# Why is Math not Logic? [duplicate]

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?

## marked as duplicate by Conifold, lemontree, curiousdannii, Eliran, YiFanSep 21 at 15:36

• 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 5 at 20:22
• 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 5 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 5 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 5 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 5 at 20:50

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.

• 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 6 at 0:12
• 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 8 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 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 at 0:27
• @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 at 14:20