Ancient Greek skeptics held to the view that nothing could be known. One of their arguments was known as Agrippa's Trilemma:
We are told to state a belief and ask "how do you know that?" Whatever justification we give for that belief, we repeat the question. This line of questioning will eventually lead one of three ways:
1. An infinite regress
2. A circle of beliefs
3. Beliefs which do not have any further justification
Option 1 is like the story of the woman who said the world is on the back of a giant turtle. When asked what the turtle is standing on, she said "Sorry, but it's turtles all the way down"
Option 2 is a simple fallacy of circular reasoning. When someone says something like "miracles are impossible because they never happen, and we know they don't happen because they are impossible" they really aren't giving a justification. What they are doing is asserting those two statements.
With option 1 and option 2 out of the way, this leaves option 3 as the only option left, which is called foundationalism. On foundationalism, certain beliefs are considered "basic" meaning that they form the foundation of one's belief system and do not require any additional justification.
The first flavor of foundationalism, and the one people think of when they hear the word, is hard foundationalism. On this view, beliefs have to meet one of three criteria to be eligible for the category of "basic." They are:
Infallible beliefs - Beliefs that cannot possibly be false
Indubitable beliefs - Beliefs that cannot possibly be doubted
Incorrigible beliefs - Beliefs that cannot possibly be corrected
An example of an infallible belief is the law of non-contradiction. To deny the law of non-contradiction is to affirm it, so one cannot possibly be wrong about it. An example of an indubitable belief is one's belief in one's own existence. One cannot assert the doubt if one does not exist. An example of incorrigible beliefs are my beliefs in my subjective experiences. I may be wrong that what I am seeing is a white shirt, but I cannot be corrected about my belief that what I am seeing looks like a white shirt.
Descartes held to hard foundationalism in his Meditations on First Philosophy. He said to imagine a situation where a demon was constantly deceiving his senses, his reasoning, his beliefs. Even if he were being deceived in such a way, Descartes would have to exist in order to be deceived.
"After having reflected well and carefully examined all things, we must come to the definite conclusion that this proposition: I am, I exist, is necessarily true each time that I pronounce it, or that I mentally conceive it."
These indubitable propositions formed the basis for Cartesian epistemology. Descartes build his system on the foundation of his own existence, which he cannot rationally deny. He then argued for the reliability of sense experience based on his idea of God, which could not have been built in his mind by anyone but God. With God as a guarantor of sense perception, Descartes could then build a system of knowledge, trusting his senses and his reasoning.
Hard foundationalism has fallen on hard times recently. The difficulty with hard foundationalism is that one is forced to justify all beliefs on the basis of the very limited number of beliefs that we can hold with certainty.
A second problem with hard foundationalism is that we do not think in this manner. We form most of our beliefs on sense experience, intuition, and heuristic devices. We do not check our beliefs for adherence to this kind of structure. This means that hard foundationalism is at best an ideal for how we ought to form our beliefs, not a description of how we do form our beliefs.
Moderate foundationalism rose in the second half of the 20th century in response to objections that our infallible, indubitable, and incorrigible beliefs are too sparse to form an adequate foundation for knowledge. Moderate foundationalism allows as basic any belief that has a strong presumption of truth. The biggest problem with moderate foundationalism is the problem of arbitrariness. What keeps us from stipulating any belief which we cannot support with other beliefs as basic? It seems like any belief could theoretically be justified on this system.
Foundherentism is a system invented by Susan Haack to combine the strengths of foundationalism and coherentism. There are certain beliefs which are considered basic, and which form the basis of our knowledge. Coherentism states that beliefs are justified by their relationship to other beliefs, like a spider's web. Systems of belief that best hang together are the most justified.
One problem with coherentism is that works of fiction and conspiracy theories can be highly coherent, and even connect with our current system of beliefs. There can be independent webs which are each fully coherent within themselves and yet contradict one another. Basic beliefs can serve to anchor that web of beliefs into reality.
Haack asks us to think of our belief systems like a crossword puzzle. Certain answers form the foundation for other answers, and yet the answers have to cohere as well. Beliefs are not built on a purely vertical system. Not every justified belief is justified on the basis of more basic beliefs. Some beliefs are basic, and we then build a web of beliefs by adding beliefs which best cohere with that belief system. This system has coherence as its basis for justification, but basic beliefs keep the web from being arbitrary. Any web consistent with itself must also be able to accommodate our basic beliefs. Critics like Laurence Bonjour argue that foundherentism is just another label for moderate foundationalism.
Reformed Epistemology gives many of the benefits of coherentism and foundherentism, and places them within a foundationalist framework. Plantinga's project seeks to provide justification for our common sense beliefs and to avoid the problem of arbitrariness. On reformed epistemology, beliefs are justified if they are produced by properly functioning mental factulties in an appropriate environment.
On Plantinga's Reformed Epistemology, most of our beliefs are foundational. Traditional foundationalism looks at our belief structure like a skyscraper. There is a narrow foundation of beliefs which supports the entire structure. On reformed epistemology, our belief structure is like bricks scattered throughout a parking lot. A few beliefs are stacked on top of one another, but most lay at the ground level. Most of our beliefs are basic.
What keeps contradictory beliefs from being considered basic is the notion of a defeater. A defeater is something that causes a belief to lose justification and/or warrant. If I see what looks like a sheep in a field, I have justification that I actually am seeing a sheep in a field. However, if I talk to someone who says that his dog is out in the field, and when seen from a distance looks like a sheep, then I have a defeater for my initial belief that there is a sheep in the field. Most of our beliefs may be basic, under this view, but they are also defeatable.
One implication of Reformed Epistemology is that belief in God can be considered justified until proven otherwise. Plantinga thinks of this as analogous to the problem of other minds. How do I know there are other minds besides my own? Philosophers have tried to give arguments for this principle, especially arguments from analogy, but they end up either being question-begging or being logically invalid. There simply are no good arguments for the existence of other minds, yet we all believe we are justified in believing in the existence of other minds.
Some beliefs are unjustified even if true. I could believe that the universe has an even number of stars, and be correct, and yet be unjustified in believing this because it is due to nothing but a random guess. Under reformed epistemology, this cannot be the case for belief in God. If a good God exists, then he could plant knowledge of his existence in some individuals.
For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse.
If this is the case, then one cannot argue that belief in the existence of God is unjustified even if God existed. In order to argue against the rationality of belief in God, one has to argue against the existence of God.
Foundationalism is the axiomatic solution to Agrippa's Trilemma, grounding our knowledge in a more basic set of axioms. Coherentism and infinitism cannot form a basis for formal systems of reasoning such as logic or mathematics, since they either form an infinite vicious regress or result in circular reasoning. This leaves us with foundationalism
Hard foundationalism is difficult to accept since it allows for too narrow a foundation to give us any real justification for our ordinary knowledge. Moderate foundationalism is too arbitrary to work. Foundherentism looks quite promising, but it might degenerate into moderate foundationalism. Reformed epistemology makes the best sense of our every day experience and coheres the best with our common sense beliefs.
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