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The Philosophy of Science
This is basically the scientific method. This is what all scientist do, all day every day (besides petitioning for grants :) ). One of the most, if not the most, important part of this process is the "test" part. This is where the scientist attempts to falsify his or her hypothesis. If a hypothesis is not falsifiable then it's not science, and the subsequent parts of the scientific process are sullied and also are no longer science.
Science rests on what is called the "Hypothetical-Deductive" model, which is a process of proposing hypotheses (during the numbered process above) that attempts to predict certain events/situations via deduction. After observing a complex series of events that is the object of study, a hypothetical explanation is proposed that is in agreement / coherent with the observations.
If the predictions predict observable instances that are contradicted by the experiment or observed facts, the prediction is falsified. The set of hypotheses from which the prediction was deduced is not so easiley falsified, because it is difficult to say which hypothesis to reject. The experiment tells us that the theory needs revision. In the case of a few or one hypothesis (like this guy is the father of the child) you can reject the hypothesis as false.
Note that rejecting an alternative hypothesis does not mean that your initial hypothesis is true.
**if someone doesn't assume (2) or (2a), then they could be a solipsist**
Accepting these premises, science begins the process of Methodological Naturalism. What is Methodological Naturalism? It's basically the process of only accepting naturalistic explanations to scientific phenomenon.
Note that if "super"natural explanations were to have falsifiable / testable evidence for their existence, they would de-facto become naturalistic explanations. However, most supernaturalist, when attempting to test their hypotheses, suffer from ad hoc apologetics (more on that later). Science really doesn't reject supernaturalism a priori (ie a pre-supposition), but a posteriori (ie a conclusion).
One assumption of Naturalism is that "nature is uniform"... for example, Naturalists assume that the speed of light here on and around Earth is the same 10 billion light years away.
An example of deductive reasoning via syllogism:
A prediction in science is the concept of taking premises or facts to their logical conclusion. This is a reductionist strategy. For example, if I take 3 feet for every stride I walk, then taking that information to one of its logical conclusions would be to assume that it would take me 30 strides to walk 90 feet. A scientific example of predictions would be the existence of black holes following the premises of the Theory of Relativity, or the existence of endogenous retroviruses using the premises of the Theory of Evolution. Predictions can be summed up by using the phrase "if this scientific theory correctly models the world, then we should see 'xyz' phenomena".
Proof vs. Evidence
A scientific theory is a collection of observable facts, hypotheses and falsifiable conclusions based on those facts. For example, it's a fact that humans and chimps have the same type and number of bones in their bodies. The theory based on this fact is Common Descent.
Using the lexicon of science, a theory is like language. Language is used to describe our thoughts and surroundings. If the language is inadequate at describing something, then the language must be reworked. For example, the word "Internet" didn't exist 300 years ago. It does now. Does this mean that the English language is "wrong"? No. It just means that the English languages needs to update itself to accomodate this new knowledge.
A hypothesis in science is like a word. It either can or cannot describe what it intends to describe. A Law in science is like a letter. Laws are simple, consice mathematical statements that succinctly describe very limited phenomena. The letter "a" describes the "ah" sound. The scientific law E = mc2 represents the relationship between enery and mass, or the law F = ma describes the relationship between force, mass, and acceleration.
There are also in the field of science things called 'auxilliary hypotheses'. The difference is that these auxilliary hypotheses bring an increased empirical content, which is testable (like instrument error). Ad hoc's are not testable / falsifiable.
Peer Review / Publishing
Either way, the editor sends your work to one to four reviewers (the number depends on the journal) - which can include the ones you suggested but doesn't have to - who are also scientists with working experience on what your work is about, or at least about similar topics.
They then look at your work to determine if the results look reasonable, if the conclusions drawn from the result are warranted, if the quality of the work is high enough, if some references or data points are missing, if the work is suited to the journal or should be sent elsewhere, etc. They can then recommend publication with minor or major changes, or reject your work entirely.
The editor then sends the reviews back to you, without indicating who wrote them. You have to make the corrections which the reviewers suggested or at least have to justify why they are not necessary. If it wasn't rejected outright, you can then submit your work again.
Then the editor decides based on the reviews and your answer what to do. If he think you have not answered the objections sufficiently (after all, all editors are themselves working scientists and are able to judge the arguments at least in part), he can reject it entirely. You can then give up or submit it to another journal. If he's unsure, he can again send it to reviewers.
If you're lucky, he thinks you've met the objections and will allow the publication.
This entire process - from submitting to publication - usually takes 6-9 months.
Over time, the term "natural philosopher" was replaced by "scientist" in the public eye, but in universities the tradition of scientists being natural philosophers - or philosophers of nature - stayed; with every new scientist earning the title "Doctor of Philosophy": Ph.D. The line demarcating "philosophy" and "theology", at least in the context of universities, is drawn by distinguishing "Th.D.s" (Theology Doctor) from Ph.Ds.
Graduate students and PhD candidates are prepared for the Peer Review process by having to propose and submit a thesis, which they have to defend in front of a board (not necessarily of peers!). Upon successful defense of their thesis (the equivalent of a publishing in a peer-reviewed journal), they can earn the title "Master" or "Philosophy Doctor (PhD)" in their designated field. Sometimes the thesis can be defended so well that does appear in a respectable peer-reviewed journal.
Finally, science says nothing about "Truth" (with a capital 'T'), science just speaks about what we observe, where the evidence leads us, and what we can predict / deduce utilizing rational conclusions from those observations. If a scientist's prediction / hypothesis / deduction comes to fruition, this still does not encompass "Truth"; it's just a predictive model of what's going on.