## fallacy of Galileo

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• If m is a light stone and M is a heavy one, according to Aristotle M should fall faster than m. Galileo attempted to show that Aristotle`s belief was
Message 1 of 9 , Dec 7, 2012
If m is a light stone and M is a heavy one, according to Aristotle M should fall faster than m. Galileo attempted to show that Aristotle`s belief was logically inconsistent by the following argument. Tie m and M together to form a double stone. Then, in falling, m should retard M, since it tends to fall more slowly, and the combination would fall faster than m but more slowly than M; but according to Aristotle the double body (M+m) is heavier than M and hence should fall faster than M.
If you accept Galileo`s reasoning as correct, can you conclude that M and m must fall at the same rate?
If you believe Galileo`s reasoning is incorrect, explain why?
• For all Aristotle knew, once you merge them into one stone, their inherent falling properties change. Maybe once merged, the original stones lose their
Message 2 of 9 , Dec 7, 2012
For all Aristotle knew, once you merge them into one stone, their inherent falling properties change. Maybe once merged, the original stones lose their original properties and gain a new one based on their new mass.

--- In mathforfun@yahoogroups.com, "kaziarafatahmed" <kaziarafatahmed@...> wrote:
>
> If m is a light stone and M is a heavy one, according to Aristotle M should fall faster than m. Galileo attempted to show that Aristotle`s belief was logically inconsistent by the following argument. Tie m and M together to form a double stone. Then, in falling, m should retard M, since it tends to fall more slowly, and the combination would fall faster than m but more slowly than M; but according to Aristotle the double body (M+m) is heavier than M and hence should fall faster than M.
> If you accept Galileo`s reasoning as correct, can you conclude that M and m must fall at the same rate?
> If you believe Galileo`s reasoning is incorrect, explain why?
>
• ... Or new size. stevo ... [Non-text portions of this message have been removed]
Message 3 of 9 , Dec 7, 2012
On Fri, Dec 7, 2012 at 3:32 PM, slim_the_dude <mygroupsemail798@...>wrote:

> **
>
>
> For all Aristotle knew, once you merge them into one stone, their inherent
> falling properties change. Maybe once merged, the original stones lose
> their original properties and gain a new one based on their new mass.
>
Or new size.

stevo

>
>
> --- In mathforfun@yahoogroups.com, "kaziarafatahmed" <kaziarafatahmed@...>
> wrote:
> >
> > If m is a light stone and M is a heavy one, according to Aristotle M
> should fall faster than m. Galileo attempted to show that Aristotle`s
> belief was logically inconsistent by the following argument. Tie m and M
> together to form a double stone. Then, in falling, m should retard M, since
> it tends to fall more slowly, and the combination would fall faster than m
> but more slowly than M; but according to Aristotle the double body (M+m) is
> heavier than M and hence should fall faster than M.
> > If you accept Galileo`s reasoning as correct, can you conclude that M
> and m must fall at the same rate?
> > If you believe Galileo`s reasoning is incorrect, explain why?
> >
>
>
>

[Non-text portions of this message have been removed]
• Galileo s argument does prove Aristotle s assertion can t apply unconditionally to all possible objects (in other words assuming object can include a pair
Message 4 of 9 , Dec 8, 2012
Galileo's argument does prove Aristotle's assertion can't apply unconditionally to all possible "objects" (in other words assuming "object" can include a pair of stones attached by a string), even though it may or may not be valid within a class of objects (like individual stones).

--- In mathforfun@yahoogroups.com, MorphemeAddict <lytlesw@...> wrote:
>
> On Fri, Dec 7, 2012 at 3:32 PM, slim_the_dude <mygroupsemail798@...>wrote:
>
> > **
> >
> >
> > For all Aristotle knew, once you merge them into one stone, their inherent
> > falling properties change. Maybe once merged, the original stones lose
> > their original properties and gain a new one based on their new mass.
> >
> Or new size.
>
> stevo
>
> >
> >
> > --- In mathforfun@yahoogroups.com, "kaziarafatahmed" <kaziarafatahmed@>
> > wrote:
> > >
> > > If m is a light stone and M is a heavy one, according to Aristotle M
> > should fall faster than m. Galileo attempted to show that Aristotle`s
> > belief was logically inconsistent by the following argument. Tie m and M
> > together to form a double stone. Then, in falling, m should retard M, since
> > it tends to fall more slowly, and the combination would fall faster than m
> > but more slowly than M; but according to Aristotle the double body (M+m) is
> > heavier than M and hence should fall faster than M.
> > > If you accept Galileo`s reasoning as correct, can you conclude that M
> > and m must fall at the same rate?
> > > If you believe Galileo`s reasoning is incorrect, explain why?
> > >
> >
> >
> >
>
>
> [Non-text portions of this message have been removed]
>
• Both Galilio and Aristotle are partially correct . If you take the opposition of air and assme the density of both masses to be same , the heavier object will
Message 5 of 9 , Dec 12, 2012
Both Galilio and Aristotle are partially correct . If you take the opposition of air and assme the density of both masses to be same , the heavier object will fall faster .If the opposition of air is neglected ,(e.g. if both masses are of iron ),then the two will fall at the same rate.
We make simple statements , without getting into the details of variabls involved . This is what leads to paradoxes or self-contradictions.

--- In mathforfun@yahoogroups.com, "video_ranger" <markjones76@...> wrote:
>
> Galileo's argument does prove Aristotle's assertion can't apply unconditionally to all possible "objects" (in other words assuming "object" can include a pair of stones attached by a string), even though it may or may not be valid within a class of objects (like individual stones).
>
>
> --- In mathforfun@yahoogroups.com, MorphemeAddict <lytlesw@> wrote:
> >
> > On Fri, Dec 7, 2012 at 3:32 PM, slim_the_dude <mygroupsemail798@>wrote:
> >
> > > **
> > >
> > >
> > > For all Aristotle knew, once you merge them into one stone, their inherent
> > > falling properties change. Maybe once merged, the original stones lose
> > > their original properties and gain a new one based on their new mass.
> > >
> > Or new size.
> >
> > stevo
> >
> > >
> > >
> > > --- In mathforfun@yahoogroups.com, "kaziarafatahmed" <kaziarafatahmed@>
> > > wrote:
> > > >
> > > > If m is a light stone and M is a heavy one, according to Aristotle M
> > > should fall faster than m. Galileo attempted to show that Aristotle`s
> > > belief was logically inconsistent by the following argument. Tie m and M
> > > together to form a double stone. Then, in falling, m should retard M, since
> > > it tends to fall more slowly, and the combination would fall faster than m
> > > but more slowly than M; but according to Aristotle the double body (M+m) is
> > > heavier than M and hence should fall faster than M.
> > > > If you accept Galileo`s reasoning as correct, can you conclude that M
> > > and m must fall at the same rate?
> > > > If you believe Galileo`s reasoning is incorrect, explain why?
> > > >
> > >
> > >
> > >
> >
> >
> > [Non-text portions of this message have been removed]
> >
>
• In vacuum, they both will fall at the same rate as there will not be air-resistance to hinder the fall. Have you ever gone up in an air-balloon? Or come down
Message 6 of 9 , Dec 12, 2012
In vacuum, they both will fall at the same rate as there will not be air-resistance to hinder the fall. Have you ever gone up in an air-balloon? Or come down with a parachute? What will happen if there is a big hole in the balloon or in the parachute?
Tofique Fatehi

________________________________
From: sahubrajabasi <sahubrajabasi@...>
To: mathforfun@yahoogroups.com
Sent: Wednesday, December 12, 2012 4:03 PM
Subject: [MATH for FUN] Re: fallacy of Galileo

Both Galilio and Aristotle are partially correct . If you take the opposition of air and assme the density of both masses to be same , the heavier object will fall faster .If the opposition of air is neglected ,(e.g. if both masses are of iron ),then the two will fall at the same rate.
We make simple statements , without getting into the details of variabls involved . This is what leads to paradoxes or self-contradictions.

--- In mailto:mathforfun%40yahoogroups.com, "video_ranger" <markjones76@...> wrote:
>
> Galileo's argument does prove Aristotle's assertion can't apply unconditionally to all possible "objects" (in other words assuming "object" can include a pair of stones attached by a string), even though it may or may not be valid within a class of objects (like individual stones).
>
>
> --- In mailto:mathforfun%40yahoogroups.com, MorphemeAddict <lytlesw@> wrote:
> >
> > On Fri, Dec 7, 2012 at 3:32 PM, slim_the_dude <mygroupsemail798@>wrote:
> >
> > > **
> > >
> > >
> > > For all Aristotle knew, once you merge them into one stone, their inherent
> > > falling properties change. Maybe once merged, the original stones lose
> > > their original properties and gain a new one based on their new mass.
> > >
> > Or new size.
> >
> > stevo
> >
> > >
> > >
> > > --- In mailto:mathforfun%40yahoogroups.com, "kaziarafatahmed" <kaziarafatahmed@>
> > > wrote:
> > > >
> > > > If m is a light stone and M is a heavy one, according to Aristotle M
> > > should fall faster than m. Galileo attempted to show that Aristotle`s
> > > belief was logically inconsistent by the following argument. Tie m and M
> > > together to form a double stone. Then, in falling, m should retard M, since
> > > it tends to fall more slowly, and the combination would fall faster than m
> > > but more slowly than M; but according to Aristotle the double body (M+m) is
> > > heavier than M and hence should fall faster than M.
> > > > If you accept Galileo`s reasoning as correct, can you conclude that M
> > > and m must fall at the same rate?
> > > > If you believe Galileo`s reasoning is incorrect, explain why?
> > > >
> > >
> > >
> > >
> >
> >
> > [Non-text portions of this message have been removed]
> >
>

[Non-text portions of this message have been removed]
• With air resistance, mass is not the only issue. The shape of the object is also vital. Compare an open umbrella with the same mass of a metal sphere. Tarcisio
Message 7 of 9 , Dec 12, 2012
With air resistance, mass is not the only issue. The shape of the object is
also vital. Compare an open umbrella with the same mass of a metal sphere.

Tarcisio

-----------------------

Both Galilio and Aristotle are partially correct . If you take the
opposition of air and assme the density of both masses to be same , the
heavier object will fall faster .If the opposition of air is neglected
,(e.g. if both masses are of iron ),then the two will fall at the same rate.
We make simple statements , without getting into the details of variabls

--- In mathforfun@yahoogroups.com <mailto:mathforfun%40yahoogroups.com> ,
"video_ranger" <markjones76@...> wrote:
>
> Galileo's argument does prove Aristotle's assertion can't apply
unconditionally to all possible "objects" (in other words assuming "object"
can include a pair of stones attached by a string), even though it may or
may not be valid within a class of objects (like individual stones).
>
>
> --- In mathforfun@yahoogroups.com <mailto:mathforfun%40yahoogroups.com> ,
> >
> > On Fri, Dec 7, 2012 at 3:32 PM, slim_the_dude <mygroupsemail798@>wrote:
> >
> > > **
> > >
> > >
> > > For all Aristotle knew, once you merge them into one stone, their
inherent
> > > falling properties change. Maybe once merged, the original stones lose
> > > their original properties and gain a new one based on their new mass.
> > >
> > Or new size.
> >
> > stevo
> >
> > >
> > >
> > > --- In mathforfun@yahoogroups.com
<mailto:mathforfun%40yahoogroups.com> , "kaziarafatahmed" <kaziarafatahmed@>
> > > wrote:
> > > >
> > > > If m is a light stone and M is a heavy one, according to Aristotle M
> > > should fall faster than m. Galileo attempted to show that Aristotle`s
> > > belief was logically inconsistent by the following argument. Tie m and
M
> > > together to form a double stone. Then, in falling, m should retard M,
since
> > > it tends to fall more slowly, and the combination would fall faster
than m
> > > but more slowly than M; but according to Aristotle the double body
(M+m) is
> > > heavier than M and hence should fall faster than M.
> > > > If you accept Galileo`s reasoning as correct, can you conclude that
M
> > > and m must fall at the same rate?
> > > > If you believe Galileo`s reasoning is incorrect, explain why?
> > > >
> > >
> > >
> > >
> >
> >
> > [Non-text portions of this message have been removed]
> >
>

[Non-text portions of this message have been removed]
• Tarcisio is correct. And linking the objects together should ordinarily make no difference except for the shape and impermeability to air. consider a man tied
Message 8 of 9 , Dec 12, 2012
Tarcisio is correct. And linking the objects together should ordinarily make no difference except for the shape and impermeability to air. consider a man tied to an open parachute compared to a man tied to a parachute that does not open.

Joey

________________________________
From: Tarcisio Goes <tcgoes.groups@...>
To: mathforfun@yahoogroups.com
Sent: Wednesday, December 12, 2012 12:09 PM
Subject: RE: [MATH for FUN] Re: fallacy of Galileo

With air resistance, mass is not the only issue. The shape of the object is
also vital. Compare an open umbrella with the same mass of a metal sphere.

Tarcisio

-----------------------

Both Galilio and Aristotle are partially correct . If you take the
opposition of air and assme the density of both masses to be same , the
heavier object will fall faster .If the opposition of air is neglected
,(e.g. if both masses are of iron ),then the two will fall at the same rate.
We make simple statements , without getting into the details of variabls

--- In mailto:mathforfun%40yahoogroups.com <mailto:mathforfun%40yahoogroups.com> ,
"video_ranger" <markjones76@...> wrote:
>
> Galileo's argument does prove Aristotle's assertion can't apply
unconditionally to all possible "objects" (in other words assuming "object"
can include a pair of stones attached by a string), even though it may or
may not be valid within a class of objects (like individual stones).
>
>
> --- In mailto:mathforfun%40yahoogroups.com <mailto:mathforfun%40yahoogroups.com> ,
> >
> > On Fri, Dec 7, 2012 at 3:32 PM, slim_the_dude <mygroupsemail798@>wrote:
> >
> > > **
> > >
> > >
> > > For all Aristotle knew, once you merge them into one stone, their
inherent
> > > falling properties change. Maybe once merged, the original stones lose
> > > their original properties and gain a new one based on their new mass.
> > >
> > Or new size.
> >
> > stevo
> >
> > >
> > >
> > > --- In mailto:mathforfun%40yahoogroups.com
<mailto:mathforfun%40yahoogroups.com> , "kaziarafatahmed" <kaziarafatahmed@>
> > > wrote:
> > > >
> > > > If m is a light stone and M is a heavy one, according to Aristotle M
> > > should fall faster than m. Galileo attempted to show that Aristotle`s
> > > belief was logically inconsistent by the following argument. Tie m and
M
> > > together to form a double stone. Then, in falling, m should retard M,
since
> > > it tends to fall more slowly, and the combination would fall faster
than m
> > > but more slowly than M; but according to Aristotle the double body
(M+m) is
> > > heavier than M and hence should fall faster than M.
> > > > If you accept Galileo`s reasoning as correct, can you conclude that
M
> > > and m must fall at the same rate?
> > > > If you believe Galileo`s reasoning is incorrect, explain why?
> > > >
> > >
> > >
> > >
> >
> >
> > [Non-text portions of this message have been removed]
> >
>

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]
• a hole in a balloon can accelerate you abnormally in a direction dependent on the position of the hole . . .  ... From: Tofique Fatehi
Message 9 of 9 , Dec 12, 2012
a hole in a balloon can accelerate you abnormally in a direction dependent on the position of the hole . . .

--- On Wed, 12/12/12, Tofique Fatehi <tofiquef@...> wrote:

From: Tofique Fatehi <tofiquef@...>
Subject: Re: [MATH for FUN] Re: fallacy of Galileo
To: "mathforfun@yahoogroups.com" <mathforfun@yahoogroups.com>
Date: Wednesday, 12 December, 2012, 16:02

In vacuum, they both will fall at the same rate as there will not be air-resistance to hinder the fall. Have you ever gone up in an air-balloon? Or come down with a parachute? What will happen if there is a big hole in the balloon or in the parachute?

Tofique Fatehi

________________________________

From: sahubrajabasi <sahubrajabasi@...>

To: mathforfun@yahoogroups.com

Sent: Wednesday, December 12, 2012 4:03 PM

Subject: [MATH for FUN] Re: fallacy of Galileo

Both Galilio and Aristotle are partially correct . If you take the opposition of air and assme the density of both masses to be same , the heavier object will fall faster .If the opposition of air is neglected ,(e.g. if both masses are of iron ),then the two will fall at the same rate.

We make simple statements , without getting into the details of variabls involved . This is what leads to paradoxes or self-contradictions.

--- In mailto:mathforfun%40yahoogroups.com, "video_ranger" <markjones76@...> wrote:

>

> Galileo's argument does prove Aristotle's assertion can't apply unconditionally to all possible "objects" (in other words assuming "object" can include a pair of stones attached by a string), even though it may or may not be valid within a class of objects (like individual stones).

>

>

> --- In mailto:mathforfun%40yahoogroups.com, MorphemeAddict <lytlesw@> wrote:

> >

> > On Fri, Dec 7, 2012 at 3:32 PM, slim_the_dude <mygroupsemail798@>wrote:

> >

> > > **

> > >

> > >

> > > For all Aristotle knew, once you merge them into one stone, their inherent

> > > falling properties change. Maybe once merged, the original stones lose

> > > their original properties and gain a new one based on their new mass.

> > >

> > Or new size.

> >

> > stevo

> >

> > >

> > >

> > > --- In mailto:mathforfun%40yahoogroups.com, "kaziarafatahmed" <kaziarafatahmed@>

> > > wrote:

> > > >

> > > > If m is a light stone and M is a heavy one, according to Aristotle M

> > > should fall faster than m. Galileo attempted to show that Aristotle`s

> > > belief was logically inconsistent by the following argument. Tie m and M

> > > together to form a double stone. Then, in falling, m should retard M, since

> > > it tends to fall more slowly, and the combination would fall faster than m

> > > but more slowly than M; but according to Aristotle the double body (M+m) is

> > > heavier than M and hence should fall faster than M.

> > > > If you accept Galileo`s reasoning as correct, can you conclude that M

> > > and m must fall at the same rate?

> > > > If you believe Galileo`s reasoning is incorrect, explain why?

> > > >

> > >

> > >

> > >

> >

> >

> > [Non-text portions of this message have been removed]

> >

>

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]
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