The "insofar as" makes your statement a bit of sophistry, since my statement does not at all "represent formal logic as logic". To refute my statement you would have to provide a statement that does not presume the fundamental principle of logic, or you would have to show an illogical statement that is not a combination of statements.
My assertion in the present sidebar is “non-classical logic” – i.e. that both predestination and free will are Truth for the simple reason that God has spoken both.
It is misleading to call it "non-classical logic", because one need give up nothing of logic to affirm it.
We cannot apply formal logic (esp. Aristotlean logic) to God because of the observer problem.
How does that follow?
Or to put it another way, faith and reason are complementary - but reason cannot substitute for faith.
One needn't give up logic to affirm that.
His ways are higher than our ways, His thoughts are higher than our thoughts.
Of course, but one needn't give up logic in order to affirm that verse. There are other ways of taking it.
As another example, even though God is perfect by definition He nevertheless has overridden the “laws” of the physical creation (including physical laws and formal logic) in performing miracles recorded throughout Scripture (and others not recorded in Scripture)
A physical law is nothing other than a conceptual generalization of a physical disposition(s). It is not something God has to "override". As far as God overriding a law of formal logic, name just one law of formal logic that God has overridden in the performance of a miracle.
If we applied formal logic to our understanding of God, we could not accept that He would make a creation less than perfect.
How would that conclusion follow?
We could accept no miracles under formal logic, i.e. we'd be Deists.
How would that conclusion follow? I hold to formal logic, and I am not a deist.
Nor could we accept both the prophesies which pointed to and were fulfilled in Christ and the commandments of God, e.g. judge not that you not be judged, forgive that you shall be forgiven, honor your father and your mother that your days may be long in the land God gives you, choose ye this day whom you will serve (and many other such if/thens.)
Why not?
As to your assertion that logic only applies to a combination of statements, whereas that is true concerning “formal logic” – especially Aristotlean logic - it does not always apply to “informal logic.”
Yes it does.
For instance, the statement ”Mr. Jones, how can you favor gun legislation when you own a pistol?” is a logical fallacy (circumstantial ad hominem.)
The question becomes a fallacy only in the context of an argument, e.g. where Mr. Jones is presenting an argument in favor of gun legislation. It is not a fallacy in isolation.
Moreover, I assert that many if not most all ad hominem arguments are not stated as a combination of statements, e.g. “The author is a liar” “You are an idiot” etc. The conclusion is not formally drawn, it is suggested.
Right, but those are still arguments, because they are enthymemes.
-A8
me: The above is a false generalization of “logic” insofar as it represents “formal logic” as “logic” ...
You: The "insofar as" makes your statement a bit of sophistry, since my statement does not at all "represent formal logic as logic". To refute my statement you would have to provide a statement that does not presume the fundamental principle of logic, or you would have to show an illogical statement that is not a combination of statements.
Logic, from Classical Greek (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. However the subject is grounded, the task of the logician is to advance an account of valid and fallacious inference, to allow one to distinguish logical from flawed arguments.
Traditionally, logic is studied as a branch of philosophy, one part of the classical trivium, which consisted of grammar, logic, and rhetoric. Since the mid-nineteenth century logic has also been commonly studied in mathematics and law. More recently logic has been applied to computer science. The parts that make up a computer chip are often called "logic gates".
As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. Logic is also commonly used today in argumentation theory.
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The crucial concept of form is central to discussions of the nature of logic, and it complicates exposition that 'formal' in "formal logic" is commonly used in an ambiguous manner. Symbolic language is actually a species or class of formal logic, and should be distinguished from another class of formal logic in traditional Aristotelian syllogistic logic, which deals solely with categorical propositions. We shall start by giving definitions that we shall adhere to in the rest of this article:
* Formal logic is the study of inference with purely formal content, where that content is made explicit. (An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. The first rules of formal logic that have come down to us were written by Aristotle. We will see later that in many definitions of logic, logical inference and inference with purely formal content are the same thing. This does not render the notion of informal logic vacuous, since one may wish to investigate logic without committing to a particular formal analysis.)
* Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference.
While formal logic is old, dating back more than two millennia, most of symbolic logic is comparatively new, and arises with the application of insights from mathematics to problems in logic. Generally, a symbolic logic is captured by a formal system, comprising a formal language including rules for creating expressions in the language, and a set of rules of derivation. The expressions will normally be intended to represent claims that we may be interested in, and likewise the rules of derivation represent inferences; such systems usually have an intended interpretation.
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Rival conceptions of logic
Logic arose (see below) from a concern with correctness of argumentation. The conception of logic as the study of argument is historically fundamental, and was how the founders of distinct traditions of logic, namely Plato, Aristotle, Mozi and Aksapada Gautama, conceived of logic. Modern logicians usually wish to ensure that logic studies just those arguments that arise from appropriately general forms of inference; so for example the Stanford Encyclopedia of Philosophy says of logic that it does not, however, cover good reasoning as a whole. That is the job of the theory of rationality. Rather it deals with inferences whose validity can be traced back to the formal features of the representations that are involved in that inference, be they linguistic, mental, or other representations (Hofweber 2004).
By contrast Immanuel Kant introduced an alternative idea as to what logic is. He argued that logic should be conceived as the science of judgement, an idea taken up in Gottlob Frege's logical and philosophical work, where thought (German: Gedanke) is substituted for judgement (German: Urteil). On this conception, the valid inferences of logic follow from the structural features of judgements or thoughts.
A third view of logic arises from the idea that logic is more fundamental than reason, and so that logic is the science of states of affairs (German: Sachverhalt) in general. Barry Smith locates Franz Brentano as the source for this idea, an idea he claims reaches its fullest development in the work of Adolf Reinach (Smith 1989). This view of logic appears radically distinct from the first: on this conception logic has no essential connection with argument, and the study of fallacies and paradoxes no longer appears essential to the discipline.
Occasionally one encounters a fourth view as to what logic is about: it is a purely formal manipulation of symbols according to some prescribed rules. This conception can be criticized on the grounds that the manipulation of just any formal system is usually not regarded as logic. Such accounts normally omit an explanation of what it is about certain formal systems that makes them systems of logic.
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The logics discussed above are all "bivalent" or "two-valued"; that is, they are most naturally understood as dividing propositions into the true and the false propositions. Systems which reject bivalence are known as non-classical logics.
In 1910 Nicolai A. Vasiliev rejected the law of excluded middle and the law of contradiction and proposed the law of excluded fourth and logic tolerant to contradiction. In the early 20th century Jan ?ukasiewicz investigated the extension of the traditional true/false values to include a third value, "possible", so inventing ternary logic, the first multi-valued logic.
Intuitionistic logic was proposed by L.E.J. Brouwer as the correct logic for reasoning about mathematics, based upon his rejection of the law of the excluded middle as part of his intuitionism. Brouwer rejected formalisation in mathematics, but his student Arend Heyting studied intuitionistic logic formally, as did Gerhard Gentzen. Intuitionistic logic has come to be of great interest to computer scientists, as it is a constructive logic, and is hence a logic of what computers can do.
Modal logic is not truth conditional, and so it has often been proposed as a non-classical logic. However, modal logic is normally formalised with the principle of the excluded middle, and its relational semantics is bivalent, so this inclusion is disputable. On the other hand, modal logic can be used to encode non-classical logics, such as intuitionistic logic.
Logics such as fuzzy logic have since been devised with an infinite number of "degrees of truth", represented by a real number between 0 and 1. Bayesian probability can be interpreted as a system of logic where probability is the subjective truth value.
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What is the epistemological status of the laws of logic? What sort of arguments is appropriate for criticising purported principles of logic? In an influential paper entitled "Is logic empirical?" Hilary Putnam, building on a suggestion of W.V. Quine, argued that in general the facts of propositional logic have a similar epistemological status as facts about the physical universe, for example as the laws of mechanics or of general relativity, and in particular that what physicists have learned about quantum mechanics provides a compelling case for abandoning certain familiar principles of classical logic: if we want to be realists about the physical phenomena described by quantum theory, then we should abandon the principle of distributivity, substituting for classical logic the quantum logic proposed by Garrett Birkhoff and John von Neumann.
Another paper by the same name by Sir Michael Dummett argues that Putnam's desire for realism mandates the law of distributivity. Distributivity of logic is essential for the realist's understanding of how propositions are true of the world in just the same way as he has argued the principle of bivalence is. In this way, the question, "Is logic empirical?" can be seen to lead naturally into the fundamental controversy in metaphysics on realism versus anti-realism.
You continued in a series of replies by stating in different words that one need give up nothing of (formal) logic to affirm or attest to various points I asserted. Therefore I challenge you to present the formal logic to affirm or attest to the following:
Faith and reason are complementary but reason cannot substitute for faith.
God’s ways are higher than our ways and His thoughts are higher than our thoughts.
Some Miracles:
Christ raised the dead, made the blind see, the lame walk, cast out demons and walked on water.
Creation took six days and occurred in the order given in Genesis 1.
Noah’s flood covered the whole earth destroying all in which there was the breath of life.
Jonah spent three days in the belly of a whale (or large fish.)
That laws discovered in an existence having boundaries apply to existence beyond those boundaries.
You continued with a challenge:
Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you. Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day. For my flesh is meat indeed, and my blood is drink indeed. He that eateth my flesh, and drinketh my blood, dwelleth in me, and I in him. – John 6:53-56
Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. – John 8:58
And Enoch walked with God: and he [was] not; for God took him. – Genesis 5:24
I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me. I do not frustrate the grace of God: for if righteousness [come] by the law, then Christ is dead in vain. – Gal 2:20-21
For ye are dead, and your life is hid with Christ in God. – Col 3:3
And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world. – Rev 13:8
You: Right, but those are still arguments, because they are enthymemes.
For Aristotle, an enthymeme is what has the function of a proof or demonstration in the domain of public speech. Since a demonstration is a kind of sullogismos, and the enthymeme is said to be a sullogismos too. The word ‘enthymeme’ (from ‘enthumeisthai - to consider’) had already been coined by Aristotle's predecessors and originally designated clever sayings, bon mots and short arguments involving a paradox or contradiction. The concepts ‘proof’ (apodeixis) and ‘sullogismos’ play a crucial role in Aristotle's logical-dialectical theory. In applying them to a term of conventional rhetoric Aristotle appeals to a well known rhetorical technique, but, at the same time, restricts and codifies the original meaning of ‘enthymeme’: properly understood, what people call ‘enthymeme’ should have the form of a sullogismos, i.e. a deductive argument.
6.2 Formal Requirements
In general, Aristotle regards deductive arguments as a set of sentences in which some sentences are premises and one is the conclusion, and the inference from the premises to the conclusion is guaranteed by the premises alone. Since enthymemes in the proper sense are expected to be deductive arguments, the minimal requirement for the formulation of enthymemes is that they have to display the premise-conclusion-structure of deductive arguments. This is why enthymemes have to include a statement as well as a kind of reason for the given statement. Typically this reason is given in a conditional ‘if’-clause or a causal ‘since’- or ‘for’-clause. Examples of the former , conditional type are: “If not even the gods know everything, human beings can hardly do so.” “If the war is the cause of present evils, things should be set right by making peace.” Examples of the latter, causal type are: “One should not be educated, for one ought not be envied (and educated people are usually envied).” “She has given birth, for she has milk.” Aristotle stresses that the sentence “There is no man among us who is free” taken for itself is a maxim, but becomes an enthymeme as soon as it is used together with a reason such as “for all are slaves of money or of chance (and no slave of money or chance is free).” Sometimes the required reason may even be implicit, as e.g. in the sentence “As a mortal do not cherish immortal anger” the reason why one should not cherish mortal anger is implicitly given in the phrase “immortal,” which alludes to the rule that is not appropriate for mortal beings to have such an attitude.
6.3 Enthymemes as Dialectical Arguments
Aristotle calls the enthymeme the “body of persuasion,” implying that everything else is only an addition or accident to the core of the persuasive process. The reason why the enthymeme as the rhetorical kind of proof or demonstration should be regarded as central for the rhetorical process of persuasion is that we are most easily persuaded when we think that something has been demonstrated. Hence, the basic idea of a rhetorical demonstration seems to be this: In order to make a target group believe that q, the orator must first select a sentence p or some sentences p1 … pn that are already accepted by the target group, secondly she has to show that q can be derived from p or p1 … pn, using p or p1 … pn as premises. Given that the target persons form their beliefs in accordance with rational standards, they will accept q as soon as they understand that q can be demonstrated on the basis of their own opinions.
Consequently, the construction of enthymemes is primarily a matter of deducing from accepted opinions (endoxa). Of course, it is also possible to use premises which are not commonly accepted by themselves, but can be derived from commonly accepted opinions; other premises are only accepted since the speaker is held to be credible; still other enthymemes are built from signs: see §6.5. That a deduction is made from accepted opinions—as opposed to deductions from first and true sentences or principles—is the defining feature of dialectical argumentation in the Aristotelian sense. Thus, the formulation of enthymemes is a matter of dialectic, and the dialectician has the competence that is needed for the construction of enthymemes. If enthymemes are a subclass of dialectical arguments then, it is natural to expect a specific difference by which one can tell enthymemes apart from all other kinds of dialectical arguments (traditionally, commentators regarded logical incompleteness as such a difference; for some objections against the traditional view see §6.4). Nevertheless, this expectation is somehow misled: The enthymeme is different from other kinds of dialectical arguments, insofar as it is used in the rhetorical context of public speech (and rhetorical arguments are called ‘enthymemes’); thus, no further formal or qualitative differences are needed.
However, in the rhetorical context there are two factors that the dialectician has to keep in mind if she wants to become a rhetorician too, and if the dialectical argument is to become a successful enthymeme. Firstly, the typical subjects of public speech do not - as the subject of dialectic and theoretical philosophy - belong to the things that are necessarily the case, but are among those things which are the goal of practical deliberation and can also be otherwise. Secondly, as opposed to well trained dialecticians the audience of public speech is characterized by an intellectual insufficiency; above all, the member of a jury or assembly are not accustomed to follow a longer chain of inferences. Therefore enthymemes must not be as precise as a scientific demonstration and should be shorter than ordinary dialectical arguments. This, however, is not to say that the enthymeme is defined by incompleteness and brevity. Rather, it is a sign of a well executed enthymeme that the content and the number of its premises are adjusted to the intellectual capacities of the public audience; but even an enthymeme which failed to incorporate these qualities would still be enthymeme.
6.4 The Brevity of the Enthymeme
In a well known passage (Rhet. I.2, 1357a7-18; similar: Rhet. II.22, 1395b24-26) Aristotle says that the enthymeme often has few or even fewer premises than some other deductions, (sullogismoi). Since most interpreters refer the word ‘sullogismos’ to the syllogistic theory (see the entry on Aristotle's logic) according to which a proper deduction has exactly two premises, those lines have led to the wide spread understanding that Aristotle defines the enthymeme as a sullogismos in which one of two premises has been suppressed, i.e. as an abbreviated, incomplete syllogism. But certainly the mentioned passages do not attempt to give a definition of the enthymeme, nor does the word ‘sullogismos’ necessarily refer to deductions with exactly two premises. Properly understood, both passages are about the selection of appropriate premises, not about logical incompleteness. The remark that enthymemes often have few or less premises concludes the discussion of two possible mistakes the orator could make (Rhet. I.2, 1357a7-10): One can draw conclusions from things that have previously been deduced or from things that have not been deduced yet. The latter method is unpersuasive, for the premises are not accepted nor have they been introduced. The former method is problematic too: if the orator has to introduce the needed premises by another deduction, and the premises of this pre-deduction too, etc., one will end up with a long chain of deductions. Arguments with several deductive steps are common in dialectical practice, but one cannot expect the audience of a public speech to follow such long arguments. This is why Aristotle says that the enthymeme is and should be from fewer premises…