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What methods do historians use to gain knowledge?

This is a very interesting question as this focus on methods specific to this AOK as some knowledge in history is recorded and persevered whereas some knowledge is lost due to lack of data.

The most commonly recognised historical methodologies include: Palaeography (study of historical handwriting), excavations, diplomatics, the study of documents, records and archives, chronology (establishing the dates of past events), the study of publications, epigraphy (study of ancient inscriptions). genealogy (study of individuals and families), historical geography, heraldry (study of weapons), codicology (the study of handwritten documents), numismatics (the study of coins), sphragistics (study of seals), and the study of new media (historical E-literacy).

Methods in history is prone to historian bias when the events have been recorded and written from a one perspective and sometimes knowledge gained through few methods is not verifiable.

The above KQ can be used to in other AoKs only in relation to understanding the historical developments and how past knowledge was acquired. For example – a lot of knowledge of medicines in Ayurveda (NS) is available due to the earlier accounts of using various ingredients.

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The "scientific method" has only been  applied and associated with "science" since the Scientific Revolution. To define the scientific method, it is  the process involving hypothesis,  testing, empiricism, deduction, and falsifiability.
Theoretical sciences (such as theoretical physics) and inductive sciences are prominent examples where the scientific method was not/cannot be applied - Einstein's theory of relativity, string theory, Kepler's determination of elliptical orbitals and even some aspects of evolutionary biology did not start off with a hypothesis. Many of these started off as theories and, for some,  as in string theory for example, ended there.
For example, Darwin was unable to experimental test his theory of evolution, because he was putting forward a theory in which direct observation and experimentation were impossible. To overcome this obstacle,  Darwin developed a new scientific procedure, which became known as the hypothetico-deductive method. It entails the development of a theory, then relies on analogy and deduction to reach a reasonable explanation (without direct empirical evidence),  then the application of that theory to a wide range of facts to show its explanatory power.
For science to progress, scientists should use whatever method suits the particular circumstances, the nature of the problem, the theory available, the tools and methods available for observation and experimentation and bring into that their own personality and imagination, so there will be a variety of starting points in any scientific investigation and many different methods of carrying it out.

But the absence of a single scientific method does not mean that scientists have no methods. In the natural sciences there are constant values such as clarity, accuracy and consistency with evidence but the specific methods  will be specific to the context.

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What does it mean to say that mathematics is an axiomatic system?
It means assuming a foundation to be true first and then building up upon it – the proof will only be true if the axioms (foundations) hold true. One of the first mathematicians to propose axiom's was Euclid, whose axioms include:

a)Things which are equal to the same thing are also equal to one another.

b) If equals be added to equals, the wholes are equal.

c) If equals be subtracted from equals, the remainders are equal.

Most proofs in geometry rely on axioms – statements such as “sum of all angles in a triangle add up to 180°” and go to build on from there.

An example of an axiom is “zero is a number” – anything that builds on this is assuming that “nothingness” is a number –without zero, binary code, calculus, place value and modern electronic would not exist.

A fun example i give to students is the one attached above - where the "glitch" is in the 4th step (you cannot divide by a zero)- from this they begin to understand that if the mathematical proof is build on an incorrect axiom, the outcome will be faulty.

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To what extent are the methods of justification different in the arts compared to other areas of knowledge?

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To what extent are the methods of justification different in the arts compared to other areas of knowledge?

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I think this question is inherently comparative and can be applied to all other AOKs. To help students answer this question, I would give them examples of knowledge claims made about art and have them brainstorm methods and tools to test those claims. Then I would do the same thing with knowledge claims about other AOKs. Then I would have students compare and contrast the methods and tools used to justify or test those claims.

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KQ - Is an understanding of the perspective of other knowers essential in the pursuit of knowledge?

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KQ - Is an understanding of the perspective of other knowers essential in the pursuit of knowledge?

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In terms of the human sciences, understanding the perspectives of other knowers is essential in the pursuit of any of the human sciences as common themes must be agreed upon to engage in the acquisition of knowledge in any one of the human science disciplines. Take for example political science, all knowers need to agree that power relationships are worthy to study and explore. In the absence of this general concept, the exploration of political science would be unattainable.

The same can be applied to other AOKs as the perspective of other knowers is of paramount importance in the exploration of any discipline. Much like thesis, antithesis and synthesis, the pursuit of knowledge is a journey shaded by the perspectives of individual konwers. Thus, making the KQ applicable to every AOK.

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The knowledge questions associated with the human sciences under methods and tools are on page 30 in the TOK Guide. Hope that helps. Marilynne

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The knowledge questions associated with the human sciences under methods and tools are on page 30 in the TOK Guide. Hope that helps. Marilynne

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I believe this KQ could relate to the human sciences - where again the methodology of study could mimic that of science - involves observation, collection of data, the formation of a  hypotheses, and an aim to test the validity of the hypothesis and possibly falsify it. But here again, there is no single method - for example research in social work could study the interaction between individual and public authorities, using qualitative research methods, metholody in economic studies is often dependent on mathematical models. So even in the human sciences there is no "single" methodology for producing knowledge

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In the natural sciences, we have a set of justified beliefs on which we base much of our scientific knowledge - very similar to how mathematical axioms form the foundation of a mathematical proof. The spped of light is believed to be constant in all directions and the implications of this have allowed the theory of relativity to evole, the study of space-time, and worm-holes etc. Without this postulate in place, upon which further scientific studies have been built, quantum mechanics may have not existed.