proof

Proof can refer to the factual evidence that helps to establish the truth of something, the act of validation or testing for truth, or to a formal series of statements showing that if one thing is true something else necessarily follows from it. We toss the word 'proof' around in vernacular usage, yet rigorous usage of the term 'proof', outside alcoholic spirits, applies only to mathematics and to philosophical syllogisms.

Whereas disproof is an achievable certainty, "proof" is technically much less easily attained. A person who was demonstrably in Hong Kong at the time of a shooting in New York city could not have committed the crime, whereas we can be much less certain of the innocence of those capable of wielding a gun among the seven million or so people who were in New York city at the time.

Scientific method involves a closing in on the best possible explanation for observed phenomena, which is ideally achieved by discarding experimentally disproven falsifiable hypotheses. The lack of absolute certainty inherent in "best possible" does not sit well with those with a rigid need for a psychological sense of certainty, yet highest probability is the best that we can reasonably demand of most of our important questions.

By comparison, all religions are invented religions (despite claims of received dogma) and demand belief without any incontrovertible evidence to support religious claims. Religious dogmatists, particularly creationists, attempt unsuccessfully to suborn facts to fit their religious dogma. Whereas science moves from fact to explanation, religion moves from dogma to distortion. Because religions are only very loosely based on observable reality, attempts to twist empirical realities to fit religious dogma are necessarily fraught with illogic and falsehoods.

Received notions of deities do not provide the best explanations for observed facts, so scientific knowledge unintentionally runs counter to, or disproves, religious claims. Claims that "God performed a miracle" do not provide any explanation at all for empirical data.

As a result of this lack of foundation in reality, there are many invented religions, yet almost universal agreement about internally logical, replicated, scientific knowledge. New information might necessitate a slight modification of scientific hypotheses to better fit the data, but scientific theories carry a high degree of likelihood, and scientific laws signify near certainty.

Fallacious argument from ignorance are much loved by creationists and advocates of intelligent [sick] design theory. In these fallacies, the arguer erroneously claims either that lack of proof must render a claim false, or that lack of disproof must render a claim true. Referring back to the shooter analogy – disproof may render false any claim that a person who was actually in Hong Kong could have shot someone in New York city, but it does not prove that a particular individual in New York was necessarily the shooter. Conversely, not knowing who shot the victim in New York does not mean that the victim of the shooting could not have been shot.

When proponents of intelligent [sick] design theory demand an explanation for evolution of a complex, functioning system they are committing the fallacy of argument from ignorance (in addition to the fallacy of shifting the burden of proof).

Quo Vadis?
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science

The commonest misconception about science involves equating science with the areas in which scientific method is applied. Thus, people mistake the topics investigated by scientific techniques as being the sum total of science. Biology, for example, is a science, but "biology" does not delimit the meaning of science.

In fact, science is a method by which knowledge about the physical world is attained. Scientific 'knowledge' inheres both observed, empirical data and the best possible explanation regarding the mechanisms by which the observed phenomena came about and the prediction, where appropriate, of any future manifestations that can reasonably be expected. This scientific method is most appropriately applied to natural, physical phenomena, so it defines the subject areas appropriate to investigation.

Scientific method is akin to formalized skepticism in that it ideally proceeds by rigorous scrutiny of falsifiable hypotheses. To achieve this, postulated explanations for observed phenomena must be expressed in such a way that they can be tested and disproven. An analogy would be determining whether a suspect in a crime has an alibi – if the suspect can be demonstrated to have been in Beijing at the time that a stabbing was committed in San Francisco, then the suspect cannot have perpetrated the stabbing (unless, that is, the suspect had impossibly long arms).

Any hypotheses that are demonstrated to be faulty will be discarded, and alternated explanations for empirical observations will be formulated and tested. (Expanding the analogy, another suspect will be sought for the stabbing.) Eventually, any reasonable hypotheses that are not disproven will be regarded as so acceptable as to be elevated to the level of scientific theory.

Scientific predictions, however, represent a subset of experimentation and are propositional – if this hypothesis is correct, then we will observe such and such a phenomenon. Failure to observe the predicted phenomenon might be taken to disprove the hypothesis. However, the failure might be a result of experimental or observational error, or might result from faulty predictions based upon a reasonable hypothesis. Alternatively, the hypothesis may be incorrect, but the predicted phenomenon is observed because of a mechanism not yet hypothetically considered.

For these reasons peer-reviewed scientific papers include analyses of current thinking, descriptions of methods, and statements of results so that other researchers might attempt replication. In science, unlike the case for mathematics, proof is not possible, while disproof – falsification – is possible. For this reason, hypotheses to be experimentally tested are ideally framed in such a way that they may be disproved – falsifiable hypotheses. When an empirically based, logical hypothesis, which has not been disproved after repeated testing, is deemed satisfactory by consensus within the scientific community, then the hypothesis graduates to the status of Theory (capitalized to differentiate the scientific term from its vernacular usage).

In practice, much of science proceeds upon positive results – repeated observations of a phenomenon under particular conditions. In the softer sciences, such as the social sciences, statistical analyses of results play an important role. Some sciences, such as paleontology are by their nature outside the possibility of experimentation – we cannot resurrect dinosaurs or recreate meteor impacts – and must proceed on the basis of accumulated empirical evidence.

We all toss around vernacular 'theories' – unproved ideas or theoretical speculations that are not necessarily even so well formulated as scientific hypotheses. Even some elaborate theories, such as intelligent [sick] design theory have considerably less conceptual merit than their promoters will ever acknowledge. For biblical literalists, such a 'theory' may have emotional appeal, but in terms of speculation concerning reality, ‘intelligent [sick] design theory’ has no more merit than the belief system of the Lambayeques.

Quo Vadis?
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inductive vs deductive

Inductive reasoning moves from the specific to the general, that is, from data to a principle. Deductive reasoning moves from the general to the specific, that is, from the principle to particulars. Abductive reasoning moves from relevant evidence (specific) to the best possible explanation (principle). Abduction is inference to the best explanation – beginning from a set of accepted facts, inference proceeds to the most likely explanation for those facts. Inference is the process of deriving a conclusion that is based solely on what is already known (a posteriori).

Inductive reasoning involves coming to a conclusion that is inferred from multiple observations. Repeated testing will help to ascertain whether first inference (conclusion derived) is correct or incorrect. In contrast, valid deductive reasoning is based in formal logic and will yield a true conclusion if the premises on which it is based are themselves true. That is, the inferred conclusion of a valid deductive inference is necessarily true when the premises are true, so a formally valid deductive inference cannot be false.

The Scottish empiricist David Hume, raised the skeptical philosophical objection that inductive reasoning might fail whenever the past cannot be taken to be a reliable guide to the future. In essence, if we have just seen 43 white swans, are we justified in assuming that all swans are white or even that the next swan that we see will be white?

The philosopher of science, Karl Popper expanded Hume's ideas of the 'problem of induction' and argued that there can be no solution to the problem of induction in that empirical observations cannot provide proof for a scientific hypothesis, theory, or law. Popper argued that, since only disproof is a certainty, science should proceed by a 'deductivist' method of conjecture and refutation, employing deductively valid reasoning that does not resort to inductive confirmation.

In practice, modern scientific method employs inductive, deductive, and abductive reasoning to move from empirical data to elucidation of principles. Ideally, hypotheses are couched so that they could be falsified should they fail to correctly predict experimental observations. However, since the hard sciences involve empirical observations of natural phenomena that can reasonably be expected to operate consistently, relevant positive results are taken to provide practical support for the likelihood that a theory is accurate.

Unlike the case for swans, would we not be fully justified in believing that all apples that fall from an apple tree will fall toward Earth rather than floating toward the moon? To stipulate that the apple tree is situated on Mars would appear to put a worm in this theory, but that problem can be avoided by asking instead, 'would we not be fully justified in believing that all apples will fall toward the planet?' Whether we talk of the force of gravity, or the more modern understanding of warping of space-time, natural laws dictate that objects are most 'attracted' to the largest nearby mass.

Quo Vadis?
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