The Oxford English Dictionary defines Purpose as “the reason for which something is done or created or for which something exists”. The Cambridge Dictionary is more concise with "why you do something or why something exists".
So purpose is the reason why we exist and do.
A purpose statement might start with
"We believe ..."
# "Don't believe it" - Disclaimer When you write "I believe ..." you may find that you may not find an absolute "foundation" of this belief. You chose it because it is something you hold dear and would like the world to be more of.
“At the core of all well-founded belief lies belief that is unfounded.” ― Ludwig Wittgenstein, On Certainty
Others may have beliefs which might conflict with yours. So the "proof" of the beliefs might be in what way they help you and others. Or if they contribute to misunderstanding, tension and conflict.
Observe which may be true for you and what effect it has on others.
“Those are my principles, and if you don't like them...well I have others.” ― Groucho Marx
# The legal reality of organisations - "any lawful act or activity"
In the articles of incorporation of a (US) business, it explicitly states what its purpose is:
Google : "The purpose of this Corporation is to engage in any lawful act or activity for which corporations may be organized under the General Corporation Law of Delaware."
Microsoft : "The Corporation is organized for the purposes of transacting any and all lawful business for which a corporation may be incorporated under the Washington Business Corporation Act."
In these examples of Google and Microsoft you can see that in the legal framework (the incorporation) you do not find the purpose in a value-oriented way which goes beyond "any lawful act or activity".
Being lawful may not be enough to guide your behavior if you reflect deeply on your values and strive to live by them.
This said, a business can be bound more specifically by other contracts, agreements and documents it has. For example a company can have supplier agreements which define criteria for choosing suppliers which can include fair pay, working conditions, social and environmental impact etc.
**Beyond "any lawful act or activity"**
Some organisations want to write their purpose and values into the core legal structure of the company, so they serve as a clear statement about the commitment to a set of values and can not be changed easily by (new) management or owners.
"It is now imperative that we move from extractive business models, to generative business models, which add value to their communities and the natural resources they use. This is what 'purpose' is about." Michel Bauwens, Founder P2P Foundation
Some organisations voluntarily adopt stricter business principles which they let audit and certify by independent third parties like B-corp .
(to do) Examples of some of these legal structures here