Are mathematics and logic themselves sciences?All part of science.
Are mathematics and logic themselves sciences?All part of science.
But if mathematical reasoning can produce knowledge, does that knowledge have to be scientific?It's inference, like figuring out a logic puzzle from some initial hints.
It is inherently limited, as Gödel proved.
So you agree that science is not the only way to gain knowledge, only the most reliable?I think the important word in the OP's question is the one I've highlighted:
There are many ways to obtain knowledge with varying degrees of reliability. In many, probably most, cases, the anecdotal evidence we accumulate as we go about our lives is perfectly adequate to successfully navigate the world. But the cognitive biases that have been built into the way the human brain works by evolution pre-dispose us to make false positive mistakes, rather than risk making (possibly fatal) false negatives, and can lead us to believe many things that simply aren't true. That's why the scientific method had to be invented, and why it is by far the most reliable way to gain knowledge about reality.
For example, mathematical proofs and logical deductions can establish conclusions without experiments. Would you consider that scientific knowledge?Give examples of each.
I am not looking for a fight. I am trying to understand the distinction you are making between scientific knowledge and general knowledge.You have a problem. You come here claiming you're not looking for a fight when you clearly are looking for one.
There is a difference between scientific knowledge, and general knowledge. Science gives us medicines, buildings that can survive earthquakes, submarines with nuclear reactors, solar panels, battery-powered cars, LCD screens, and science allows us to send robots to other planets.
Science cannot tell us who will win the Super Bowl this year, who the good movie actors are, why two peaches from the same tree don't taste equally sweet, or if watching the sunrise is clinically good for you.
A good example of science vs general knowledge is the Money Ball concept of building a baseball team using On-Base Percentage to win enough games to get into the playoffs while on a small budget. The Oakland A's have done well with this concept, but they have not been to the World Series while using this model...because their owner is a cheapskate. Other teams that have embraced the O-BP model while at the same time spending money on proven clutch players (something that often is not quantified with statistics) have won multiple World Series championships. Science helps the A's do well, but organic knowledge of baseball has defeated them when the championships are on the line.
And any sports fan can point to multiple examples where the team that had all the stats loaded in their favor lost their big game to the underdog.
But if a baseball player gets hit in the head by a 95mph fastball? Science is his only savior. MRIs, neurologists, and a long list of medical techniques come into play. "Manning up" and "Walking it off" are a thing of the past.
It all comes down to staying in your lane.
Reliable, and repeatable, yes it is.I am not looking for a fight. I am trying to understand the distinction you are making between scientific knowledge and general knowledge.
If general knowledge can be reliable, does that mean science is not the only way to gain knowledge?
Good grief.I agree that science uses logic, mathematics, and philosophy.
But if they are part of the scientific method, does that make them science?
Or does it show that science depends on things that are not themselves science?

How do you know whether those conclusions are true or not?For example, mathematical proofs and logical deductions can establish conclusions without experiments. Would you consider that scientific knowledge?
Late to this thread but isn't that the crux of the question?How do you know whether those conclusions are true or not?
I understand the analogy. My question is whether mathematics and logic are themselves sciences, and whether they can produce knowledge without empirical testing.Good grief.
A car needs wheels, but a wheel by itself is not a car. An engine by itself is not a car. These are silly questions.
Does that show that a car "depends on things that are not themselves a car?"![]()
Through logical proof, given valid premises and rules of inference. That is different from empirical testing.How do you know whether those conclusions are true or not?
Does every kind of knowledge need empirical testing to be justified?Late to this thread but isn't that the crux of the question?
If you have found a result by using something other than science, how do you prove it to be true? Surely the only way is by the scientific method?
That's circular.Through logical proof, given valid premises and rules of inference. That is different from empirical testing.
They are not and they can not.I understand the analogy. My question is whether mathematics and logic are themselves sciences, and whether they can produce knowledge without empirical testing.
Isn't some degree of circularity unavoidable when we try to justify our basic methods of reasoning?That's circular.
But if they can establish conclusions through deduction without empirical testing, why can't they produce knowledge?They are not and they can not.
They are the tools, not a separate method.
If you have a Sudoku puzzle in front of you, you can come to the correct solution using logic. But the solution was given by the setup, not the logic.But if they can establish conclusions through deduction without empirical testing, why can't they produce knowledge?
I agree that logic cannot establish whether empirical assumptions about reality are true. But does that mean logical and mathematical knowledge is not knowledge?If you have a Sudoku puzzle in front of you, you can come to the correct solution using logic. But the solution was given by the setup, not the logic.
You cannot use deductions by themselves to generate knowledge, only to reveal all the information provided by your initial set of information about a system that might not have been obvious from the start.
If there is any flaw in your initial assumptions, logic will not reveal them unless they are contradictory.
Maths and Logic create systems that are internally consistent, nothing more.