The discovery of oxygen 1773 which was made in an era where Joseph Priestley (1733-1804), Carl Wilhelm Scheele (1742-1786) and Antoine Laurent Lavoisier (1743-1794) all contributed to the discovery. Lavoisier, despite being a member of the French Academy of Sciences was beheaded during the French Revolution. The judge said "The Republic needs neither scientists nor chemists; the course of justice cannot be delayed". Priestley due to his unitarianism and support for the French Revolution had to flee to the United States, his house and church torched by a mob. Scheele, although probably the first to discover oxygen, did not get credit for it since Priestley did publish it earlier. Scheele, like Linné, made Sweden a front nation in science during the 18th century.
Robert Boyle (1627-1691) showed in the end of the 17th century that air was necessary for combustion. He was among the founding members of the Royal Society in London 1660, the first institute dedicated to scientific pursuit.
These scientists in essence all worked to disprove the 1667 theory of phlogiston. It was believed that a fire-like element called phlogiston was contained in combustible bodies, and released during combustion. The theory was an attempt to explain combustion and rusting which is today understood as oxidations.
Lavoisier was the first to publish the disproof of the phlogiston theory. Priestley and Scheele did not use their discoveries of oxygen to bring down the phlogiston theory. This is a very important discovery since the understanding on the metabolism of biological cells rest on oxidation and the continuation of Harvey's discovery of the systemic blood circulation follows from this understanding. Ibn al-Nafis (born 1213) was also closing in on biological oxidation but could not have understood it completely since he only discovered the lung-heart circulation and not the systemic circulation that brought something in the air to the tissues in the body.
People believed in vitalism, a doctrine where the functions of a living organism are due to a vital principle distinct from biochemical reactions. It was not until Louis Pasteur (1822-1895)demonstrated that biochemical reactions took place in biological tissues with fermentation in yeast that this paradigm changed. Lavoisier had also worked with Pierre-Simon Laplace (1749-1827) demonstrating that respiration in essence was a slow combustion of organic material using inhaled oxygen, "la respiration est donc une combustion". He had used a calorimeter to investigate respiration and heat production in a guinea pig.
Leonardo da Vinci (1452-1519) is also believed to have discovered that a portion of air is consumed during combustion and respiration. However, many with him have obviously realized that humans and animals cannot live without air.
Data from Wikipedia