Assumptions

[Suggestion Box]

there are three main reasons we disagree in arguments:
1.) we see our opponent's argument as invalid (i.e. not self-consistent)
2.) we claim that his argument is valid, but unsound (i.e. there's a false premise)
3.) his argument begs the question (i.e. circular logic)

this thread takes a look at number 2. the reason we consider one of our opponent's premises to be false is because we assume something he doesn't. the problem with this is, how do we know our own assumption is sound, aside from the fact that it is valid and non-circular?

another way of putting this: given two perfectly valid but opposing arguments, how do we decide which argument makes correct assumptions, and which makes incorrect assumptions?

 

[ToddNotTodd]

there are three main reasons we disagree in arguments:
1.) we see our opponent's argument as invalid (i.e. not self-consistent)
2.) we claim that his argument is valid, but unsound (i.e. there's a false premise)
3.) his argument begs the question (i.e. circular logic)

this thread takes a look at number 2. the reason we consider one of our opponent's premises to be false is because we assume something he doesn't. the problem with this is, how do we know our own assumption is sound, aside from the fact that it is valid and non-circular?

another way of putting this: given two perfectly valid but opposing arguments, how do we decide which argument makes correct assumptions, and which makes incorrect assumptions?

We judge a premise on the evidence for or against it. If we find the evidence compelling, we're more likely to believe the premise. What we find compelling is largely a personal experience.

 

[R3quiem]

another way of putting this: given two perfectly valid but opposing arguments, how do we decide which argument makes correct assumptions, and which makes incorrect assumptions?

Are these arguments about subjective things or objective things? This is important because my answer will change depending on whether two arguments are meant to be about subjective things or objective things.

If the two arguments are subjective, such as two parents arguing over whether to paint the baby's room green or tan, or whether to buy a minivan or an suv, then both could be equally acceptable answers, and it is quite possible that both arguments make correct assumptions but are from different points of view with different priorities in mind.

If the two arguments are about objective things, such as over whether there is a god or not, whether the higgs boson exists, or what killed the dinosaurs- then we should decide which argument makes correct assumptions based on how closely these assumptions match the data. More importantly, I'd argue that, in such a process, one should try to make as few assumptions as possible, and realize that if they are making certain leaps and certain assumptions, then the probability of their argument being correct decreases.

 

[Suggestion Box]

i guess i'm more referring to objective things... though i question whether objective things are just subjective things with a majority following. it seems sometimes that the provided evidence does itself rest on assumptions - though these underlying assumptions are perceived as so obvious that no one thinks to examine them.

kinda like the difference between observing the road from a moving vehicle and observing it from the sidewalk. if i spend my whole life on the sidewalk, then the world is obviously stationary, with things moving on it. but if i spend my whole life on the vehicle, the world is moving, and only I am stationary.

except more philosophical.

 

[Gracchus]

I have pointed this out before in other threads:

From the five assumptions of Euclid's postulates, we can deduce that the sum of the areas of the squares on the two shorter sides of a plane right triangle is equal to the area of the square on the third side.

I have seen this theorem tested by repeated measurements by various methods. From this and other predictions deduced from Euclid's postulates, we have determined that euclid's postulates are reasonable assumptions, and, moreover, are self-consistent: They do not lead to contradictions.

So if assumptions lead to deductions that are consistent with observation, without leading to contradictions, we can have some confidence in those assumptions.

 

[blook]

So if assumptions lead to deductions that are consistent with observation, without leading to contradictions, we can have some confidence in those assumptions.

So basically what you are saying: prove it.

An assumption is either true or false. The only way to know is to test it.

 

[KingCrimson250]

Some would argue that you cannot even truly test the assumption because the tests you use are based on assumptions themselves, and are thus prone to failure. The best you can really do is assume that the assumptions are correct, and hope for the best, which you can do if the assumed assumptions assume a non-contradictory facet, assuming, of course, that the assumption is otherwise logically sound.

 

[Gracchus]

Some would argue that you cannot even truly test the assumption because the tests you use are based on assumptions themselves, and are thus prone to failure. The best you can really do is assume that the assumptions are correct, and hope for the best, which you can do if the assumed assumptions assume a non-contradictory facet, assuming, of course, that the assumption is otherwise logically sound.

If the predictions that arise from your assumptions are not born out by observations then you can be fairly certain that either your assumptions are incorrect or your reasoning is faulty.

Note that it was by trying to show that denying Euclid's fifth postulate, and failing to arrive at a contradiction that non-Euclidean geometries were discovered.

Please note moreover, that some assumptions, like the Peano axioms are pretty much self-evident. (e.g. If two numbers are equal to a third number, then they are equal to each other. If equals are added to equals the sums are equal.) This is actually a refinement of magical thinking, with its laws of contagion and similarity, or should we say that magical thinking is trying to carry the obvious too far?

 

[quatona]

there are three main reasons we disagree in arguments:
1.) we see our opponent's argument as invalid (i.e. not self-consistent)
2.) we claim that his argument is valid, but unsound (i.e. there's a false premise)
3.) his argument begs the question (i.e. circular logic)

this thread takes a look at number 2. the reason we consider one of our opponent's premises to be false is because we assume something he doesn't. the problem with this is, how do we know our own assumption is sound, aside from the fact that it is valid and non-circular?

another way of putting this: given two perfectly valid but opposing arguments, how do we decide which argument makes correct assumptions, and which makes incorrect assumptions?

I don´t. I avoid making my own assumptions. I check whether the conclusion follows from the premise (i.e. the logic), and I ask for evidence for the premises to be accurate. If there is no such evidence, the conclusion can be rejected.
IOW your wording "we assume something he doesn´t" is not necessarily correct. It´s sufficient not to assume what he assumes.

 

[nadroj1985]

I have pointed this out before in other threads:

From the five assumptions of Euclid's postulates, we can deduce that the sum of the areas of the squares on the two shorter sides of a plane right triangle is equal to the area of the square on the third side.

I have seen this theorem tested by repeated measurements by various methods. From this and other predictions deduced from Euclid's postulates, we have determined that euclid's postulates are reasonable assumptions, and, moreover, are self-consistent: They do not lead to contradictions.

So if assumptions lead to deductions that are consistent with observation, without leading to contradictions, we can have some confidence in those assumptions.

An odd choice for an example! Wouldn't Euclid's postulates provide a particularly problematic case for such an analysis of assumptions? We've come to find one of Euclid's postulates to be, if not false, at least difficult to verify. You could certainly make the argument, if you really wanted to, that all of Euclid's postulates (including the fifth) are consistent with observation without leading to contradictions, but that doesn't necessarily mean that they're all true, or that we can have confidence in them (I don't know if you'd want to hold these two things to be distinct). In the case of multiple possible geometries, the problem is precisely that there is more than one assumption set consistent with observation. What do we do then?

 

[Gracchus]

An odd choice for an example! Wouldn't Euclid's postulates provide a particularly problematic case for such an analysis of assumptions? We've come to find one of Euclid's postulates to be, if not false, at least difficult to verify. You could certainly make the argument, if you really wanted to, that all of Euclid's postulates (including the fifth) are consistent with observation without leading to contradictions, but that doesn't necessarily mean that they're all true, or that we can have confidence in them (I don't know if you'd want to hold these two things to be distinct).

The fifth postulate state that through any point outside a given line there passes exactly one line parallel to the given line.
The fifth postulate leads to plane geometry.

If we replace the fifth postulate to say that through any point outside a given line, there are no lines parallel to the given line, we obtain elliptical geometry.

Think here of the service of a sphere. The shortest distance between any two points on the surface of a sphere is a segment of a great circle. Through any point on the surface of a sphere there exists exactly one great circle that intersects the first great circle at exactly two points.

This is a valid observation.

And if we replace the fifth postulate so that is says that through any point outside a given line, there exist an infinite number of parallel lines, we have hyperbolic geometry.

And in hyperbolic geometry the shortest distance between two points is a hyperbola and through any point outside a given hyperbola, there exist infinitely many hyperbolae that do not intersect with the first.

This also is a valid observation.

The fifth postulate is not false, but is one case out of three logically consistent and verifiable geometries.

In the case of multiple possible geometries, the problem is precisely that there is more than one assumption set consistent with observation. What do we do then?

We understand that the assumption is dependent on the geometry of the space we are describing. It is problematic only to the mathematically unsophisticated.

 

[nadroj1985]

We understand that the assumption is dependent on the geometry of the space we are describing. It is problematic only to the mathematically unsophisticated.

Well, it's not quite as simple as all that. Our interest in these geometries is not merely theoretical -- we're rather interested in the question of whether the space that confronts us in experience is Euclidean or not, and if it's not, whether it's correctly described by hyperbolic geometry, or elliptical geometry, or some geometry that describes a space of variable curvature. The problem is that it's not clear that this question is an empirical one -- it's not clear that we can decide upon the correct geometry based on what's consistent with observation.

 

[Gracchus]

Well, it's not quite as simple as all that. Our interest in these geometries is not merely theoretical -- we're rather interested in the question of whether the space that confronts us in experience is Euclidean or not, and if it's not, whether it's correctly described by hyperbolic geometry, or elliptical geometry, or some geometry that describes a space of variable curvature. The problem is that it's not clear that this question is an empirical one -- it's not clear that we can decide upon the correct geometry based on what's consistent with observation.

We know that space-time is curved elliptically by gravity, as indicated by the inverse square law. Whether the universe as a whole is open or closed is, at present, unknown.

That decision will have to wait on observation. It would be foolish to try and shoehorn the universe into a preconceived assumption.

My point remains: We can, in principle, test our assumptions by reason and observation. If we cannot, we are not dealing with science, but with religion or superstition.