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So I've heard, "Math is not logic," because logic has no notion of order. However, consider the following argument:

There once was a man on a mountaintop. He came down, murdered a villager's cat, and went back up again.

Now, you may think the Police would like to catch this man. So they asked a logitician: "Where is he?" The logitician pondered the question, then, having no notion of chronological order, responded: "He is either somewhere else, or on the mountain top."

The Police officer, not being a logitician, thanked him and promptly visited the mountain top to apprehended the murderer. This is an example of interpreted logic: It takes a layman to add order to the logitician's orderless analysis.

Am I making sense, or is there some other aspect of mathematics that is incompatible with logic?

Jonathan Graef
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    That question is about the culture difference between the two fields of study. I am asking if logic definitionally circumscribes mathematics. But you can answer culturally if you want to, seeing as how definitions are created from shared meaning. Edit: Specifically, what symbols are incompatible? (aside from being drawn differently on the page) – Jonathan Graef Sep 05 '19 at 20:22
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    I am not sure what you mean by either "culture difference" or "definitionally circumscribes" (there are no uncontroversial "definitions" to circumscribe either). Who says that "logic has no notion of order" and what that means is also unclear. – Conifold Sep 05 '19 at 20:28
  • Well, they took down the article I was basing my question on. Go figure. It's just that, in general, people say, "Math isn't logic because math has x." What is x? – Jonathan Graef Sep 05 '19 at 20:39
  • @JonathanGraef Order is at the very heart of logic. Logical order is most plausibly what underpins any notion of order we may come to think of, including that of spatial order, order in time, causality, social order etc. That being said, yes, maths is not logic.Mathematics is just a formal language, one which is particularly rigorous. We use it to think logically but there is nothing specific to mathematics in that respect. English or French are also languages, and all languages are primarily used to think logically. – Speakpigeon Sep 05 '19 at 20:46
  • So you're saying, "Math is not logic because it is just a rigorous system of formal thought." I find that to be a very tough pill to swallow. Your theory about languages intrigues me, however. – Jonathan Graef Sep 05 '19 at 20:50
  • There are several reasons why math and logic are not identical. One is the purpose or intent of such a topic. Deductive reasoning can be done with absolute no Mathematical knowledge by an ordinary human being. I give you a classic syllogism & I am sure most humans would draw the correct conclusion. No assumption or axioms needed. Deductive reasoning as opposed to math is more concerning knowledge & understanding.. – Logikal Sep 05 '19 at 21:22
  • Mathematical logic is a man made entity whereas deductive reasoning was an observation. Mathematical logic was created to attempt to formalize arguments into Mathematical notation & should be capable if logic was strictly about form. Many concepts have changed since Mathematical logic grew. Concepts influenced were contraposition, proposition, tautology, validity, existential import, soundness, contradiction, the whole if . . . Then construct (aka the conditional). Old school philosophy & people who study Mathematical logic today will likely have different meanings of these same terms. – Logikal Sep 05 '19 at 22:26

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What does "logic has no notion of order" mean? "No notion of chronological order" is a specific instance of this, and still doesn't make sense. Logic itself has no notion of anything. Order is simply one of many concepts that logic can be applied to, as in defining this rule: "A comes before B" and "B comes before C", therefore "A comes before C". Logic can apply rules, but it has no concept of what the rules actually mean.

Logic is simply a way of combining existing facts to produce new facts.

Mathematics is a set of specific formal applications of logic, with each branch of mathematics starting with a different set of initial facts.

Those initial facts (axioms) are not necessarily true in the real world, but are simply assumed to be true within the branch of mathematics being used.

Logic (deductive reasoning) is the process used by mathematics to produce new facts that are guaranteed to be at least as true as the initial facts.

Ray Butterworth
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  • I would disagree with your use of the term LOGIC. 99.999 percent of the time people who study math use the word like you & refer to math. Deductive reasoning is not identical to Mathematical logic as math people tend to communicate. All subjects use deductive reasoning. Mathematical logic is a specific type of logic just as fuzzy logic ,Aristotelian logic or modal logic. These are not identical. Mathematical logic has prerequisites. That without knowing some math already the Mathematical logic is extremely difficult to pull off or impossible to do. Deductive reasoning has no prerequisites. – Logikal Sep 06 '19 at 00:12
  • Mathematical logic presumably has no prerequisites, as Math was invented. While it is possible that math is built into the species just as deductive logic is, I find no evidence for that theory. Although I agree, math is a more difficult variant of deductive reasoning. – Jonathan Graef Sep 08 '19 at 23:58
  • @Logikal Mathematical logic isn't a type of logic in the way fuzzy, or modal, logics are. It's a field that studies how mathematics applies to logic and how logic applies to certain areas of mathematics. It's more akin to the field of "philosophical logic", which, again, isn't a specific type of logic, but the philosophical study of logic – Daniel Prendergast Sep 13 '19 at 20:46
  • @daniel prendergast, you are wrong. You can't prove what you claim. Perhaps you should GOOGLE theTERM MATHEMATICAL LOGIC. Find out when it was invented since you are duped into thinking logic is logic just like an overwhelming number of math students. I wonder why people is let's say chemistry or Psychology are not making this mistake as frequently. Mathematical logic is a TYPE OF LOGIC with a very SPECIFIC NAME. It is not just logic as you have been told. Mathematical logic was not always around. Did people forget to mention it? You act like it has been centuries it has been around. – Logikal Sep 14 '19 at 00:27
  • @Logikal It's not a type of logic, it's a field of research within logic. Type theory is a part of mathematical logic, but clearly isn't a specific type of logic. It's like saying philosophical logic is a type of logic; it's not, it's a field of research related to logic. Logic itself is any one of the specific systems of logic out there. – Daniel Prendergast Sep 14 '19 at 14:20
  • @Daniel prendergast, you are wrong. In the past there have been book titles that specifically state Mathematical logic in their titles. Mathematical logic is a type of logic as it differs a lot from the OTHER TYPES of logic. Philosophical logic is not a TYPE but expresses how mathematics teaches the topic as opposed to many philosophy lead logic classes. Again I must emphasize the purpose or intent of math compared to philosophy are not identical. Did you look up when the topic Mathematical logic was invented? Note the term invented which implies created with special things in mind or purpose – Logikal Sep 14 '19 at 14:42
  • @Logikal https://en.wikipedia.org/wiki/Mathematical_logic "Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory." none of these are a "type of logic". In precisely the same as in philosophical logic, Vagueness, logical pluralism, are areas of study within the field, but are not types of logic. – Daniel Prendergast Sep 14 '19 at 14:51
  • @Daniel prendergast, you are't reading correctly. It specifically says Mathematical Logic which is a BRANCH OF MATHEMATICS. Before the 19 century all types of logic were SPECIFICALLY under PHILOSOPHY --not mathematics. It is important you find out how Mathematical Logic was created from a mathematical conference in the 19th century. This type of argumentation is NOT identical to how philosophers argued prior to that time. It is STILL not identical to how average human being argue today. Mathematical logic has to be LEARNED. You must know some math concepts to do it. It is not pure deduction – Logikal Sep 14 '19 at 14:58
  • @Logikal that's a sociological point. Whether logic comes under philosophy or is a mathematical discipline is an interesting question, but not what I'm talking about. I'm talking about whether the mathematical field of mathematical logic, is itself a specific kind of logic. It isn't. You can study multiple types of logic in mathematical logic; 0th order, first order, second order etc, non classical etc. But its not any specific kind. Also, pre 19th century logic had to be learned to; aristotle had to invent it. And people reason badly; logic has always been about fixing that, not modelling it – Daniel Prendergast Sep 14 '19 at 15:09
  • @Daniel Prendergast, Aristotelian logic is not invented. What most subject founders did was to observe & write down the patterns or characteristics of what they observed. That is NOT identical to inventing something for a purpose. People we already thinking in patterns & deductive. Aristotelian logic is about deduction & patterns. All logic has a form. So there is NO SPECIAL knowledge required to reason deductively. You can not say the same for people use Mathematical logic as a direct invention in some MATHEMATICANS HEAD. This is not identical. As far as a college SUBJECT logic was philosophy – Logikal Sep 14 '19 at 15:29