An infinite regress in a series of propositions arises if the truth of proposition P₁ requires the support of proposition P₂, the truth of proposition P₂ requires the support of proposition P₃, ... , and the truth of proposition P_n-1 requires the support of proposition P_n and n approaches

Limit (mathematics)

In mathematics, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. The concept of limit allows mathematicians to define a new point from a Cauchy sequence of previously defined points within a complete metric...

 infinity.

Distinction is made between infinite regresses that are "vicious" and those that are not. One definition given is that a vicious regress is "an attempt to solve a problem which re-introduced the same problem in the proposed solution. If one continues along the same lines, the initial problem will recur infinitely and will never be solved. Not all regresses, however, are vicious."http://www.michaelridge.com/mr/course/glossary.asp#v

Aristotle's answer

Aristotle argued that knowing does not necessitate an infinite regress because some knowledge does not depend on demonstration:

Consciousness

Infinite regress in consciousness

Consciousness

Consciousness is a term that refers to the relationship between the mind and the world with which it interacts. It has been defined as: subjectivity, awareness, the ability to experience or to feel, wakefulness, having a sense of selfhood, and the executive control system of the mind...

 is the formation of an infinite series of "inner observers" as we ask the question of who is observing the output of the neural correlates of consciousness

Neural correlates of consciousness

The neural correlates of consciousness constitute the minimal set of neuronal events and mechanisms sufficient for a specific conscious percept. Neuroscientists use empirical approaches to discover neural correlates of subjective phenomena...

 in the study of subjective consciousness

Subjective consciousness

Subjective consciousness refers to a state of consciousness, in which a person is constantly aware of his or her self as well as outside factors. The study of this state has achieved high priority in the modern philosophy of mind, the mind-body problem or consciousness studies, as made popular by,...

.

Optics

Infinite regress in optics

Optics

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

 is the formation of an infinite series of receding images created in two parallel

Parallel (geometry)

Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not...

 facing mirror

Mirror

A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...

s.

See also

• Begging the question
  Begging the question
  Begging the question is a type of logical fallacy in which the proposition to be proven is assumed implicitly or explicitly in the premise....
  
  
• Cosmological argument
  Cosmological argument
  The cosmological argument is an argument for the existence of a First Cause to the universe, and by extension is often used as an argument for the existence of an "unconditioned" or "supreme" being, usually then identified as God...
  
  
• Regress argument
• Turtles all the way down
  Turtles all the way down
  "Turtles all the way down" is a jocular expression of the infinite regress problem in cosmology posed by the "unmoved mover" paradox. The phrase was popularized by Stephen Hawking in 1988. The "turtle" metaphor in the anecdote represents a popular notion of a "primitive cosmological myth", viz...
  
  
• Chicken or the egg
• Münchhausen Trilemma and Fallibilism
  Fallibilism
  Fallibilism is the philosophical principle that human beings could be wrong about their beliefs, expectations, or their understanding of the world...
  
  
• Self-evidence
  Self-evidence
  In epistemology , a self-evident proposition is one that is known to be true by understanding its meaning without proof....
  
  
• Antecedent-contained deletion
  Antecedent-contained deletion
  Antecedent-contained deletion is a phenomenon found in Verb phrase ellipsis contexts containing a quantifier. To understand the issue involved, it is necessary to understand how VP-elision works. Consider the following examples, where the expected, but missing, VP is represented with the symbol Δ....
  
  
• First Cause
• Tabula Rasa
  Tabula rasa
  Tabula rasa is the epistemological theory that individuals are born without built-in mental content and that their knowledge comes from experience and perception. Generally proponents of the tabula rasa thesis favour the "nurture" side of the nature versus nurture debate, when it comes to aspects...
  
  
• Infinite regress
  Infinite regress
  An infinite regress in a series of propositions arises if the truth of proposition P1 requires the support of proposition P2, the truth of proposition P2 requires the support of proposition P3, .....