Cognitive linguistics

Cognitive Linguistics arose in opposition to Chomsky's idea that language is in the mind alone, and do not relate to objects outside or the body.
Chomskian thought is more Cartesian,that is,it is more concerned with the inherent properties of the mind,whereas Cognitive linguists believe in the intricate relationship between the mind and body.While they do not outrightly deny the existence of an universal grammar,they say that even this universal grammar, if it exists,should have its roots in cognition.Some key ideas in Cognitive Linguistics are:

CONSTRUAL -
There are different ways of paraphrasing the same sentence,which often convey the same meaning,perhaps.But,we chose to use one of them given a situation.While generative grammarians would treat the different choices as compositional differences alone,cognitive linguists emphasise that there is a reason ,we choose one construal over another and this reason talks a lot about how our language is structured.
John gave the book to Mary vs John gave Mary the book - construes different and only one of the constructions seems natural in a given situation.

METAPHOR - It is not the exclusive domain of poets,it is the fundamental property of everyday language.It is about how we conceptualise one experience in terms of other(Lakoff)Eg:someone is very hot - extends the idea of heat to represent some aspect of the person.

PERSPECTIVE - The path falls steeply into the valley.The path climbs out of the valley.Both these sentences have this inherent notion of an observer,even though the actual position of the speaker is irrelevant.
Fundamentality of space:Spatial thoughts are often fundamental and extend to other domains via metaphor :This is best demonstrated in this way:We say "foot in the stirrup" but not "finger in the ring" because when we look at our palm,it seems to us that the finger is a 2-dimensional surface on which you have the projection of the ring.So we say "ring on the finger"

Another example is the containment metaphor - "In" I am in this classroom - indeed enclosed - so consistent with the base definition of containment

Bird is in the garden -here there is no definite three dimensional enclosure,but we do have the idea that the bird is hovering at a height close to the ground and we do have a fuzzy notion of a ceiling.I am in the class , We can look at it as belonging to an abstract set."words on the paper" (surface attachment)"words in the margin" (margin is a region,so containment)"up" points to vertical movement,so logically consistent to associate with increase in quantity -"prices shot up"."

"He ran up to meet him" ,is perhaps due to enlargement of retinal image on approach.
Some of these metaphors may be cultural - mole may be on the cheek(for English) or in the cheek(for other languages).It tells us about the cultural differences between the places where the different languages are spoken.But many of these metaphors are universal.Basically,beginning from the most basic dimensions like cognition to societal traits,everything influences language deeply.
Concept of schema:For example,the core meaning of out,where an entity(trajector ) is located outside a container or containing space(landmark)."The cat is out of the house."Here,cat is the trajector and house is the landmark.Such schema can be constructed for many locative prepositions.And these schema can be adjusted to explain pretty well,the varied usage of the same preposition in different contexts.

An interesting idea I came across is how lakoff argues even mathematics to be influenced by cognition.You may want to explore it.

Reference:

An Introduction to Cognitive Linguistics by David lee