Laws are descriptive. They do not say why something is the way it is. Newton's laws of motion describe the motion of physical objects, but they do not say why things in the universe move as they do. Laws only apply to what they apply to; they may not like theories allow us to gain new knowledge, once their boundaries are discovered.
Theories are the most interesting to explore as they can explain new and different things. Theories can change and can be subject to confirming or disconfirming evidence for claims. Looking at what can justify theories can tell us more about the nature of philosophy. The "how" and "why" about what we can know to be true.
A theory is a general understanding of phenomena which can be applied to any of the relevant phenomena. A theory is made up of statements which support each other, and can go on to explain the phenomena they purport to explain. A theory is a body of knowledge which is supposed to be greater than the sum of its parts.
The tricky aspect of theories is that they attempt to go beyond the factual value of their claims and assert something else. Theories derive conclusions about new information from certain assumptions, and if they work together the theory continues to be useful. This is where theories are more useful than laws, we can derive new knowledge about things. That something else is a relation which ideally can be an explanation. From theories we derives hypotheses, which relate to the specific phenomena the theory covers.
Theories are the most interesting to explore as they can explain new and different things. Theories can change and can be subject to confirming or disconfirming evidence for claims. Looking at what can justify theories can tell us more about the nature of philosophy. The "how" and "why" about what we can know to be true.
A theory is a general understanding of phenomena which can be applied to any of the relevant phenomena. A theory is made up of statements which support each other, and can go on to explain the phenomena they purport to explain. A theory is a body of knowledge which is supposed to be greater than the sum of its parts.
The tricky aspect of theories is that they attempt to go beyond the factual value of their claims and assert something else. Theories derive conclusions about new information from certain assumptions, and if they work together the theory continues to be useful. This is where theories are more useful than laws, we can derive new knowledge about things. That something else is a relation which ideally can be an explanation. From theories we derives hypotheses, which relate to the specific phenomena the theory covers.
All theorizing involves language, which essentially is the intentional manipulation of symbols to assert something about the symbols or a relationship between symbols themselves. Statements are simply assertions about the symbols, this is this or this is that, this is not that etc. It is the connection between symbols and phenomena, the connection itself explained in symbols, that theory works with.The rules governing statements derive from non-contradiction, that "this" is this and cannot not be this if it is this. One can assert this is not that, this is that and so on because these are relationship between different things. As will be explained later, just because something is not contradictory doesn't mean it is meaningful. Something can be true as a tautology or have the possibility of being true.
The something else which is the aim of theory can only be understood by looking at what constitutes theories, which are statements. What makes a statement true? Well, what is a statement? A statement asserts or denies a relationship between a subject and a predicate. A subject is supposed to be a particular aspect of some larger general concept, which is a predicate. Both are connected by the copula asserting a relationship, universal or particular and affirmative or negative, between subject and predicate.
A is B.
A is the subject, B is the predicate. B is supposed to apply to all instances of A by the copula is.
Once we have statements, we can make claims about other statements using arguments. An argument takes at least two statements about the world and derives another (a conclusion). which follows from the original statements (premises). A basic argument is the syllogism, which has three statements in which two statements support a third. Each statement has a subject and predicate related by a copula and are related by which term is distributed throughout the argument. In a syllogism there is a major term, a minor term, and a middle term. A major term is the predicate found in the conclusion, the minor term is the subject in the conclusion, and the middle term is predicated in both premises and links them to the conclusion.
The something else which is the aim of theory can only be understood by looking at what constitutes theories, which are statements. What makes a statement true? Well, what is a statement? A statement asserts or denies a relationship between a subject and a predicate. A subject is supposed to be a particular aspect of some larger general concept, which is a predicate. Both are connected by the copula asserting a relationship, universal or particular and affirmative or negative, between subject and predicate.
A is B.
A is the subject, B is the predicate. B is supposed to apply to all instances of A by the copula is.
Once we have statements, we can make claims about other statements using arguments. An argument takes at least two statements about the world and derives another (a conclusion). which follows from the original statements (premises). A basic argument is the syllogism, which has three statements in which two statements support a third. Each statement has a subject and predicate related by a copula and are related by which term is distributed throughout the argument. In a syllogism there is a major term, a minor term, and a middle term. A major term is the predicate found in the conclusion, the minor term is the subject in the conclusion, and the middle term is predicated in both premises and links them to the conclusion.
All carp are fish
All fish are found in water
All carp are found in water
Major-found in water
Minor-carp
Middle-fish
This is a valid syllogism since the middle term (fish) is distributed at least once in the premises and the predicate distributed to the conclusion (found in water) is also in a premise.
Given the truth of an statement, we can establish the truth of other statements involving the same terms. The truth values of syllogisms are represented in what is called a square of oppositions. Starting with one of the four corners of the square (A for affirmative universal statements, E for negative universals, I for particular positives, and O for negative particulars) one derives the relation between the chosen kind of statement and what it means for the truth value of another statement. Note the direction of the arrows. If an A statement is true, then an E or O statement cannot be true (among the same thing of course). If an A statement is true, an I statement is true. If all bachelors and single men (A), then some bachelors are single men (I). But it cannot be that no bachelors are single men (E) or some bachelors are not single men (O).

Logic has developed much since Aristotle's syllogisms. For the purpose of theories, the syllogistic structure is a useful demonstration but quite unwieldy in practice. We have to know the relationships between subjects and predicates for the arguments to be true. A practical tool called Occam's Razor became popular after the Middle Ages to simplify the amount of assumptions we should make. Occam's Razor states that we should not multiply explanations without necessity. The more simple explanation is more preferable among valid explanations. Two big problems we run into with theories are underdetermination and overdetermination; explanations are either not sufficient by themselves (under) or are all sufficient (over). Which one should we pick? Occam's Razor tells us to favor the explanation with fewer assumptions since there is less to prove and less that can be disproved, go "wrong" as an explanation. This isn't an absolute law since the opposite is true, that we shouldn't simplify explanations if a more complex explanation is needed. The razor is a useful tool, but more of a practical nature.
An important logical tool which can cut down the number of syllogisms we have to do to prove something is the identity of indiscernibles. Also called Leibniz's law, the law states that two things which share the same properties are the same thing. If everything about A can be said about B, then they are the same thing. If A is identical to B, then we can replace the symbol A in any statement with B and mean the same thing. A is B and B is A.
Instead of
All A are B
All B are C
All A are C
Instead of
All A are B
All B are C
All A are C
we can just write all A are C, since A and B are the same.
This limits the amount of true sentences to only four, rather than having to prove each statement one by one.
The first two Aristotle accepted
1) A=A
2) A is B, B is C, A is C. "All men are mortal...Socrates is mortal"
Leibniz added two more
3) A is not not-A (excluded middle). This is a considered by me a tautology, but with Leibniz's law we can get a more exact idea of what is indistinguishable from A so that it also applies.
"If Socrates is mortal, then Socrates is no immortal" By Leibniz's law, If P(Plato) does not share mortality, then he isn't the same as S(Socrates) .
This limits the amount of true sentences to only four, rather than having to prove each statement one by one.
The first two Aristotle accepted
1) A=A
2) A is B, B is C, A is C. "All men are mortal...Socrates is mortal"
Leibniz added two more
3) A is not not-A (excluded middle). This is a considered by me a tautology, but with Leibniz's law we can get a more exact idea of what is indistinguishable from A so that it also applies.
"If Socrates is mortal, then Socrates is no immortal" By Leibniz's law, If P(Plato) does not share mortality, then he isn't the same as S(Socrates) .
4) A is B= not-B is not-A
"Socrates is a man, if you are not a man then you are not Socrates" By the converse of Leibniz's law, both S and P are mortal means the same as immortal P is not S.
The result is that the truth of syllogistic arguments is due to the meaning of their terms, not just their form. We can dismiss arguments based on the meaning of terms and not have to go through the syllogism.
Leibniz liked to use the proof by contradiction, aka reductio ad absurdum. One goes about assuming a statement to be true and following the consequences to see if there is a contradiction. If there is a contradiction, then prima facie the argument cannot be true. This argument doesn't prove the statement, but only demonstrates that it is possibly true. Non-contradiction is a law governing thought, but doesn't demonstrate that something is true, just that it isn't inherently false. Shared terms may mean both statements mean the same thing, and so doesn't tell us anything.
Also different today is the notion of existential import, which further limits the power of purely logical arguments. A statement has existential import if its truth depends on the existence of members of the subject's class. Propositions including "some are" or "some are not", I and O in the square, have existential import. They are true or false based on the existence of at least one existing member. But does the truth of statements about all or none members entail the existence of these members?
Put another way, if all unicorns have a single horn is true by definition, does that entail that some unicorns have horns (subalternation)? Well no, because there are as of yet no instances of unicorns. But then how is all unicorns have horns true? It is true, but it does not have existential import. One cannot infer the existence of something based on logical necessity. This complicates traditional arguments for the existence of God based on the necessity of a prime mover (cosmological argument) or as the explanation for the idea of God (ontological argument). In any case, syllogisms are not the only way to prove arguments, and can derive absurd conclusions.
Also different today is the notion of existential import, which further limits the power of purely logical arguments. A statement has existential import if its truth depends on the existence of members of the subject's class. Propositions including "some are" or "some are not", I and O in the square, have existential import. They are true or false based on the existence of at least one existing member. But does the truth of statements about all or none members entail the existence of these members?
Put another way, if all unicorns have a single horn is true by definition, does that entail that some unicorns have horns (subalternation)? Well no, because there are as of yet no instances of unicorns. But then how is all unicorns have horns true? It is true, but it does not have existential import. One cannot infer the existence of something based on logical necessity. This complicates traditional arguments for the existence of God based on the necessity of a prime mover (cosmological argument) or as the explanation for the idea of God (ontological argument). In any case, syllogisms are not the only way to prove arguments, and can derive absurd conclusions.
Here is George Boole's square of opposition with existential import. There is no subalternation (one implies the other) from A to I or E to O. The contrary relation between A and E does not hold as both can be true without existential import. There are subcontraries between A and O and E and I. If O "some are not", then A "all are" can't be true; if I "some are" is true, then E "there are no" can't be true.
Logical arguments are now more about the connections between statements rather than shared terms. A proposition must itself be true for us to derive anything from it. The syllogism reflects the essentialism of classical thinkers, that there are necessary attributes for every true subject. The syllogism worked within a hierarchical taxonomy of things, be it forms or species, with essential characteristics. A horse is a mammal, a mammal is an animal, all animals are mortal etc. The distributed terms making things the same are part of a higher category in this chain of being. Leibniz's law is so vulgar, judging identity by properties rather than "real" qualities. Of course there is no total agreement about what makes things more real than others (are things more or less real..?). Today's categorization of things like species or race has pretty much done away with essentialism as it became dogma against new discoveries and changes in social values (i.e. politically incorrect). Scientific realism only requires that the concepts refer to something in the world, relating to facts.
Leibniz's innovations change how we individuate and how we categorize things. For the scholastics, things were individuated by number alone, "solo numero." Medieval scholasticism had it that different things like individual humans are still the same because of certain essential traits belonging to the higher category of "man." Differences were divided into essential and accidental. Differences in height, weight, hair color etc are not essential differences, they do not individuate us. The radical take of Leibniz's law is that any differences things have are what make them different. That human nature is a collection of various attributes around a mean number. Categories must be based on factual similarity, not on some specific similarities. Without existential import we cannot make inferences from a generalized humanity to all individual humans unless all people have these traits (this is called the ecological fallacy).
Logical arguments are now more about the connections between statements rather than shared terms. A proposition must itself be true for us to derive anything from it. The syllogism reflects the essentialism of classical thinkers, that there are necessary attributes for every true subject. The syllogism worked within a hierarchical taxonomy of things, be it forms or species, with essential characteristics. A horse is a mammal, a mammal is an animal, all animals are mortal etc. The distributed terms making things the same are part of a higher category in this chain of being. Leibniz's law is so vulgar, judging identity by properties rather than "real" qualities. Of course there is no total agreement about what makes things more real than others (are things more or less real..?). Today's categorization of things like species or race has pretty much done away with essentialism as it became dogma against new discoveries and changes in social values (i.e. politically incorrect). Scientific realism only requires that the concepts refer to something in the world, relating to facts.
Leibniz's innovations change how we individuate and how we categorize things. For the scholastics, things were individuated by number alone, "solo numero." Medieval scholasticism had it that different things like individual humans are still the same because of certain essential traits belonging to the higher category of "man." Differences were divided into essential and accidental. Differences in height, weight, hair color etc are not essential differences, they do not individuate us. The radical take of Leibniz's law is that any differences things have are what make them different. That human nature is a collection of various attributes around a mean number. Categories must be based on factual similarity, not on some specific similarities. Without existential import we cannot make inferences from a generalized humanity to all individual humans unless all people have these traits (this is called the ecological fallacy).
Today we use quantifiers to simplify things so we can get these answers. There are two big ones: existential and universal. The existential quantifier is there exists at least one, so the statement is true. Rather than saying black swans exist we say there is at least swan which is black, which makes the statement black swans exist true. The universal quantifier is "for all"; the property applies for all members so that the statement is true. For all dogs, the statement all dogs are mammals is true. This statement is true or false based on whether all dogs are in fact animals. This quantification makes it so what we are talking about can have definite answers.
Summary: formal logical arguments aren't enough to justify a theory. Many arguments require an assertion between different things which either exist or do not.
All of this Leibniz law, reductio ad absurdum, existential import, and quantification brings us to a simplification of the kinds of two kinds of statements which are true. Statements can now be true which do not refer to anything actually existing, due to the relations of language and thought. So long as something is not contradictory it is not absurd, but it is not necessarily true. What is conceivable without contradiction is not necessarily true, but possibly true. A correct statement is one where the subject and the predicate are related, but their relation can either be true by definition or by fact, referring to itself or to reality. These two truths are analytic truths and synthetic truths.
Analytic truths are true by definition, as essentially tautologies. Analytic statements are those in which the subject is contained in the predicate. The subject is a particular, while the predicate is the universal. To say All Men are Mortal is to say the particular phenomena Men is contained in the universal concept Mortal, which they are. Analytic truths are true because they don't assert anything new. They can clarify our concepts, but do not offer any new inferences than what is contained in the concept. A true analytic statement is such that the opposite of that statement cannot be true.
Synthetic truths are true because their meaning relates to something about the world. All birds are yellow is only true if both concepts, bird and yellow, correspond to observation. The subject is not contained within the predicate, the nature of a bird does not require it to be yellow. Synthetic truths are true by example, not by demonstration. The opposite can be true without contradiction.
Further, analytic truths are a priori; they do not have to refer to anything that actually exists in the external world. That a square has four sides can be demonstrated by thought alone, we don't need to look for squares in nature which have five sides. Synthetic truths are a posteriori, they depend on empirical verification. That all single men are lonely is only true so long as single men are observed as being lonely. Immanuel Kant derived a third category, the synthetic a priori, though such judgements are true because of how the mind conditions reality. It's complicated, but most or at least a lot of philosophers accept Kant's third category.
"All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic ...discoverable by the mere operation of thought ... Matters of fact, which are the second object of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing."- David Hume
The distinction summarizes the advancements made in logic since the syllogism, and whether theories can be proven true or false. The very first test is whether the theory's claims are mutually contradictory. If they are not, then the theory is possibly true. If the claims can be verified factually, given clear parameters, then they are true. But we cannot derive new knowledge from necessary truths. Once we have defined the phenomena laws apply to, such as Newton's second law F=MA to speeds not approaching the speed of light, they cannot give us new knowledge.
Hume's little distinction also means that theories can be judged on a descriptive basis and on a moral basis. Some theories of human society like Marxism mix both together because they determine right behavior based on facts or in Marxism's case see humans as creating their essence (I guess). But there is a leap from fact to value that isn't itself factual. Ought implies can in Kant's famous formulation; right action involves a choice. If I can do something or not, a moral command does not describe the fact I did or am doing something but judge that fact or action compared to what could be done otherwise, be it good or bad. Theories therefore have descriptive and prescriptive elements.
Moral values using Hume's Fork are not matters of fact or relations of ideas. Morality seems to depend on some kind of responsibility. How can I prove that I am responsible for my right or wrong actions since what happens happens and there isn't a way to prove it could be otherwise? To imagine it otherwise would be a relation of different ideas, which do not have to correspond to reality and do not have a necessary logical relation. If morality involves choice, then it is of what could have been, which is not the verifiable state of affairs. Thus morals are not to be derived straightforwardly from facts.

Hume's distinctions also cause trouble for inferential logical arguments like modus ponens and modus tollens.
Modus ponens: If p then q; p, therefore q.
If it rains I will stay inside. It rains, therefore I stay inside.
Modus tollens: If p then q; not q, therefore not p.
I didn't stay inside, therefore it rained.
The conclusion of these arguments are only true if the premises are not in error, and the conclusion is only a hypothetical relation between the premises, so they're a step up from syllogisms. But both are still deductive arguments where we must have certainty that the content of premises are accurate. If it is almost raining, I can't conclude with absolute certainty that I will stay inside. If one of the conditions isn't exactly like what is described, then the other condition isn't certain to occur. We must be careful when using these arguments to establish a relationship among different things.
Most of what I've said applies to deductive arguments. Induction promises that as the number of observations increase, we can be more certain about the relationship. That the sun in the past has risen everyday in the east gives us a very high degree of certainty that it will occur tomorrow. We cannot make this inference with complete certainty, but we can expect the event with a high degree of probability. Induction is for most of our questions more useful.
"These two propositions are far from the same: I have found that such an object has always been attended with such an effect, and I forsee that other objects which are in appearance similar will be attended with similar effect. I shall allow, if you please, that the one proposition may justly be inferred. But if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connection between these propositions is not intuitive. There is required a medium which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is I must confess passes my comprehension; and it is incumbent on those to produce it who assert that really exists and is the original of all our conclusion concerning matter of fact." Hume
To sum up: there is no necessary relationship between different things. Non-contradiction is a law of thought rather than proof. Necessary truths are at bottom tautologous or inductive reasoning disguised by regularity. The first test of a good theory is if it isn't internally contradictory. The second test is if its particular claims are subject to verification or falsification.
Now to the important part. What makes a theory, the totality of relations between true statements, true? There are I think two ways of looking at justification which aren't just skepticism: whether a theory corresponds to something outside of itself like true facts, or if a theory is internally coherent and is compatible, can adjust, to new facts.
The first is characteristic of "traditional" philosophy like Plato and Aristotle. Truth is true justified belief, our conviction relates to something external, ideally unchanging, and objective of human thought. This conception of truth gave birth to the "laws of thought": the laws of identity, contradiction, and the excluded middle. All are based on this: that something is something and not nothing. The pre-socratic philosopher Parmenides is credited with the idea that truth is at bottom non-contradiction. “The great Parmenides from beginning to end testified . . . Never shall this be proved – that things that are not are.” Foundationalism as it is called asserts that there are basic beliefs which cannot be criticized which all correct reasoning is inferred from. These foundations can be logical axioms, empirical facts, or religious experience. This is called the correspondence theory of truth, true belief corresponds to something "in the world". Truth is supposed to transcend a particular time and space and be objective.
The latter theory of justification is called coherentism. A belief is true if it doesn't contradict our other beliefs. There are always background assumptions we have about the world, and these are justified if they are compatible, don't contradict, new information. It can be best summarized in an analogy first made by Otto Neurath.
"We are like sailors who on the open sea must reconstruct their ship but are never able to start afresh from the bottom. Where a beam is taken away a new one must at once be put there, and for this the rest of the ship is used as support. In this way, by using the old beams and driftwood the ship can be shaped entirely anew, but only by gradual reconstruction."
Coherentism is even better understood by its relation to the infinite regress problem. If everything requires an explanation, then so does any explanation. This is a problem because whatever we assert to be true, that truth relies on another truth. For sanity's sake and to prove that philosophy has any use at all, we want to find a way out of this. There appears to be three:
1) there is no ultimate stopping point, so we can always ask for further justification
2) there are statements which justify themselves
3) truth is circular, a truth is part of its own justification
Skepticism accepts the first solution, foundationalism accepts the second solution, and coherentism the third. The coherentist would accept as true belief that which accords with a person's other beliefs. If I say that god causes school shootings, that belief's truth depends on the truth of my other beliefs like god existing, playing an active role in human affairs, and this god being opposed to secularism in public schools. This is only wrong if some of my beliefs are wrong. The truth of any single statement is based on the truth of an interconnected system of belief, what Quine called the "web of belief".
“Physical objects are conceptually imported into the situation as convenient intermediaries not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer . . . For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing, the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conceptions only as cultural posits.”- W.V. Quine
The first is characteristic of "traditional" philosophy like Plato and Aristotle. Truth is true justified belief, our conviction relates to something external, ideally unchanging, and objective of human thought. This conception of truth gave birth to the "laws of thought": the laws of identity, contradiction, and the excluded middle. All are based on this: that something is something and not nothing. The pre-socratic philosopher Parmenides is credited with the idea that truth is at bottom non-contradiction. “The great Parmenides from beginning to end testified . . . Never shall this be proved – that things that are not are.” Foundationalism as it is called asserts that there are basic beliefs which cannot be criticized which all correct reasoning is inferred from. These foundations can be logical axioms, empirical facts, or religious experience. This is called the correspondence theory of truth, true belief corresponds to something "in the world". Truth is supposed to transcend a particular time and space and be objective.

"We are like sailors who on the open sea must reconstruct their ship but are never able to start afresh from the bottom. Where a beam is taken away a new one must at once be put there, and for this the rest of the ship is used as support. In this way, by using the old beams and driftwood the ship can be shaped entirely anew, but only by gradual reconstruction."
Coherentism is even better understood by its relation to the infinite regress problem. If everything requires an explanation, then so does any explanation. This is a problem because whatever we assert to be true, that truth relies on another truth. For sanity's sake and to prove that philosophy has any use at all, we want to find a way out of this. There appears to be three:
1) there is no ultimate stopping point, so we can always ask for further justification
2) there are statements which justify themselves
3) truth is circular, a truth is part of its own justification
Skepticism accepts the first solution, foundationalism accepts the second solution, and coherentism the third. The coherentist would accept as true belief that which accords with a person's other beliefs. If I say that god causes school shootings, that belief's truth depends on the truth of my other beliefs like god existing, playing an active role in human affairs, and this god being opposed to secularism in public schools. This is only wrong if some of my beliefs are wrong. The truth of any single statement is based on the truth of an interconnected system of belief, what Quine called the "web of belief".
“Physical objects are conceptually imported into the situation as convenient intermediaries not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer . . . For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing, the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conceptions only as cultural posits.”- W.V. Quine
Falsification of a theory won't bring us closer to the truth for coherentism, because each theory we create is built on prior "auxiliary" assumptions we had prior. Individual claims, by theories, can be proven or disproven, but not entire systematic worldviews. The Quine-Duhem thesis states that any seemingly falsifying evidence can always be accommodated by any theory. Theories are never tested in isolation. They require background assumptions in order to make testable predictions. Newton's theory of gravity depends on assumptions about the mass of planets and presence or absence of other forces to make predictions about the world. If the theory is disconfirmed in some instance, the background assumptions remain. What often happens is a theory, like Newton's, explains phenomena so well we change the theory to accommodate inconsistent information.
Popper's falsification criteria however isn't about the ultimate truth of statements, but a means to demarcate scientific theories from pseudoscientific theories. Falsification means that a single instance (fact, event) could invalidate the entire theory. Religions aren't falsifiable but they have other values than toward scientific discoveries. The problem with strict verification is that a theory which is tailored to fit all facts doesn't give us meaningful predictions as whatever occurs can be justified by making auxiliary assumptions. Marxism is commonly cited as being unfalsifiable because it doesn't give exact dates for when the revolution will happen and when events go against particular Marxist claims, like the collapse of the USSR, the theory is reinterpreted or changed to accommodate these previously disconfirming facts. Science is in the business of explaining facts and predicting new ones. Newton's theories weren't disproven by the discovery of relativity, but were shown to not be enough. And so falsification is a popular criteria for scientific versus unscientific theories, and I suppose could be accepted on a pragmatic basis for coherentists.
I wonder if its possible to combine aspects of foundationalism and coherentism. Theories which are internally contradictory (coherentism) or inconsistent with facts (foundationalism) are prima facie absurd. Such theories can be changed and continue on. Theories can be criticized from the outside by fact and logical analysis, and changed from the inside to meet these criticisms. Theories which have something meaningful to say are those which can both make wrong claims and can change. This follows from the two basic kinds of statements which can be true; purely logical ones and verifiable ones. Theories involve self-justification and empirical data, a fundamental duality. If either are bad or are confused together, then the theory is no good.
Full Summary:
Formal logical arguments aren't enough to justify a theory. Many arguments require an assertion between different things which can be found to either exist or don't exist. One cannot infer the factual existence of something beyond what one already knows.
There is no necessary relationship between different things. Non-contradiction is a law of thought rather than proof. Necessary truths emptied of factual content are at bottom tautologous or inductive reasoning disguised by regularity. The first test of a good theory is if it isn't internally contradictory. The second test is if its particular claims are subject to verification or falsification.
Non-contradiction and verification/falsification are our guides to life. What is conceivable without contradiction is possibly true. There are two kinds of truth: by definition of terms or by reference to experience. A good theory is based in fact and has a coherent internal logic.