I was responding to Eric. But now that you mention it, can you explain how faith winds up in either mathematics or science? In mathematics you pose a set of axioms and use logic to provide a larger set of conditionally true statements. When we talk about the truth of these statements it is purely in a logical sense, not an ontological sense.

While a scientific theory can often be posed axiomatically, scientists do not consider the axioms to be ontologically true either. They are hypothetical assumptions whose usefulness can be measured in the correspondence of the theory's predictions with the outcomes of experiments. I fail to see the "faith" in this approach.

Additionally, it isn't necessary to make assumptions regarding the nature of an objective reality (or even whether or not such a thing exists). I need only note my observations and attempt to optimize a predictive model for future observations in order to carry out the algorithm of the scientific method. Ideas I may have about the ontological nature underlying my observations are, in fact, metaphysical. The scientific method does not address such things and it is perfectly possible to carry on the work of science without entertaining a particular assumption regarding the nature of reality. Science steadfastly concerns itself with things that can be perceived (with or without the help of instruments). Assumptions about the fundamental nature of things are not part of science. As Eric pointed out, they are not falsifiable. Those assumptions are, by definition, metaphysical.

I think scientific theory is more like something you can disprove. You can't ever demonstrate truth of a theory in a philosophical sense.

Can you explain what Goedel's work has to do with faith in science? I'm not seeing it.

Most well-developed theories can be described axiomatically. Newtonian mechanics takes Newton's laws of motion as axioms. Special relativity takes the principle of relativity and the constancy of the speed of light as axioms. Both theories can be developed based on these assumptions alone.

I don't consider adopting a set of axioms as a matter of faith either in either math or physics (though seemingly for different reasons). Mathematical theories are isolated logical structures that follow from whatever axioms you assert. But posing a set of axioms does not involve any assumption of ontological truth, so I fail to see what faith has to do with this course of study. In physics, our observations are used to judge the fitness of a given theory (and by proxy the axioms that underly it). One way of looking at it is that mathematics works in the forward direction using logical deduction while physics seeks to reverse engineer a sufficient set of axioms to produce a theory that corresponds to experiment. Science relies on what Goedel called the metamathematical step. At each point where a theory is found to be inconsistent with experiment it must perform this metamathematical step to find a new set of axioms and theory. While the theories of physics apply to our observations of nature, physicists do not take the axioms underlying their theories as fixed truths. Future theories must be allowed to adapt and to keep, change, discard or add axioms as necessary to accommodate the findings of experiment.

Thank you for an awesome post.

I don't understand why you must do these things. Modern industry relies on scientific knowledge. You are typing on a piece of technology that exemplifies that science is useful. Science delivers useful models and technology is the demonstration of that usefulness. We aren't talking about scientific theories being true because no scientific theory can ever be shown to be true. That is a moot point in science. Science aims to provide useful understanding of things. The proof of science's usefulness can be found in the technological pudding.

A theory must make a physically testable prediction in order to be a scientific theory. Without this it is more like a type of applied mathematics. I will not be surprised if the legacy of string theory lies not in science but in the field of mathematics.

A bigger problem for string theory seems to be the landscape problem. String theory describes the universe in terms of strings occupying four expanded dimensions of spacetime and a number of extra dimensions that are rolled up into a distance shorter than the Planck length. The particular way that the extra dimensions roll up determines the physics in the remaining expanded dimensions. There are an infinite number of ways to do this. If a string theory makes a prediction that is shown to be inconsistent with experiment then it can be claimed that we were simply looking at the wrong theory. So, we pick a new theory and start again. Unfortunately, we don't have a notion of where in the infinite "landscape" the correct string theory lies, so it leaves us picking points at random and hoping that we get the right one.

Back to terminology: A theory is a logical system that explains observed phenomena and allows us to predict the outcomes of future experiments. A hypothesis is a specific prediction regarding the outcome of an experiment (not the same thing as a theory). A law has no predictive or explanatory power. It simply describes an empirical relationship between measurable quantities. Often it is used as an axiom of a theory (Newton's laws of motion are axioms in Newton's theory of mechanics). Newton's law of gravity is still valid in steady state. We have found it unsuitable as an axiom for a theory of gravity (i.e. it is not an assumption of general relativity). Axioms are not immutable in science. We search for the right set of axioms to generate a useful theory. Science does not declare a given set of axioms as fact. Experiment is the final arbiter.

Parent post was by me, by the way.

You might say that changes in our perception correlate with changes in some objective reality. They are not directly equivalent, however, and you cannot start with perception and extract reality because the map from reality to perception is not one-to-one (so mathematically there is no inverse map). That is why subjectively we have many different accounts and many independent perceptions.

If I ingest hallucinogenics have I changed the underlying reality?

At best we can reference a consensus reality built up from our collective agreement about repeatable, consistent observations. We cannot actually make contact between our perceptions and an ultimate reality that underlies everything. However, as I mentioned in the previous comment (as an Anonymous Coward) this agreement ends when we observe the microscopic world.

Axioms are just assumptions used as the foundation of a logical system. They are considered true only in mathematics. In science we don't know the validity of our axioms and so we cannot know the validity of logical deductions (which is why we have to test them against observations). I.e. I can find no absolute truth in modern science.

Actually, I can formulate science as a collection of predictive models that merely help me to predict future observations. I do not have to assert any external, objective reality.

A theory can be consistent with current data but can never be proved.

The question of whether a given person understands a certain theory seems largely irrelevant to me. This is about the philosophy of science. The details of any particular theory don't have any tangible impact on that.

The write-up makes some statements that seem a bit misguided given my understanding of the philosophy of science. For example, "The fact is that it takes years of dedicated study before scientific truth in its truest, mathematical and symbolic forms can be understood." I can identify no object that corresponds to scientific truth in modern science. Truth is a philosophical ideal and doesn't actually belong in the modern language of science. Our theories are models that are used to explain various observations that we make of nature. A model should not be confused with a truth. A model can be useful, but to mistake it for truth makes a serious misstep and a conflation of two very different things.

No matter how accurate the predictions of a theory may be, we cannot know whether experiments carried out under different conditions will yield unpredicted outcomes. In fact, it is these events that drive science forward. As Karl Popper has told us, falsification is the engine that drives science, not verification. We can never prove the truth of one of our theories. We can only demonstrate consistency with current data. However, a single counterexample can demonstrate the non-truth of a theory. By discarding theories that don't work and keeping those that do, we can improve the fitness of the candidate theories. However, it's impossible to arrive at a unique, true theory by this process of elimination. Science consists of a collection of falsifiable models. Where do I find the supposed scientific truth in which I should place faith?

People who talk about science as truth seem to be making an unconscious appeal to authority: "Because scientists know more than I do, the theory they are talking about must be true."

Actually, from our perspective all objects are caught forever at the horizon. An object will never fall into a black hole according to the description from our coordinates. However, the principle of relativity really applies to inertial reference frames, which we are not talking about here. Simply put, our coordinates are insufficient (deficient, defective, etc.) for describing anything in the vicinity of a compact mass.

It's also not a given that a black hole will simply evaporate. You have to balance the energy budget. The black hole is predicted to lose energy via Hawking radiation. However, it's perfectly possible that due to infalling matter and radiation it is actually increasing in energy despite this.

If you insist on describing things from our perspective, you might claim that the Hawking radiation slowly radiates the information about objects that appear to be caught at the horizon. Certainly the entropy (information content) of a black hole is proportional to the surface area of its horizon, so from an information theory perspective maybe this could seem reasonable. However, the failure of a coordinate system should generally prod you to find a coordinate system that does work in the region you wish to describe rather than to trust predictions that rely on the defective coordinate system.

According to my understanding of the theory: In special relativity, descriptions from any inertial reference frame are equally valid in relativity. However, in general relativity no coordinate system can cover the whole spacetime manifold. Our coordinate system's time variable reaches an end at the event horizon and so our coordinates simply cannot be used to describe events at or beyond the horizon.

Of course, deducing the presence of a singularity within a black hole relies on GR being valid across all length scales. GR is inconsistent with QM (our most successful theory for describing phenomena on small length scales), which should make us question the validity of singularities. This coupled with our inability to gather information from the interior of a horizon doesn't give much firm ground for claiming what things are like inside of a horizon.