PHILOSOPHY is truth subjective?

[induction]

You still have the system that is math, no? It has form, we can call the number 3 whatever, but we know what that means. So the object is not subjective still. That's why someone said it is semantics, confusing the language for what it represents.

for math its more than just semantics, you can get whole different systems by picking different axioms and logics.

 

[The alchemist]

for math its more than just semantics, you can get whole different systems by picking different axioms and logics.

The systems are what we call the objects though. So we don't disagree on that I think, (if you go to the philosophy of math in the other thread, you can see different thoughts on math by various users, myself included in crude explication).

 

[TheManWhoIsAlive]

Objective truth simply means that a concept exists and is true irrespective of whether or not we exist. It's not dependent on our existence. For example, the Sun exists objectively.

Now how we understand the Sun is subjective. It's based on our personal information and analysis. It's based on our limited sensory perception. It's based on our limited mental processing capabilities. This is subjective, because the specific understanding of the Sun this was is dependent on the subject's existence.

There's also collectivistic truth, as we are all humans, we have a shared understanding of things as well.

 

[induction]

The systems are what we call the objects though. So we don't disagree on that I think, (if you go to the philosophy of math in the other thread, you can see different thoughts on math by various users, myself included in crude explication).

oh, yeah. then i think we are talking about the same thing. So, truth is relative with respect to the system. but once you adopt a system, then truth in that system is not relative.

 

[The alchemist]

oh, yeah. then i think we are talking about the same thing. So, truth is relative with respect to the system. but once you adopt a system, then truth in that system is not relative.

No, I don't think the truth is relative. Truth is truth, regardless. We're either talking of different truths, i.e., not addressing the same thing, or either of us is wrong if we are in fact speaking about the same thing.

Maybe you can outline your philosophical basis for what you mean by truth. I follow something like the correspondence theory. Meaning, I think whatever corresponds with reality is truth. Whatever does not, is not truth.

Maybe you are using the word "relative" too loosely or liberal about it which betrays your intention, perhaps something you might need to clarify. Relative in this case would mean that truth intrinsically changes by the change of perspective. I reject this. Are there different ways to derive the truth? Sure. But that does not mean the truth is relative.

 

[Garaad diinle]

Their is physical truth and a mental truth. The physical one is Itus oo itaabsii whatever you can grab and see is an objective truth. Everything else is a matter of perception, opinion and believe that requires convincing and arguments. Much like the elephant story. Four men all agree that there is something in front of them but since they can't see it their perception solely depends on what they're touching and how it feels.

Two people looking at an abstract painting might have wiled interpretation of the painting but if both were looking at a mirror no interpretation is required and both agree on what they see. From this you can further reason that we're trapped to our own senses. The men who couldn't see the elephant were unable to determine what was in front of them despite still retaining the ability of touch and feel on their hands.

What about the other human? Is there a sense similar to sight touch and smell that we're lacking. Could it be that we're unable to perceive the truth of the world like the men and the elephant. Well this is one truth that cannot be demonstrated but argued for.

 

[induction]

No, I don't think the truth is relative. Truth is truth, regardless. We're either talking of different truths, i.e., not addressing the same thing, or either of us is wrong if we are in fact speaking about the same thing.

Maybe you can outline your philosophical basis for what you mean by truth. I follow something like the correspondence theory. Meaning, I think whatever corresponds with reality is truth. Whatever does not, is not truth.

Maybe you are using the word "relative" too loosely or liberal about it which betrays your intention, perhaps something you might need to clarify. Relative in this case would mean that truth intrinsically changes by the change of perspective. I reject this. Are there different ways to derive the truth? Sure. But that does not mean the truth is relative.

ok, so my definition/understanding of truth in the context of math is different from my understanding of truth in the context of the real world (in this, i too, lean towards correspondence theory). but , correspondence theory doesn't really make sense for math because most of the time we are dealing with things that are very far removed from reality.

So, in math, a statement is true if using the logic you adopted in your system and the axioms of your system you can prove that statement. Now, depending on the axioms and the logic of the system, a statement that is true in one system might be is false in another.

Take for example, Euclid's 5th axiom which states "If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.". if you reject this axiom, then you will end up in a system where 2 "parallel" lines eventually cross (none euclidian geometry). this is obviously very different from the system we are usually familiar with.

So, thats an example of how the truth value of the statement: "two 'parallel' lines never meet" is relative/dependent on whether your system excepts axiom 5 or not. At least thats how i understand it

 

[induction]

Their is physical truth and a mental truth. The physical one is Itus oo itaabsii whatever you can grab and see is an objective truth. Everything else is a matter of perception, opinion and believe that requires convincing and arguments. Much like the elephant story. Four men all agree that there is something in front of them but since they can't see it their perception solely depends on what they're touching and how it feels.

Two people looking at an abstract painting might have wiled interpretation of the painting but if both were looking at a mirror no interpretation is required and both agree on what they see. From this you can further reason that we're trapped to our own senses. The men who couldn't see the elephant were unable to determine what was in front of them despite still retaining the ability of touch and feel on their hands.

What about the other human? Is there a sense similar to sight touch and smell that we're lacking. Could it be that we're unable to perceive the truth of the world like the men and the elephant. Well this is one truth that cannot be demonstrated but argued for.

pretty cool example . but even the things we perceive with our senses might be relative/wrong. take for example the sun, to our eyes it looks no bigger than a coin yet, from science we know that its much bigger than that.

 

[Garaad diinle]

pretty cool example . but even the things we perceive with our senses might be relative/wrong. take for example the sun, to our eyes it looks no bigger than a coin yet, from science we know that its much bigger than that.

Huh! What an interesting come back. I find myself agreeing with you, turns out even senses can be unreelable tools at times but this is at rear cases i must say. Most humans if not all humans can agree to a number of things that are empirically objective truth such as your example. No one with sight can deny the existence of the sun.

 

[induction]

ok, so my definition/understanding of truth in the context of math is different from my understanding of truth in the context of the real world (in this, i too, lean towards correspondence theory). but , correspondence theory doesn't really make sense for math because most of the time we are dealing with things that are very far removed from reality.

So, in math, a statement is true if using the logic you adopted in your system and the axioms of your system you can prove that statement. Now, depending on the axioms and the logic of the system, a statement that is true in one system might be is false in another.

Take for example, Euclid's 5th axiom which states "If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.". if you reject this axiom, then you will end up in a system where 2 "parallel" lines eventually cross (none euclidian geometry). this is obviously very different from the system we are usually familiar with.

So, thats an example of how the truth value of the statement: "two 'parallel' lines never meet" is relative/dependent on whether your system excepts axiom 5 or not. At least thats how i understand it

can't delete/edit this anymore, and it has mistakes in it, so if your reading it please ignore it

 

[induction]

Huh! What an interesting come back. I find myself agreeing with you, turns out even senses can be unreelable tools at times but this is at rear cases i must say. Most humans if not all humans can agree to a number of things that are empirically objective truth such as your example. No one with sight can deny the existence of the sun.

well what about mirages, they don't exist yet we "see" them. maybe the sun is something similar?

 

[Garaad diinle]

well what about mirages, they don't exist yet we "see" them. maybe the sun is something similar?

I see what you did there. If you stretch the argument long enough you'll eventually get me to agree with you. In our current bubble of reality us humans agrees that the sun is real. We determine this by our senses.

We feel it with our body we see how it effects the world the ocean the wind and living organisms. There are some stuff that are simply self-evident that we all agree on. Outside of our collective bubble different truth my or my not exist but that is undeterminable sort of like the multiverse.

A number of people believe in a multiverse a sea of bubble universe but you see we cant even travel to the centre of our bubble universe let alone the edge of the bubble so how can we determine that other bubble universes even exist. We can only confirm our bubble universe but not the other bubble universes and as such we can only acknowledge our bubble of truth and not any other bubble or bubbles of truth, we can only speculate.

 

[induction]

I see what you did there. If you stretch the argument long enough you'll eventually get me to agree with you. In our current bubble of reality us humans agrees that the sun is real. We determine this by our senses.

We feel it with our body we see how it effects the world the ocean the wind and living organisms. There are some stuff that are simply self-evident that we all agree on. Outside of our collective bubble different truth my or my not exist but that is undeterminable sort of like the multiverse.

A number of people believe in a multiverse a sea of bubble universe but you see we cant even travel to the centre of our bubble universe let alone the edge of the bubble so how can we determine that other bubble universes even exist. We can only confirm our bubble universe but not the other bubble universes and as such we can only acknowledge our bubble of truth and not any other bubble or bubbles of truth, we can only speculate.

yeah, it's just too difficult to know ig. better off not really thinking about it

 

[The alchemist]

ok, so my definition/understanding of truth in the context of math is different from my understanding of truth in the context of the real world (in this, i too, lean towards correspondence theory). but , correspondence theory doesn't really make sense for math because most of the time we are dealing with things that are very far removed from reality.

You are right in one way about this, mathematical knowledge is different from philosophy about the other sciences. And contrary to the subjective pre-conditions that you deem is relative, mathematics no matter how philosophically elusive in its status, carries systematized nature that is even more certain than the other sciences and way less error-prone as a methodology from its bodied composition, no matter how incomplete. Going into ontology and epistemology, mathematics got a strange quality in the knowledge sphere. I really encourage you to read my perspective on the other thread if you haven't because its philosophical status is a lengthy process of discussion in itself.

Godel's Platonism claims abstract objects and concepts are as objective as physical things in the real world. I believe it is another form of thing that we cannot conceptually describe properly, mathematics just so happens the language we use to imperfectly superimpose upon our knowledge-seeking behavior to align understanding of reality. If we had hold of that thing, it would be a better navigator to infer upon reality.

I think not math itself, but where it exists is a miracle.

So, in math, a statement is true if using the logic you adopted in your system and the axioms of your system you can prove that statement. Now, depending on the axioms and the logic of the system, a statement that is true in one system might be is false in another.

Take for example, Euclid's 5th axiom which states "If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.". if you reject this axiom, then you will end up in a system where 2 "parallel" lines eventually cross (none euclidian geometry). this is obviously very different from the system we are usually familiar with.

So, thats an example of how the truth value of the statement: "two 'parallel' lines never meet" is relative/dependent on whether your system excepts axiom 5 or not. At least thats how i understand it

For example in a related note with logic, something needs a defined truth value to be validated or not. But you're on to a separate matter from general truth here, kind of. I think math and the philosophy of math are other conversations, to be honest. Even when prescribing logic as a methodology, you already need to know if the statement (axiom) carries properties of set defined parameters that carry truth values. This means that the statement and methodology are two different things and that by carrying on the process you already accept that truth is separate from the methodology.

And yes, logical consistency might not mean it is correct. That's why deductive reasoning is not always reflective of real things. For example, there are valid statements that are not sound.

For example:

If it's raining, then cows will fly.

It's raining.

Therefore, cows will fly.

This above argument is valid but carries no soundness. A statement being sound means it is true. So, what you conclude is, that contrived deductive inferences do not necessarily carry correspondence with the truth.

Simply put, if the total of α and β is less than 180°, then the two lines are not parallel and will eventually meet. If the amount of the angles combined is over 180° then the lines will never meet. The thought was, how do we know if two parallel lines are truly parallel and will never meet if it hypothetically is infinite in length?

I think this is a weird one to set an example of as an axiom, not going to lie.

 

[Shangani]

You are right in one way about this, mathematical knowledge is different from philosophy about the other sciences. And contrary to the subjective pre-conditions that you deem is relative, mathematics no matter how philosophically elusive in its status, carries systematized nature that is even more certain than the other sciences and way less error-prone as a methodology from its bodied composition, no matter how incomplete. Going into ontology and epistemology, mathematics got a strange quality in the knowledge sphere. I really encourage you to read my perspective on the other thread if you haven't because its philosophical status is a lengthy process of discussion in itself.

Godel's Platonism claims abstract objects and concepts are as objective as physical things in the real world. I believe it is another form of thing that we cannot conceptually describe properly, mathematics just so happens the language we use to imperfectly superimpose upon our knowledge-seeking behavior to align understanding of reality. If we had hold of that thing, it would be a better navigator to infer upon reality.

I think not math itself, but where it exists is a miracle.


For example in a related note with logic, something needs a defined truth value to be validated or not. But you're on to a separate matter from general truth here, kind of. I think math and the philosophy of math are other conversations, to be honest. Even when prescribing logic as a methodology, you already need to know if the statement (axiom) carries properties of set defined parameters that carry truth values. This means that the statement and methodology are two different things and that by carrying on the process you already accept that truth is separate from the methodology.

And yes, logical consistency might not mean it is correct. That's why deductive reasoning is not always reflective of real things. For example, there are valid statements that are not sound.

For example:

If it's raining, then cows will fly.

It's raining.

Therefore, cows will fly.

This above argument is valid but carries no soundness. A statement being sound means it is true. So, what you conclude is, that contrived deductive inferences do not necessarily carry correspondence with the truth.

View attachment 257438
Simply put, if the total of α and β is less than 180°, then the two lines are not parallel and will eventually meet. If the amount of the angles combined is over 180° then the lines will never meet. The thought was, how do we know if two parallel lines are truly parallel and will never meet if it hypothetically is infinite in length?

I think this is a weird one to set an example of as an axiom, not going to lie.

Truth and logic are separate concepts, and that a statement's logical validity does not necessarily correspond to its truth value. The example you provided demonstrates the difference between validity and soundness in deductive reasoning to my understanding.

Regarding your question about parallel lines, in Euclidean geometry, parallel lines are defined as lines that do not intersect, no matter how far they are extended. This definition assumes the truth of the parallel postulate, which states that for any given line and point not on the line, there is exactly one line through the point that is parallel to the given line. This postulate cannot be proven from the other axioms of Euclidean geometry, and it is therefore sometimes considered as an axiom itself.

In non-Euclidean geometries, such as hyperbolic geometry, the parallel postulate is not true, and parallel lines can intersect at some points. In these geometries, the truth value of statements about parallel lines is different from that in Euclidean geometry.

 

[The alchemist]

Truth and logic are separate concepts, and that a statement's logical validity does not necessarily correspond to its truth value. The example you provided demonstrates the difference between validity and soundness in deductive reasoning to my understanding.

Regarding your question about parallel lines, in Euclidean geometry, parallel lines are defined as lines that do not intersect, no matter how far they are extended. This definition assumes the truth of the parallel postulate, which states that for any given line and point not on the line, there is exactly one line through the point that is parallel to the given line. This postulate cannot be proven from the other axioms of Euclidean geometry, and it is therefore sometimes considered as an axiom itself.

In non-Euclidean geometries, such as hyperbolic geometry, the parallel postulate is not true, and parallel lines can intersect at some points. In these geometries, the truth value of statements about parallel lines is different from that in Euclidean geometry.

I think we agree. My response was sort of denying the notion that even the models using other methods had consistency too, and that it should not be used to prove that truth is subjective. There is consistency within the floating variates of systems so to speak.

I see. But I'm sure my explanation of the conditions of when the parallel lines should meet extends to the correct on simple bases, with the model specifically.