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= Intellectual Courage =

Intellectual courage falls under the family of philosophical intellectual virtues, which stems from each individual’s own doxastic logic.

Branches include (but not exclusive to): Intellectual humility, Intellectual responsibility and Intellectual conscientiousness. Existing under numerous different definitions, the form that intellectual courage takes is dependent on the context and/or situation it falls under, and is prevalent in everyone.

As such, famous philosophers have studied and observed this virtue to a great extent, so as to understand and grasp the impacts of intellectual courage on the human mind.

Definitions
Although very much related to its parent term, intellectual courage ventures in much deeper towards specifically ensuring that an action any person may take, is aligned with the unwavering rational beliefs that that said person holds. On a daily basis, many emotions such as fear and desire easily influence decisions, and the degree to which a person is able to control or give in to those, determines the strength of one's intellectual courage.

Cognitive thoughts, which eventually turn into cognitive actions, will mostly require the combined involvement of not only intellectual courage, but also moral courage, philosophical courage and physical courage. Some also generalise intellectual courage into the family of courage, together with social courage and physical courage.

It has also been said that intellectual courage serves as a "character strength", along with other personality aspects such as self-generated curiosity and open-mindedness. All of this takes a highly iterative process, stemmed from the collective and ongoing influence of daily happenings and exposure, such as one's social surroundings and environment. As these traits are very implicitly formed, it explains the varying degrees of intellectual courage present in each and every individual.

Manifestation
Virtues have been a topic at hand for philosophers from all over the globe, dating back to as far as the Middle Ages.

Although the birth of intellectual virtues specifically, come shortly after, the foundational layer of interpretations can be traced all the way to ancient Roman, Greek and Latin philosophical theories and traditions, with even religions such as Buddhism having their own take and perspective on specific virtues, and what classifies as a virtue. History has proven time and time again that courage does not always take form in its physical and common connotation, but also in its cognitive form, being an attribute that one can possess, as a "courageous thinker".

Ryan, A. claims that intellectual courage is also widely used and present in political situations. This occurs when one demonstrates the notion of sticking with one's proclamation, despite being exposed to unreasonable and counter intuitive influence that is usually filled with non-aligning agendas sprouting from other political parties. The demonstration of intellectual courage in this sense is highly sought after as a leader and is often followed by new found heights of respect from people.

A more casual day to day situation in which an individual's intellectual courage would arise in, is when contemplation between more than two pathways are present, and the usage of knowledge and reasoning is crucial. Many aspects and foreseeable situations must then be carefully assessed to confidently single out the best possible route. This can then be backed up and weighed upon factors such as the chosen option being one of either the most ethical, the most logical, the most reasonable, or the most beneficial to the individual.

Intellectual courage is highly compared and dependent on a person's self-reliance.



Aristotle
Aristotle is a well known figure in Greek philosophy who has extensively written on virtues such as intellectual courage in his books, Eudemian Ethics and Nicomachean Ethics. As Ryan, A. writes, Aristotle defines courage as "the virtue that occupies a mean between cowardice and recklessness".

Although initially insinuating the physical and literal conception of courage, Aristotle does not exclude the discussion of the terminology in the less straightforward sense.

Aristotle makes a connection for morality and intellectual virtues in being collectively exhaustive, in order to achieve the fulfilment of reading a situation to the best of abilities and thus coming to a sound and righteous conclusion. The act of displaying intellectual courage in this sense, would be to stand one's ground in the situation where in a conflict of interest arises. This will in turn, result in an expense or an opportunity cost, inducing a vital decision making road block (a drawback is present), in choosing the most righteous and moral conclusion.

Role in Mathematical Creativity
This section is purely to define intellectual courage in the perspective of mathematicians, and aims to demonstrate the underlying relationship between one's intellectual courage in contrast to their respective mathematical creativity.

In reference to Hadar, N. and Kleiner, I.'s 20 year long research, it has been shown that academic privilege is in fact, not the only factor that contributes to the minds of mathematically talented students. This is seen from delving deeper into not just the end results that mathematicians establish, but the actual process and the emotional investment that is put into each practice.

While personal traits and characteristics such as curiosity and the amount of passion and drive one possesses have widely been discussed among the community to be additional contributing factors, intellectual courage, proved to play a crucial and notable role in the success of mathematicians as well. Although a drawback from this study would be the complexity of obtaining and quantifying the emotional and intangible efforts put into the events that eventually lead up to the assertion of new findings, Hadar and Kleiner have ensured that the methods of data collection they have sought after and utilised, will provide a sound and accurate result and representation of the study.

The act of intellectual courage in this perspective entails 4 main key drivers: persistence, self-confidence, insight and motivation.

With all these drivers co-existing, intellectual courage will come into play at the time when an individual experiences a situation that is coupled with the presence of risk and the uncertainty of a finish line. In other words, it is simply to take the risk of putting in an ample amount of time and resource into something that may lead to nothing.

Being aware that there are two possible outcomes for the investment of effort put into said experience, and accepting that their efforts may go unrewarded, is what mathematicians describe as taking a leap with intellectual courage.