Justified True Belief

(P1) Everything that begins to exist has a cause. Something cannot come into being from nothing.

(P2) The universe began to exist.

(C1) Therefore, the universe has a cause.

(P3) If the universe has a cause, then an uncaused, personal Creator of the universe exists who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful. Personal: The first state of the universe cannot have a scientific explanation, since there is nothing before it, and therefore, it cannot be accounted for in terms of laws operating on initial conditions. It can only be accounted for in terms of an unembodied mind and his free volitions, a personal explanation.

(P4) The universe has a cause.

(C2) Therefore, an uncaused, personal Creator of the universe exists who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful.

(P1) Anything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. (modest PSR) 17th century Leibniz original Principle of Sufficient Reason (PSR): "no fact can be real or existent, no statement true, unless there be a sufficient reason why it is so and not otherwise."

(P2) If the universe has an explanation of its existence, that explanation is grounded in a necessary being.

(P3) The universe exists.

(C1) Therefore, the universe has an explanation of its existence (from P1, P3).

(C2) Therefore, the explanation of the existence of the universe is grounded in a necessary being (from P2, C1).

(C3) Therefore, a necessary being exists (God).

(P1) The fine-tuning of the universe is due to either physical necessity, chance, or design.

(P2) It is not due to physical necessity or chance.

(C1) Therefore, it is due to design.

(P1) If God does not exist, the applicability of mathematics to the physical world is just a happy coincidence.

(P2) The applicability of mathematics to the physical world is not just a happy coincidence.

(C1) Therefore, God exists.

(P1) If God does not exist, objective moral values and duties do not exist.

(P2) Objective moral values and duties do exist.

(C1) Therefore, God exists.

(P1) If robust naturalism is true, then God or things like God do not exist. Robust naturalism is the idea that only physical things exist.

(P2) If God or things like God do not exist, then humanity does not freely think in the libertarian sense. via Naturalistic Determinism

(P3) If humanity does not freely think in the libertarian sense, then humanity is never epistemically responsible.

(P4) Humanity is occasionally epistemically responsible.

(C1) Therefore, humanity freely thinks in the libertarian sense. (from P3 and P4, modus tollens)

(C2) Therefore, God or things like God exist. (from P2 and C1, modus tollens)

(C3) Therefore, robust naturalism is false. (from P1 and C2, modus tollens)

(P5) The biblical account of reality is one possible explanation for the existence of God, things like God, and the libertarian freedom of humanity.

(P6) If the biblical account provides a better explanation of these facts than alternative accounts, then it is reasonable to accept it as the best explanation.

(C4) Therefore, if the biblical account provides the best explanation, it is reasonable to accept it. (from P5 and P6, abduction)

(P1) It is possible that a maximally great being exists.

(P2) If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.

(P3) If a maximally great being exists in some possible world, then it exists in every possible world.

(P4) If a maximally great being exists in every possible world, then it exists in the actual world.

(P5) If a maximally great being exists in the actual world, then a maximally great being exists.

(C1) Therefore, a maximally great being exists.

(P1) The most reasonable explanation for a set of historical facts is the one that best accounts for all the evidence.

(P2) There exists a set of minimal facts (Jesus's crucifixion, the disciples' reported experiences, their transformation from fearful to bold, and Paul's conversion) that are accepted by virtually all critical scholars in the field, based on standard historical methodologies.

(P3) Against all other theories, the resurrection theory best accounts for these widely accepted minimal facts.

(P4) A resurrection from the dead requires supernatural intervention beyond natural laws.

(P5) Supernatural intervention that suspends natural laws requires the existence of a supernatural being with power over nature.

(P6) Such a supernatural being with power over nature corresponds to what we mean by "God."

(C1) Therefore, the resurrection of Jesus is the most reasonable explanation for these widely accepted minimal facts.

(C2) Therefore, God's existence is the most reasonable explanation for the resurrection of Jesus.

(P1) If a set of specific historical facts (F) is overwhelmingly better explained by one hypothesis (H) than by any plausible alternative hypothesis under the negation of H (~H), then those facts provide strong cumulative evidence for H, particularly when analyzed probabilistically using a Bayesian framework. Bayes' theorem gives a mathematical rule for inverting conditional probabilities, allowing one to find the probability of a cause given its effect. The strength of the evidence is measured by the ratio of the probability of the facts given H to the probability of the facts given ~H (the Bayes factor), with a very high ratio indicating strong confirmation for H.

(P2) There exists a set of specific historical facts (F) concerning the period immediately following Jesus' death that are well-attested in historical sources which, despite minor variations common in historical documents, can be regarded as basically historically reliable, comparable to other secular history sources. These facts include the testimony of the women regarding the empty tomb and their sight of the resurrected Christ (W), the testimony of the disciples regarding seeing Christ alive and their willingness to die for this testimony (D), and the conversion of Paul (P). The reliability of the Gospels and Acts as sources is supported by external evidence for early dating and eyewitness access, contrary to sweeping negative conclusions of form and redaction criticism, which are often driven by philosophical naturalism and based on flawed methodology like the argumentum ex silentio or circular reasoning. It is also almost universally acknowledged by scholars that Jesus died on the cross.

(P3) The hypothesis that Jesus miraculously rose from the dead (R) provides an overwhelmingly better explanation for the conjunction of these specific historical facts (F = W&D&P) than any plausible alternative hypothesis under the negation of R (~R). Alternative naturalistic explanations like the swoon theory, theft hypothesis, alternative burial theories, hallucination theory (individual or collective), and conspiracy theory are shown to be highly improbable, inadequate to explain the specific details of the evidence, or contradicted by the evidence itself (e.g., the disciples' willingness to die for a claim they knew was false is highly improbable). A generic objective vision theory under ~R also fails to account for the specific nature of the testimony. The cumulative Bayes factor P(W&D&P|R) / P(W&D&P|~R) is extremely large, with estimates for individual components being significant (e.g., P(W|R)/P(W|~R) at least 100, P(D|R)/P(D|~R) possibly 10³⁹ under independence assumption which may underestimate the true strength, P(P|R)/P(P|~R) at least 10³).

(P4) The resurrection of Jesus (R), if it occurred, is understood as a paradigm case of a miracle. The truth of R stands in a relation to the evidence (F) and to Christianity (C) and theism (T) such that the evidential force of F flows through R to T and C; thus, R acts as a conduit of evidence for T and C. Evidence that strongly supports R consequently provides strong support for T and C.

(C1) Therefore, based on the overwhelming cumulative evidence provided by the well-attested historical facts (W, D, P) which are vastly better explained by the hypothesis of the resurrection (R) than by any alternative, it is highly probable that Jesus miraculously rose from the dead (R), and this provides a strong cumulative case argument for the truth of Christianity (C) and, by extension, theism (T). This argument is not undermined by general skeptical strategies such as Hume's maxim, worldview objections, or the Principle of Dwindling Probabilities, which either require engaging with the specific evidence (which the critics often fail to do adequately) or are based on flawed probabilistic reasoning.

(●) First principles in logic are the most basic foundational rules or assumptions upon which logical reasoning is built. These principles are considered self-evident and do not require proof within the system—they are the starting points for all logical arguments and deductions. The most commonly recognized first principles in classical logic are:

(●) The Law of Identity: Everything is identical to itself. Any object or statement is the same as itself. A=A "For the same thing to belong and not belong simultaneously to the same thing and in the same respect is impossible..." -Aristotle

(●) The Law of Non-Contradiction: A statement cannot be both true and false at the same time and in the same respect. This means that "A and not A" cannot both be true. ¬(A ∧ ¬A) "It is impossible for the same thing at the same time to belong and not to belong to the same thing and in the same respect." -Aristotle

(●) The Law of Excluded Middle: For any proposition, either that proposition is true, or its negation is true. This means that there is no third (middle) option between a statement being true or false. A ∨ ¬A "But on the other hand, there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate." -Aristotle

(●) What Are Deductive Arguments?
Deductive arguments are a fundamental part of logical reasoning. In a deductive argument, the conclusion is intended to follow necessarily from the premises. This means that if the premises are true and the reasoning is valid, the conclusion must also be true.

(●) Key Features of Deductive Arguments

- Certainty: Deductive arguments aim for certainty, not just probability. If the logic is valid and the premises are true, the conclusion cannot be false.
- Validity: An argument is valid if the conclusion logically follows from the premises, regardless of whether the premises are actually true.
- Soundness: An argument is sound if it is valid and all its premises are actually true.

(●) Multiple Premises in Deductive Arguments
Unlike syllogisms, which always have exactly two premises, deductive arguments can have any number of premises. For example, a mathematical proof might use several established facts (premises) to reach a conclusion. The key is that the conclusion must logically follow from all the premises taken together.

Example with Multiple Premises:

(P1) All mammals are warm-blooded.
(P2) All whales are mammals.
(P3) All warm-blooded animals need oxygen.
(C) Therefore, all whales need oxygen.
Here, three premises are used to reach the conclusion.

So how are Syllogisms different? What Is a Syllogism?
A syllogism is a special kind of deductive argument with a very specific structure. First formalized by Aristotle, syllogisms have been a foundation of logical thinking for centuries. They are designed to show how a conclusion necessarily follows from two premises.

The Structure of a Syllogism
A standard (categorical) syllogism consists of:

-Major premise: A general statement about a group or category.
-Minor premise: A statement about a specific member or subset of that group.
-Conclusion: A statement that follows from the two premises.

Each statement contains two of three terms:

-Major term: The predicate of the conclusion.
-Minor term: The subject of the conclusion.
-Middle term: The term that links the major and minor terms, appearing in both premises but not in the conclusion.

Example (Categorical Syllogism):
-All mammals are warm-blooded. (major premise)
-All whales are mammals. (minor premise)
-Therefore, all whales are warm-blooded. (conclusion)

-Major term: warm-blooded
-Minor term: whales
-Middle term: mammals

Rules of Syllogisms
To be valid, a syllogism must follow certain rules:
-It must have exactly three terms, each used consistently.
-The middle term must be distributed (refer to all members of its class) at least once.
-No term can be distributed in the conclusion unless it was distributed in the premises.
-It cannot have two negative premises.
-If a premise is negative, the conclusion must also be negative.
-No conclusion can be drawn from two particular premises.

(●) Types of Deductive Arguments
Deductive arguments come in several forms, each with its own rules and applications. Here are the main types:

1. Categorical Deductive Arguments
These use statements about categories or classes, such as "All A are B." Syllogisms are the classic example of categorical arguments, focusing on relationships between groups or sets.

Example:
All birds have feathers.
All robins are birds.
Therefore, all robins have feathers.

2. Propositional Deductive Arguments
These use logical connectives to relate whole statements (propositions), such as "and," "or," and "if...then." Common forms within propositional logic include:

- Modus Ponens:
If P, then Q.
P.
Therefore, Q.

- Modus Tollens:
If P, then Q.
Not Q.
Therefore, not P.

- Disjunctive Syllogism:
P or Q.
Not P.
Therefore, Q.
(Disjunctive arguments use "either...or" statements and are a subtype of propositional logic.)

- Hypothetical Syllogism:
If P, then Q.
If Q, then R.
Therefore, if P, then R.
(Hypothetical arguments use conditional "if...then" statements and are also a subtype of propositional logic.)

3. Modal Deductive Arguments
These involve concepts of necessity and possibility, using modal operators like "necessarily" and "possibly."

Example:
Necessarily, if it is a square, then it is a rectangle.
It is a square.
Therefore, it is necessarily a rectangle.

4. Mathematical Deductive Arguments
These use axioms, definitions, and theorems to reach conclusions. Mathematical arguments often employ both categorical and propositional logic, but are structured around mathematical principles.

Example:
A triangle has three sides.
Figure X is a triangle.
Therefore, Figure X has three sides.

(●) Why Are Deductive Arguments Important?
Deductive arguments are used in mathematics, science, law, computer science, and everyday reasoning. They help us build strong, reliable conclusions from established facts or principles. Understanding deductive arguments helps you think more clearly, spot errors in reasoning, and communicate your ideas more effectively.

(●) What is Inductive Reasoning?
In an inductive argument, it's possible for the premises to be true and the conclusion still be false. The premises don't guarantee the conclusion, but instead make it more probable than its competitors. The evidence used "underdetermines" the conclusion, meaning it makes it likely or plausible, but not certain. A good inductive argument must have true premises that are more plausible than their contradictories, and be informally valid (avoiding fallacies). However, they are not assessed for formal validity because the premises don't necessitate the conclusion's truth.

Here's a key example:
- 1. Groups A, B, and C were similar people with the same disease.
- 2. Group A got a new drug, B got a placebo, C got no treatment.
- 3. Death rate was 75% lower in Group A than B and C.
- 4. Therefore, the new drug is effective.

The conclusion is likely true based on the evidence, but it's not guaranteed – perhaps luck or another factor caused the difference.

(●) How Do We Understand Inductive Reasoning?
Philosophers approach understanding inductive reasoning in different ways. Two prominent methods are:

1. Bayes's Theorem:
This approach uses the rules of probability calculus. Bayes's theorem provides formulas to calculate the probability of a hypothesis (H) given certain evidence (E), symbolized as Pr(H|E). Probabilities range from 0 (lowest) to 1 (highest), with values above 0.5 suggesting positive probability. The probability of a hypothesis given evidence depends on its intrinsic probability (its likelihood based on general background knowledge) and its explanatory power (how likely the evidence would be if the hypothesis were true). A challenge in philosophy is assigning precise numerical values to these probabilities, often relying on vague approximations. An "odds form" of the theorem can compare the probability of two competing hypotheses given the evidence.

2. Inference to the Best Explanation (IBE)
A perhaps more practically useful approach in philosophy is inference to the best explanation (Also sometimes called Abduction). This method involves starting with data that needs explaining, identifying a set of possible explanations ("a pool of live options"), and then selecting the explanation that, if true, would best explain the data. Several criteria are commonly used to determine which explanation is "best":

• Explanatory scope: Does it explain a wider range of data than rivals?
• Explanatory power: Does it make the observable data more likely than rivals?
• Plausibility: Is it implied by a greater variety of accepted truths and its negation by fewer?
• Less ad hoc: Does it involve fewer new, unsupported assumptions than rivals?
• Accord with accepted beliefs: When combined with accepted truths, does it imply fewer falsehoods than rivals?
• Comparative superiority: Does it significantly outperform its rivals across these criteria?

The neo-Darwinian theory of biological evolution is presented as a good example of IBE. Supporters argue that even though the evidence (like micro-evolutionary change) doesn't prove macro-evolutionary development, the theory is the best explanation for the data due to its scope, power, and other factors. Critics, however, argue that the perceived superiority of Darwinism only holds if the pool of possible explanations is artificially limited (e.g., to only naturalistic ones). If other hypotheses, such as intelligent design, are allowed, the picture changes. This debate itself illustrates how IBE works and how disagreements about the criteria or the pool of options can arise.

(●) Symbolic logic is a subdiscipline of philosophy akin to mathematics that deals with the rules of reasoning. In symbolic logic, letters and symbols are used to stand for sentences and the words that connect them. This approach helps to make the logical form of a sentence clear without being distracted by its grammatical form, as sentences with different grammatical structures may still have the same logical form.

Here is a legend of some common symbols:

Letters (P, Q, R, S, etc.)
Meaning: These capital letters stand for any arbitrary sentences.
Example: In the argument "If today is Sunday, the library is closed. Today is Sunday. Therefore, the library is closed," we can let P = "Today is Sunday" and Q = "the library is closed".

Arrow (→)
Meaning: The arrow stands for the connecting words, "if . . . , then . . ." or it can be read as "implies". In a sentence of the form P → Q, P is the antecedent clause and states a sufficient condition of the consequent clause Q. Q is the consequent clause and states a necessary condition of the antecedent clause P. The clause that follows a simple "if" is symbolized P (sufficient condition), and the clause that follows "only if" is symbolized Q (necessary condition).
Example: The sentence "If John studies hard, then he will get a good grade in logic" can be symbolized as P → Q, where P = "John studies hard" and Q = "he will get a good grade in logic". The sentence "Extra credit will be permitted only if you have completed all the required work" can be symbolized as P → Q, where P = "You may do extra credit work" and Q = "You have completed the required work".

Negation (¬)
Meaning: This symbol stands for "not" and is the sign of negation.
Example: ¬Q is read as "Not-Q". If Q is the sentence "My roommate is sleeping in," then ¬Q is "My roommate is not sleeping in". ¬¬Q is logically equivalent to Q.

Conjunction (&)
Meaning: This symbol is read as "and". It symbolizes any conjunction, including words like but, while, although, whereas, and many other words when they function as conjunctions. For a conjunction P & Q to be true, both P and Q must be true.
Example: The sentence "Charity is playing the piano, and Jimmy is trying to play the piano" can be symbolized as P & Q, where P = "Charity is playing the piano" and Q = "Jimmy is trying to play the piano". The sentence "They ate their spinach, even though they didn’t like it" would be symbolized P & Q, where P symbolizes "They ate their spinach" and Q symbolizes "they didn’t like it".

Disjunction (v)
Meaning: This symbol is read as "or". A sentence composed of two sentences connected by "or" is called a disjunction. In order for a disjunction to be true, only one part has to be true (or both).
Example: The sentence "Either Mallory will carefully work on decorating their new apartment, or she will allow it to degenerate into a pigsty" can be symbolized as P v Q, where P = "Mallory will carefully work on decorating their new apartment" and Q = "she will allow it to degenerate into a pigsty". Note that in logic, both parts of a disjunction can be true.

Universal Quantification ((x))
Meaning: This symbol is used in first-order predicate logic to deal with quantified sentences, specifically those about all or none of a group. It can be read as "For any x, . . .". Universally quantified statements turn out to be disguised "if . . . , then . . ." statements. The variable 'x' can be replaced by any individual thing.
Example: The statement "All bears are mammals" can be symbolized as (x) (Bx → Mx), where Bx = "x is a bear" and Mx = "x is a mammal". This is read as "For any x, if x is a bear, then x is a mammal". A negative universal statement like "No goose is hairy" is symbolized by negating the consequent: (x) (Gx → ¬Hx), read as "For any x, if x is a goose, then x is not hairy".

Existential Quantification (∃x)
Meaning: This symbol is used in first-order predicate logic for statements about only some members of a group. It tells us that there really exists at least one thing that has the property in question. It may be read as "There is at least one ___ such that . . .". Existentially quantified statements are typically symbolized using & (conjunction), not → (conditional).
Example: The statement "Some bears are white" can be symbolized as (∃x) (Bx & Wx), where Bx = "x is a bear" and Wx = "x is white". This is read as "There is at least one x such that x is a bear and x is white". The statement "Some bears are not white" is symbolized as (∃x) (Bx & ¬Wx).

Necessity (□)
Meaning: This symbol is used in modal logic to stand for the mode of necessity. □P is read as "Necessarily, P" and indicates that the statement P is necessarily true (true in every possible world). □¬P indicates that P is necessarily false (false in every possible world).
Example: □P is read as "Necessarily, P". □¬P is read as "Necessarily, not-P".

Possibility (◊)
Meaning: This symbol is used in modal logic to stand for the mode of possibility. ◊P is read as "Possibly, P" and indicates that the statement P is possible (true in at least one possible world). ¬◊P is read as "Not-possibly, P," meaning it is impossible for P to be true.
Example: ◊P is read as "Possibly, P".

"Would" Counterfactual (□→)
Meaning: This symbol is used in counterfactual logic for conditional statements in the subjunctive mood that state what would happen if the antecedent were true. P □→ Q is read as "If it were the case that P, then it would be the case that Q".
Example: The conditional "If Oswald hadn’t shot Kennedy, then somebody else would have" is a "would" counterfactual. It would be symbolized using □→.

"Might" Counterfactual (◊→)
Meaning: This symbol is used in counterfactual logic for conditional statements in the subjunctive mood that state what might happen if the antecedent were true. P ◊→ Q is read as "If it were the case that P, then it might be the case that Q". It is defined as the contradictory of P □→ ¬Q. "Might" indicates a genuine, live option under the circumstances.
Example: While the source doesn't provide a specific example using the symbol ◊→, it explains its meaning in contrast to □→.

(●) Acquaintance Knowledge (Knowing-by-acquaintance): Knowing something because the object of knowledge is directly present to one’s consciousness. For example, Dan knows the ball in front of him because he sees it and is directly aware of it—he knows it by sensory intuition. In this context, intuition does not mean a guess or irrational hunch, but rather a direct awareness of something present to consciousness. People know many things by acquaintance or intuition, such as their own mental states (thoughts, feelings, sensations), physical objects they perceive through the five senses, and, according to some, even basic principles of mathematics. When asked how people know that 2 + 2 = 4 or that if it is raining outside then it must be wet outside, the answer seems to be that people can simply “see” these truths. This kind of “seeing” is often thought to involve an intuitional form of awareness or perception of abstract, immaterial objects and the relationships among them—such as numbers, mathematical relations, propositions, and the laws of logic. Thus, all these examples are arguably cases of knowledge by acquaintance.

(●) Procedural Knowledge (Knowing-how): The ability or skill to behave in a certain way and perform some task or set of behaviors. One can know how to speak Greek, play golf, ride a bicycle, or perform a number of other skills. Know-how does not always involve conscious awareness of what one is doing. Someone can learn how to do something by repeated practice without being consciously aware that one is doing the activity in question or without having any idea of the theory behind the practice. For example, one can know how to adjust one’s swing for a curve ball without consciously being aware that one’s stride is changing or without knowing any background theory of hitting technique.

(●) Propositional Knowledge (Knowing-by-description): This is knowledge of facts or truths, expressed in declarative sentences. For example, "I know that water boils at 100 degrees Celsius." It is the most discussed type in philosophy and is often analyzed as "justified true belief."

(●) The Quest to Define Knowledge
Since the time of Plato, philosophers have debated the nature of propositional knowledge—what it means to truly "know" something. In his dialogue Theaetetus, Plato explored the idea that knowledge might be "true belief with an account," a view that later evolved into the well-known "justified true belief" (JTB) analysis. "true judgment with an account"—is the closest to what later philosophers called "justified true belief." However, Plato ultimately finds problems with each definition and does not endorse any as a final answer in the dialogue.

(●) The Standard Definition: Justified True Belief (JTB)
The standard definition states that knowledge consists of three essential components: justification, truth, and belief. To say someone knows a proposition (for example, "milk is in the refrigerator") means that three conditions must be met: the proposition must be true, the person must believe it, and the belief must be justified.

(●) Truth as a Necessary Condition
For someone to know something, it must be true. It would be nonsensical to claim that someone knows a falsehood. However, truth alone is not enough for knowledge. There are countless truths that no one knows or has even considered.

(●) Belief as a Necessary Condition
In addition to truth, belief is required. If a person does not believe a proposition, it cannot be said that they know it. However, simply believing something does not make it knowledge, since people can believe many things that are not true.

(●) The Insufficiency of True Belief
Even when a belief is true, that alone does not guarantee knowledge. A person might believe something that happens to be true purely by chance, without any justification. For example, if someone randomly thinks, "It is raining in Moscow right now," and it happens to be true, this is not knowledge—just a lucky guess.

(●) The Role of Justification
What distinguishes knowledge from mere true belief is justification or warrant. Justification means having sufficient evidence, forming beliefs in a reliable way (such as through the senses or expert testimony), and having properly functioning intellectual faculties in a suitable environment. The difference between a true belief and knowledge is that knowledge requires this additional element of justification.

(●) The Tripartite Analysis
The traditional or standard definition of propositional knowledge can be summarized as follows:
A person S knows that P if and only if:
1. S believes that P.
2. P is true.
3. S is justified in believing that P at the time S believes it.
This tripartite analysis remains a foundational concept in the philosophical study of knowledge.

(●) Socrates was an Athenian philosopher who is widely regarded as one of the founders of Western philosophy. He wrote no philosophical texts himself; instead, his ideas and methods are known through the works of his students, especially Plato and Xenophon, as well as the playwright Aristophanes. Socrates is famous for his method of questioning (the Socratic method or elenchus), which sought to expose contradictions in his interlocutors’ beliefs and to stimulate critical thinking and self-examination. He focused on ethical questions and the pursuit of virtue, famously claiming that he knew nothing except his own ignorance. Socrates was tried and executed by the city of Athens on charges of impiety and corrupting the youth, choosing to die rather than renounce his philosophical mission.

(Q) "The unexamined life is not worth living." Source: Plato, Apology 38a

(Q) "I know that I know nothing." Source: Plato, Apology 21d (paraphrased; the exact phrase is "I am wiser than this man; it is likely that neither of us knows anything worthwhile, but he thinks he knows something when he does not, whereas when I do not know, neither do I think I know.")