Large Language Models reason do not reason like we do. In a sense, they don’t really logically reason at all.
But in a way, they reason more brilliantly than humans ever could. So how do LLMs “think”? Three words: sophisticated pattern matching.
They’re incredible at predicting what word is statistically likely to come next based on patterns in my training data. And the training data is immenese. LifeArchitect claims GPT-5 training data is ~114,000,000,000,000 tokens. And given the King James Bible is about 1,000,000 tokens worth of text, that means GPT-5 was trained on 114,000,000 Bibles worth of text. So now you know why they’re called “Large” Language Models.
In the early decades of AI through the 1980s, AI systems were built on formal logic and symbolic reasoning. These systems didn’t learn from data like modern neural networks do. They applied hand-crafted rules to deduce conclusions.
LLMs represent fundamentally different approaches to artificial intelligence with distinct strengths and critical weaknesses that complement each other. Understanding this crucial distinction is absolutely key to using AI systems effectively for different types of problems.
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What is Logical Reasoning
Aristotle, the father of formal logic, created the foundation we still use 2,300 years later: “All A are B, all B are C, therefore all A are C”. This was the first systematic approach to logical truth. Aristotle was a great philosopher, who wrote: “The least initial deviation from the truth is multiplied later a thousandfold.” He knew that logical precision matters. One wrong assumption can snowball into catastrophic errors.
Formal logical systems start with assumptions, apply formal rules of inference, and reach certain conclusions with 100% confidence. The classic example is “All humans are mortal, Socrates is human, therefore Socrates must be mortal with absolute certainty.” This perfectly exemplifies Aristotelian logic in action. If the premises are genuinely true, the conclusion MUST be true by logical necessity.
The core strength of logic: In short, the assumptions made are true, it provides pure confidence in truth.
The core weakness of logic: It requires perfect information. And if economic theory has taught us anything, it is that assymetric knowledge is the natural state of information systems.
What is Probabilistic Reasoning
Probabilistic reasoning is statistical in nature. It assigns probabilities to different outcomes, models uncertainty through probability distributions, and selects the most likely outcome based on statistical evidence. This is how weather is predicted.
Similarly, LLMs predict the next token in a sequence where seeing “What’s the capital of France” triggers 95% probability for “Paris” as the next token, using no logical reasoning whatsoever. Just pure statistical patterns learned from billions of training examples.
The core strength of probability: It gracefully handles uncertainty in an uncertain world.
Weaknesses of probabilistic reasoning: It cannot provide certainty. And at times, this can create seemingly insane arguments.
A ridiculous story I am a history nerd, and I once wasted 30 minutes of my life explaining to ChatGPT that a certain 1910’s US Senator, was in fact, a US Senator. ChatGPT insisted this was not true, and even gave me the contact info of the Smithsonian, to tell them to change their records. Debating logic with a probabilistic machine is like that.
When to Use Which
Use logical reasoning when: Absolute correctness is critical. For example, compiling code requires logic, because your code must translate to binary in a reliable way.
Use probabilistic reasoning when: “Good enough” results are acceptable. Whereas compiling code must be logical, writing new code can be done probabilistically.
Hybrid Approaches Are The Best
As an optimist, I’d say that logical reasoning alone is pure precision. Probabilistic reasoning alone is pure flexiblilty.
So you want to be smarter? Use a hybrid approach. Combine both paradigms to achieve the best of both worlds.
Generate, then verify: Use LLMs to generate ideas, content, analysis, or anything else. Then verify logic, and fine tune it yourself. You’ll be like Aristotle meets Alan Turing. A marrying of math and art. Logic and creation.
Applying The Philosophy to Real-World Examples
Cancer screening systems: Doctors are generally very smart, but even the best trained eye may miss odd looking abnormalitics in scans. So that’s where probabilistic AI can and does come in.
Companies like iCAD already use AI in breast cancer screening. But if a screen indicates positivity, a doctor still verifies the logic of the test before sending a patient into treatment.
Code generation systems: Software developers are also very smart, but they can be limited in speed and bredth of knowledge. But generative AI is filling these gaps.
Claude, ChatGPT, OpenAI Codex, Cursor, Lovable, and many more AI coding tools allow for developers to generate code quickly, and debug and audit to verify quality.
Legal research systems: Lawyers, you too are very smart. You deserve a pat in the head. But even the best attorney can miss a precedent or obscure statute buried in thousands of pages of case law. That’s where AI-powered legal research comes in—helping surface relevant cases, arguments, and interpretations far faster than a human could manually.
Platforms like Westlaw Edge, Lexis+ AI, and Casetext use natural language processing to scan vast databases of legal texts. Still, attorneys remain the final authority—reviewing AI-suggested citations, arguments, and case matches to ensure accuracy and reliability before filing motions or presenting in court.
How They May Combine Logic and Probability in the Future
Applying these philosophies: In the future, we may bake logical reasoning capabilities directly into transformer architectures. This would be a guided generation techniques that constrain LLM outputs to follow specified syntax and semantic rules. Check out my article on Creating Great Markdown Files For Bulk Claude Code Operations for an example of this.
The ambitious long-term: Some say Artificial General Intelligence will be able to marry logic and probability into an all-powerful system. Personally, I think it that’s speculative. For now, only humans have a unique gift of synthesizing like this.
Conclusion
Logical reasoning provides certainty. Probabilistic reasoning offers impressive flexibility. Neither approach is inherently superior to the other, they simply solve fundamentally different types of problems and serve different use cases.
Most genuinely interesting real-world problems need both reasoning paradigms working together in hybrid architectures. Probabilistic reasoning handles the inherent messiness and uncertainty of real-world data and human language, while logical reasoning ensures critical constraints and safety properties are guaranteed to hold. The real art of modern AI engineering is knowing when to use which approach and how to combine them effectively.
The future of AI isn’t choosing between logical OR probabilistic reasoning, but rather AND where we build integrated systems that simultaneously learn from data, reason with logical precision, handle uncertainty gracefully, and provide formal guarantees. We’re not there yet with fully integrated systems, but some say that’s the direction we are headed.