump (BP) produces more energy than is necessary to operate its own mechanisms. Running the BP at a lower altitude would tend to increase the pressure gradient and therefore the energy output. But it would also mean your valves would have to work harder against the pressure differentials involved. Same with a larger box, I think. --- That's what makes fossil fuels so amazing. They've been packed with energy by ridiculously expensive processes, that cannot be profitably synthesized. Same with radioactive minerals as fuels. They have a huge energy density, but it takes a rapidly-expanding matter-dense universe with a *lot* of supernovae, to produce them in industrial quantities.
 19th August 2019, 09:30 AM #34 CORed Philosopher   Join Date: Dec 2008 Location: Central City, Colorado, USA Posts: 8,928 Originally Posted by BillC I'm pretty sure pressure differences can be readily measured between the ground and top floors inside tall buildings. Also: the pressure can be measured to increase at the rear of an accelerating, sealed car. The helium balloon experiment shows this: https://www.youtube.com/watch?v=2-UzBitLmf8 A bit off topic, but that reminds me of the old story where a physics exam has a question asking how to determine the height of a building using a baramoter. A student answers the question that this would be done by dropping the barometer from the roof of the building, timing the fall, and using the formula: d = 1/2 at*2.
 19th August 2019, 09:59 AM #35 theprestige Penultimate Amazing   Join Date: Aug 2007 Posts: 36,892 Originally Posted by CORed A bit off topic, but that reminds me of the old story where a physics exam has a question asking how to determine the height of a building using a baramoter. A student answers the question that this would be done by dropping the barometer from the roof of the building, timing the fall, and using the formula: d = 1/2 at*2. Without knowing the drag on the barometer, that method is going to have a margin of error. On a very tall building, you'll end up ordering the wrong number of stair-steps, and the wrong length of elevator cable. On a very tall building, you might even end up ordering the wrong number of fixtures for each floor, due to miscalculating the number of floors from the height of the building.
 19th August 2019, 10:01 AM #36 RecoveringYuppy Philosopher   Join Date: Nov 2006 Posts: 8,983 Moving the barometer from the bottom to the top of the building can take time and that can introduce errors in to that method too. __________________ REJ (Robert E Jones) posting anonymously under my real name for 30 years. Make a fire for a man and you keep him warm for a day. Set him on fire and you keep him warm for the rest of his life.
 19th August 2019, 10:20 AM #37 Dr.Sid Graduate Poster   Join Date: Sep 2009 Location: Olomouc, Czech Republic Posts: 1,965 Guys please, if you make a joke, use smiley face. It should be norm at least on forums like these where ignorance, wisdom, and severe sarcasm meet on daily basis.
 19th August 2019, 10:35 AM #38 Jack by the hedge Safely Ignored     Join Date: Oct 2009 Posts: 9,657 Originally Posted by theprestige Without knowing the drag on the barometer, that method is going to have a margin of error... A typical barometer measures to the nearest millibar, so unless the building is extraordinarily tall the answer is going to be that it's height is zero +/- 250m. On balance I think I'll throw the thing off and count seconds.
 19th August 2019, 01:17 PM #39 Robin Philosopher   Join Date: Apr 2004 Posts: 9,943 Oh well, I was wrong on the second count too then. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 19th August 2019, 01:23 PM #40 Robin Philosopher   Join Date: Apr 2004 Posts: 9,943 Originally Posted by CORed A bit off topic, but that reminds me of the old story where a physics exam has a question asking how to determine the height of a building using a baramoter. A student answers the question that this would be done by dropping the barometer from the roof of the building, timing the fall, and using the formula: d = 1/2 at*2. I heard it on the radio from a guy who claimed to be the person setting the exam. The first answer the student gives is that he would tie a string to the barometer, lower it to the ground and then measure the length of the string. When he gets this marked wrong he goes and complains saying 'why don't you think my method would work?'. The lecturer then gives him a second chance to do the question. This time he provides two methods, the first was the formula given above and the second was that he would offer it as a gift to the building manager in exchange for the information about the height of the building. So the lecturer says "Do you know the answer I was expecting?" and the student says "Yes" and he gives him the marks. I doubt it is actually true, so more of a tall tale than a gag. I forget the point the guy on the radio was making. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"

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