Wednesday, March 26, 2008
Wednesday, March 5, 2008
Experience Matters... In a Bad Way
“Sure, Obama is the superior candidate who has the ability to lead and unite this country, but he just doesn’t have the experience.” –Irrational Hillary supporter
Lately there has been quite the ruckus regarding Obama and his level of experience in Washington. Apparently, Americans consider it “experience” when you happen to sleep under the same roof as the president. Had it not been for Hillary’s eight years as First Lady, Obama would be considered more experienced. She only served seven years as a senator while Obama was a state legislator for seven years and three in the senate. Let’s put this debacle aside for a moment and ask whether experience is necessary to begin with.
In general, someone experienced can be more over-confident and careless than their inexperienced counterpart. Experienced people might only have an advantage over operations they have repeated many times and not necessarily better at their job. These speculations are a few possible arguments for why an experienced person might not have the upper hand in succeeding.
Assuming that none of these are the case, I would still prefer the candidate with less experience in Washington.
Unlike most professions, working in the White House for many years does not imply success or quality work. It is hard for a bad dentist to continue being a dentist for 20 years – he would be sued to bankruptcy before his first year. Government officials have it easy, just don’t get your dick sucked by someone other than your wife and you have a free ride until your term ends. You can even illegally send your country to war killing more than a million innocent people and keep your day job.
Citizens don’t care enough to monitor their politicians’ behaviors and nor do they bother to educate themselves before voting. All the politician needs to do is pummel their face with Botox and make-up every couple years and appeal to people’s primitive emotions. The more experience they have, the better they are at looking pretty.
Where do experienced politicians get their money for campaigning in their 20 year run? Another thing experience in the White House implies is corruption. Big corporations grow fond of power hungry politicians and make sure they stay in the game. The government likes to have and obedient citizenry; the same logic applies to why the rich want an obedient government.
Just take a look at Bush and his whopping 14 years of experience. I’d rather have my dead pet hamster run the country.
Lately there has been quite the ruckus regarding Obama and his level of experience in Washington. Apparently, Americans consider it “experience” when you happen to sleep under the same roof as the president. Had it not been for Hillary’s eight years as First Lady, Obama would be considered more experienced. She only served seven years as a senator while Obama was a state legislator for seven years and three in the senate. Let’s put this debacle aside for a moment and ask whether experience is necessary to begin with.
In general, someone experienced can be more over-confident and careless than their inexperienced counterpart. Experienced people might only have an advantage over operations they have repeated many times and not necessarily better at their job. These speculations are a few possible arguments for why an experienced person might not have the upper hand in succeeding.
Assuming that none of these are the case, I would still prefer the candidate with less experience in Washington.
Unlike most professions, working in the White House for many years does not imply success or quality work. It is hard for a bad dentist to continue being a dentist for 20 years – he would be sued to bankruptcy before his first year. Government officials have it easy, just don’t get your dick sucked by someone other than your wife and you have a free ride until your term ends. You can even illegally send your country to war killing more than a million innocent people and keep your day job.
Citizens don’t care enough to monitor their politicians’ behaviors and nor do they bother to educate themselves before voting. All the politician needs to do is pummel their face with Botox and make-up every couple years and appeal to people’s primitive emotions. The more experience they have, the better they are at looking pretty.
Where do experienced politicians get their money for campaigning in their 20 year run? Another thing experience in the White House implies is corruption. Big corporations grow fond of power hungry politicians and make sure they stay in the game. The government likes to have and obedient citizenry; the same logic applies to why the rich want an obedient government.
Just take a look at Bush and his whopping 14 years of experience. I’d rather have my dead pet hamster run the country.
Monday, March 3, 2008
What it Means to be More Rational
In my previous post, It’s Not Easy Being Rational, I said that being irrational meant that you behaved contrary to your utility function. Following this line of logic, being rational would mean that you behaved in accordance with your preferences i.e. you did what you wanted to do. This brings up an important question: can one be more rational than another without both being irrational? If both of you did what you wanted to do, how can one be more rational than the other? Yes, allow me to demonstrate.
Being a rational agent requires a purpose or direction. In this case, the purpose is to maximize utility in the most desirable way possible. Once your preferences are determined, there exist a theoretical set of actions that will lead you to maximizing your utility function in the most desirable way. If you currently desire a coke from the fridge, there exists a set of actions that will satisfy this demand in the most desirable way. (It is important to understand that you may not have the prerequisite knowledge to know what these set of actions are).
Assume that the optimal action set includes: getting out of your chair, walk slowly not to wake up the dog, say ‘hi’ to grandma, open the fridge, grab the coke and run back to your room. The closer you in executing this theoretical optimal set of actions, the more rational you are. Unfortunately, when you assess your strategy profiles, you don’t include the action of saying ‘hi’ to grandma. You know that grandma always asks you what you are doing if you don’t say ‘hi’ and you know she doesn’t like you drinking coke. You end up having a quarrel with grandma and fail to execute the optimal set of actions.
Part of being more rational means that you can better predict the consequences of your actions. It is impossible to predict with 100% accuracy (all the time), but the closer to 100% the more rational. After predicting each action’s respective outcome, you must decide which outcomes are most desirable. Of course, the last step would be to follow through with the action set you’ve devised for yourself. Regarding the coke example, if you were more rational, you would have figured out that grandma needed a genuine ‘hi’ from you.
The moral of the story: strive to be more rational, you’ll only be benefiting yourself.
Being a rational agent requires a purpose or direction. In this case, the purpose is to maximize utility in the most desirable way possible. Once your preferences are determined, there exist a theoretical set of actions that will lead you to maximizing your utility function in the most desirable way. If you currently desire a coke from the fridge, there exists a set of actions that will satisfy this demand in the most desirable way. (It is important to understand that you may not have the prerequisite knowledge to know what these set of actions are).
Assume that the optimal action set includes: getting out of your chair, walk slowly not to wake up the dog, say ‘hi’ to grandma, open the fridge, grab the coke and run back to your room. The closer you in executing this theoretical optimal set of actions, the more rational you are. Unfortunately, when you assess your strategy profiles, you don’t include the action of saying ‘hi’ to grandma. You know that grandma always asks you what you are doing if you don’t say ‘hi’ and you know she doesn’t like you drinking coke. You end up having a quarrel with grandma and fail to execute the optimal set of actions.
Part of being more rational means that you can better predict the consequences of your actions. It is impossible to predict with 100% accuracy (all the time), but the closer to 100% the more rational. After predicting each action’s respective outcome, you must decide which outcomes are most desirable. Of course, the last step would be to follow through with the action set you’ve devised for yourself. Regarding the coke example, if you were more rational, you would have figured out that grandma needed a genuine ‘hi’ from you.
The moral of the story: strive to be more rational, you’ll only be benefiting yourself.
Sunday, March 2, 2008
It’s Not Easy Being Rational
If you’ve ever met a disguised anti-rationalist you’ve probably heard the “but it’s rational to be irrational” line. They believe themselves to be clever in finding the rationalist’s loop hole in being irrational. For instance, ‘irrationally’ going on a shopping spree once a month should be deemed a rational act. Clearly, it is easy to point out how such a proposition has no merit. For one, it posits the definition of ‘rational’ to mean the same thing as it’s opposite. These fundamental problems, however, only transpire when you interpret the proposition literally and not for its implicit message.
Saying that a shopping spree is rational and irrational at the same time implies two things about a person 1) their arrogance in throwing around intellectual words they don’t understand 2) the satisfaction and non-regret they get from having a shopping spree once a month. If the former wasn’t the case, the person would understand their once a month shopping spree was never irrational to begin with.
Assigning value to something, and therefore creating a utility function, is not where irrationality is committed. For example, preferring your coffee with two spoons of sugar is just as rational as preferring it with ten. You only act irrationally if behave contrary to your preferences/utility function. A trivial example is if you knowingly added no sugar in your coffee when in the past you’ve always preferred at least one spoonful. For a non-trivial example see Allais Paradox.
You might be thinking to yourself, “If behaving rationally only requires me to do what I want, I must be pretty damn rational.” This reasoning depends on a flawed assumption that you know what you want. If you’ve ever experienced regret or remorse, one of your past actions/choices contradicted your original utility function. These emotions serve as a nice defense mechanism against irrationality because they make us think harder before acting. (Obviously, if you prefer to stray from regret and remorse then you’ll think twice before acting). Unfortunately, not all of us possess such an accurate defense mechanism and therefore must think harder whether or not we believe regret might supervene on our decisions.
Saying that a shopping spree is rational and irrational at the same time implies two things about a person 1) their arrogance in throwing around intellectual words they don’t understand 2) the satisfaction and non-regret they get from having a shopping spree once a month. If the former wasn’t the case, the person would understand their once a month shopping spree was never irrational to begin with.
Assigning value to something, and therefore creating a utility function, is not where irrationality is committed. For example, preferring your coffee with two spoons of sugar is just as rational as preferring it with ten. You only act irrationally if behave contrary to your preferences/utility function. A trivial example is if you knowingly added no sugar in your coffee when in the past you’ve always preferred at least one spoonful. For a non-trivial example see Allais Paradox.
You might be thinking to yourself, “If behaving rationally only requires me to do what I want, I must be pretty damn rational.” This reasoning depends on a flawed assumption that you know what you want. If you’ve ever experienced regret or remorse, one of your past actions/choices contradicted your original utility function. These emotions serve as a nice defense mechanism against irrationality because they make us think harder before acting. (Obviously, if you prefer to stray from regret and remorse then you’ll think twice before acting). Unfortunately, not all of us possess such an accurate defense mechanism and therefore must think harder whether or not we believe regret might supervene on our decisions.
Sunday, February 24, 2008
America's Economy Thrives on Unhappy People
Americans are obsessed with their mass accumulation of stuff. The bigger the heap of stuff they have, the happier they are. And nothing, not even loved ones, dare get in their way of amassing more stuff. People abandon their families for higher paying jobs and divorce their spouses because of avoidable money issues. Americans have reached a gloomy social frontier as they prioritize over-priced handbags over a genuine relationship.
Of course we could point fingers at the advertisers and marketers for mind-fucking the younger generation. However, a flickering banner ad is not enough to bring a whole country in a delusional mind-set. The real culprit lays in the structure our economy is built on: capitalism. America isn’t completely capitalistic – it does provide some social programs like well-fare and Medicaid, but it mostly relies on private decision-making and economic freedom. The free markets take charge in America and the free markets always know best. The idea that the markets will guide us towards what we collectively desire is not a novel one. This wisdom has been around for centuries, but only recently do we see its negative social repercussions.
The fact is - capitalism thrives on dissatisfaction. It’s true that the free market allows individuals to choose their optimum consumption bundles at a fair price, but what else is going on? Let’s scope in on the consumer’s mind-set when going through the decision process in maximizing utility. Imagine a consumer strolling down the labyrinth of aisles at his local Costco. He gazes at an ocean of stuff as he decides what he should buy. He pictures the stuff he already owns as he passes by newer and more expensive substitutes. He would only have the incentive to purchase a new substitute if he is dissatisfied with the one he already has. As he passes by more stuff he may realize he will be dissatisfied if he doesn’t buy that stuff.
Dissatisfaction is the fuel behind consumer spending and consumer spending is the crux behind GDP. And believe me, America cares about GDP growing every year. A recession is defined as negative economic growth for two or more successive quarters of a year. Just mentioning the word makes the market sentiment haywire (I apologize). With the government’s and the market’s incentive for growing GDP, they make sure Americans spend their achy breaky hearts out.
Pressured to spend, Americans adapted obediently as dissatisfaction became engrained in the culture. American’s discontent now extends beyond their aspiration for consumables. If you are dissatisfied with your family or girlfriend there supposedly exists a ‘free market’ out there for you to choose a better one. Things aren’t working out between you and your wife? Don’t worry, just return your current one and get a new one that fits you better! Commoditizing intimate relationships has never been this easy!
Americans have lost the ability to be ‘happy with what they have’ when it comes to consumables and relationships. By chronically being dissatisfied, they lose their happiness in the free market abyss.
Of course we could point fingers at the advertisers and marketers for mind-fucking the younger generation. However, a flickering banner ad is not enough to bring a whole country in a delusional mind-set. The real culprit lays in the structure our economy is built on: capitalism. America isn’t completely capitalistic – it does provide some social programs like well-fare and Medicaid, but it mostly relies on private decision-making and economic freedom. The free markets take charge in America and the free markets always know best. The idea that the markets will guide us towards what we collectively desire is not a novel one. This wisdom has been around for centuries, but only recently do we see its negative social repercussions.
The fact is - capitalism thrives on dissatisfaction. It’s true that the free market allows individuals to choose their optimum consumption bundles at a fair price, but what else is going on? Let’s scope in on the consumer’s mind-set when going through the decision process in maximizing utility. Imagine a consumer strolling down the labyrinth of aisles at his local Costco. He gazes at an ocean of stuff as he decides what he should buy. He pictures the stuff he already owns as he passes by newer and more expensive substitutes. He would only have the incentive to purchase a new substitute if he is dissatisfied with the one he already has. As he passes by more stuff he may realize he will be dissatisfied if he doesn’t buy that stuff.
Dissatisfaction is the fuel behind consumer spending and consumer spending is the crux behind GDP. And believe me, America cares about GDP growing every year. A recession is defined as negative economic growth for two or more successive quarters of a year. Just mentioning the word makes the market sentiment haywire (I apologize). With the government’s and the market’s incentive for growing GDP, they make sure Americans spend their achy breaky hearts out.
Pressured to spend, Americans adapted obediently as dissatisfaction became engrained in the culture. American’s discontent now extends beyond their aspiration for consumables. If you are dissatisfied with your family or girlfriend there supposedly exists a ‘free market’ out there for you to choose a better one. Things aren’t working out between you and your wife? Don’t worry, just return your current one and get a new one that fits you better! Commoditizing intimate relationships has never been this easy!
Americans have lost the ability to be ‘happy with what they have’ when it comes to consumables and relationships. By chronically being dissatisfied, they lose their happiness in the free market abyss.
Tuesday, February 5, 2008
The Bullies You'll Meet Throughout Life
Bullies range in all shapes, sizes, age, motives, testosterone levels, and more. Wielding my power of stereotyping, I will attempt to categorize bullies in some meaningful way. Throughout our lives we encounter different types of bullies. There are about three variables that change as the bullies change throughout time: 1) Source of bully power 2) Prospective victims 3) Means of torment. Lets begin with the earliest known form of a bully usually found on the kindergarten playground.
The Future Rapist - Kindergarten playground
This young fellow is normally found on Kindergarten playground. This bully has enough libido to fuel an army of erectile dysfunctional penises. His sex craving genetic gift mixed in with the stupidity of being a five-year-old gives him his bully potential. His victims are a mix of boys and girls ranging from ages 1 – 6; he takes advantage of the younger ones who don’t yet have the vocabulary or mental capacity to say “No!” First he taunts his victims by yelling obscenities at them like, “Want to taste my poop?” After breaking his victim’s comfort zone he swiftly reaches for their genitals and retreats back to the swing sets. This process occurs anywhere from four to seven times during recess.
The Fatty – Elementary school
This child’s weight is about two standard deviations above the mean. Assuming that a person can lift their own weight, this bully automatically has the ability to choke slam two upper graders simultaneously. His love for Twinkies and French Fries has made his strength unmatched. His victims include anyone who tampers with his fragile emotional state induced by his constant struggle of coping with be so fucking fat... or the guy who took the last Jell-o pudding from the cafeteria. His means of torment include: wedgies, knuckle sandwiches, hurts donut, or basically any acts of violence that have euphemisms which sound like they could be eatable.
The Meathead – High School
Due to either a high consumption of hormone induced chicken or ungodly genes, this bully started puberty at age 8 and by his first year in High School, he has reached his top physical shape. While the other boys are still shorter and scrawnier than most girls, this bully physically dominates his high school peers. His victims include anyone his older brother tells him to beat up. With great power comes great responsibility; unfortunately, The Meathead only has a middle school education with a skull thicker than his femur. This unstable combination of power and stupidity is as dangerous as a ten-year-old with flammable ninja stars. With this imagery in your mind, you can imagine the pain inflicted on his victims.
The Corporate Cunt – Corporation
Back in the schoolyard, power was derived from physical strength; in the corporate world, power comes with the ability to make others work on Saturdays. As a corporate peon who happens to be one rung higher than you, The Corporate Cunt never hesitates to make you work on Saturday. His victims usually consist of employees on the verge of a nervous breakdown. He will torment his victims by assigning mandatory Saturday work on the grounds of “because I said so.” Furthermore, he will remind employees every day of the week that there is a mandatory meeting on Saturday. He flips a coin and says that if it lands on heads there is work on Saturday and if it lands on tails there isn’t work on Saturday. Then he has it land on tails and says “Actually there will be work on Saturday.”
The Old Bastard – Retirement Home
He is the old guy who still maintains his youthful vigor and rubs it in everyone’s face. He usually preys on old people who have lost the will to live and/or vegetables. He torments his victims by showing off his erection through his pants too all the wallflowers at the senior ball. He also lifts weights in front of the guys who can barely lift themselves out of bed. Moreover, he tells the old people with chronic depression that all their pills are placebos and they should do something active instead of sob all day. The Old Bastard always outlives his victims.
I assure you that no nerds were hurt in the making of this post.
The Future Rapist - Kindergarten playground
This young fellow is normally found on Kindergarten playground. This bully has enough libido to fuel an army of erectile dysfunctional penises. His sex craving genetic gift mixed in with the stupidity of being a five-year-old gives him his bully potential. His victims are a mix of boys and girls ranging from ages 1 – 6; he takes advantage of the younger ones who don’t yet have the vocabulary or mental capacity to say “No!” First he taunts his victims by yelling obscenities at them like, “Want to taste my poop?” After breaking his victim’s comfort zone he swiftly reaches for their genitals and retreats back to the swing sets. This process occurs anywhere from four to seven times during recess.
The Fatty – Elementary school
This child’s weight is about two standard deviations above the mean. Assuming that a person can lift their own weight, this bully automatically has the ability to choke slam two upper graders simultaneously. His love for Twinkies and French Fries has made his strength unmatched. His victims include anyone who tampers with his fragile emotional state induced by his constant struggle of coping with be so fucking fat... or the guy who took the last Jell-o pudding from the cafeteria. His means of torment include: wedgies, knuckle sandwiches, hurts donut, or basically any acts of violence that have euphemisms which sound like they could be eatable.
The Meathead – High School
Due to either a high consumption of hormone induced chicken or ungodly genes, this bully started puberty at age 8 and by his first year in High School, he has reached his top physical shape. While the other boys are still shorter and scrawnier than most girls, this bully physically dominates his high school peers. His victims include anyone his older brother tells him to beat up. With great power comes great responsibility; unfortunately, The Meathead only has a middle school education with a skull thicker than his femur. This unstable combination of power and stupidity is as dangerous as a ten-year-old with flammable ninja stars. With this imagery in your mind, you can imagine the pain inflicted on his victims.
The Corporate Cunt – Corporation
Back in the schoolyard, power was derived from physical strength; in the corporate world, power comes with the ability to make others work on Saturdays. As a corporate peon who happens to be one rung higher than you, The Corporate Cunt never hesitates to make you work on Saturday. His victims usually consist of employees on the verge of a nervous breakdown. He will torment his victims by assigning mandatory Saturday work on the grounds of “because I said so.” Furthermore, he will remind employees every day of the week that there is a mandatory meeting on Saturday. He flips a coin and says that if it lands on heads there is work on Saturday and if it lands on tails there isn’t work on Saturday. Then he has it land on tails and says “Actually there will be work on Saturday.”
The Old Bastard – Retirement Home
He is the old guy who still maintains his youthful vigor and rubs it in everyone’s face. He usually preys on old people who have lost the will to live and/or vegetables. He torments his victims by showing off his erection through his pants too all the wallflowers at the senior ball. He also lifts weights in front of the guys who can barely lift themselves out of bed. Moreover, he tells the old people with chronic depression that all their pills are placebos and they should do something active instead of sob all day. The Old Bastard always outlives his victims.
I assure you that no nerds were hurt in the making of this post.
Wednesday, January 30, 2008
Do we Know Anything?
“I would never die for my beliefs because I might be wrong.” -Bertrand Russell
I found this quote to be deeply insightful and thought provoking for reasons that may not seem obvious. For one, this quote makes apparent the irony proliferated by theists in their argument for God. As a typical theist would cry, “…but you can’t prove or disprove anything 100% and therefore it is wrong to say that God does not exist!” Considering that theists are willing to die in the name of God, they must believe in his existence to be true and therefore fall into their own trap.
But what struck me by surprise was the fact that Russell has no beliefs in which he finds certainly true. How can the guy who helped lay the groundwork of math be uncertain of every belief he has acquired? Is there really nothing we can be certain about? Instead of giving a cop-out answer like “I think, therefore I am” I sought after a more sufficient answer. From my findings, math and philosophy are inadequate in finding absolute truth and/or falsity.
Aristotle established classical logic in his attempt to use reason in finding true arguments. This logic allowed him to make propositional expressions true for all input values. All you would need to know is whether the value of your proposition is true or false and using a predefined function variable, you would arrive at a valid prepositional expression. These variables would be defined by truth tables like this conjunction for the p and q:
According to this truth table, if your P is true and your Q is true then the expression ‘P and Q’ is true. Here we seem to have arrived at a way to know something for certain. Using ‘and’ as our truth function, shouldn’t we know for certain that (true P) ^ (true Q) must be a true expression? Shouldn’t this statement be has valid as saying 2 + 2 = 4? Sure, but don’t try extracting any real meaning from these equations and expect a true statement.
It turns out that this sort of syntactic manipulation is the closest thing to the truth you will get. Don’t get me wrong, it is quite useful to logically derive true statements via truth functions, but remember that, at most, you’re just throwing around symbols.
Whenever we input a value for P or Q, regardless of what logical variable (‘and’, ‘or’, ‘then’, etc) we choose, we are bound to reach a meaningless conclusion. For example, take P to be “I love cake,” which is true, and Q to be “I live in the US,” which is also true. Therefore the sentence “I love cake and I live in the US,” must be true. All right, am I ready to die for my love of cake yet? Nope
For a logical argument to be true, the premises must also be true. If I have one premise that happens to be meaningless and the other true, my functional argument will also be meaningless. Take my love for cake for example. If the cake has fruits on it I will no longer love the cake. Ah, I see my problem is in my weak definition of the word ‘cake’; I’ll just update my definition and be one my way to the truth. “I love cake that doesn’t have any fruits.” Here too I have encountered vagueness in my word choice. If I cut the fruit in half, is it still a fruit? Maybe, but if I cut it down to one atom, is it still a fruit?
Maybe I just need to find better word choice to escape vagueness. How about, “If I can lift 200 lbs, then I am strong” This sounds like a true statement, but it doesn’t reveal any truth of what it means to be strong. What if you give me 200 – .001 lbs, would I still be strong? How many times can I remove .001 lbs before I am no longer strong? No matter what proposition I fill in for P and Q, there will always be an undefined answer.
Even the mapping of mathematical equations to the natural world proves inadequate in revealing truths. We find the equation 2+2=4 as quite useful, but what does that reveal about truth or certainty in the real world? If I have two pairs of shoes, I'll get four shoes total. But what is a shoe? And what does combining this vague definition of a shoe with our equation even mean? The only thing we can know for certain is the syntactical manipulation in accordance with our predefined connectives.
But lets not forget:
“When one admits that nothing is certain one must, I think, also admit that some things are much more nearly certain than others.” - Bertrand Russell
I found this quote to be deeply insightful and thought provoking for reasons that may not seem obvious. For one, this quote makes apparent the irony proliferated by theists in their argument for God. As a typical theist would cry, “…but you can’t prove or disprove anything 100% and therefore it is wrong to say that God does not exist!” Considering that theists are willing to die in the name of God, they must believe in his existence to be true and therefore fall into their own trap.
But what struck me by surprise was the fact that Russell has no beliefs in which he finds certainly true. How can the guy who helped lay the groundwork of math be uncertain of every belief he has acquired? Is there really nothing we can be certain about? Instead of giving a cop-out answer like “I think, therefore I am” I sought after a more sufficient answer. From my findings, math and philosophy are inadequate in finding absolute truth and/or falsity.
Aristotle established classical logic in his attempt to use reason in finding true arguments. This logic allowed him to make propositional expressions true for all input values. All you would need to know is whether the value of your proposition is true or false and using a predefined function variable, you would arrive at a valid prepositional expression. These variables would be defined by truth tables like this conjunction for the p and q:
| p | q | p ^q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
According to this truth table, if your P is true and your Q is true then the expression ‘P and Q’ is true. Here we seem to have arrived at a way to know something for certain. Using ‘and’ as our truth function, shouldn’t we know for certain that (true P) ^ (true Q) must be a true expression? Shouldn’t this statement be has valid as saying 2 + 2 = 4? Sure, but don’t try extracting any real meaning from these equations and expect a true statement.
It turns out that this sort of syntactic manipulation is the closest thing to the truth you will get. Don’t get me wrong, it is quite useful to logically derive true statements via truth functions, but remember that, at most, you’re just throwing around symbols.
Whenever we input a value for P or Q, regardless of what logical variable (‘and’, ‘or’, ‘then’, etc) we choose, we are bound to reach a meaningless conclusion. For example, take P to be “I love cake,” which is true, and Q to be “I live in the US,” which is also true. Therefore the sentence “I love cake and I live in the US,” must be true. All right, am I ready to die for my love of cake yet? Nope
For a logical argument to be true, the premises must also be true. If I have one premise that happens to be meaningless and the other true, my functional argument will also be meaningless. Take my love for cake for example. If the cake has fruits on it I will no longer love the cake. Ah, I see my problem is in my weak definition of the word ‘cake’; I’ll just update my definition and be one my way to the truth. “I love cake that doesn’t have any fruits.” Here too I have encountered vagueness in my word choice. If I cut the fruit in half, is it still a fruit? Maybe, but if I cut it down to one atom, is it still a fruit?
Maybe I just need to find better word choice to escape vagueness. How about, “If I can lift 200 lbs, then I am strong” This sounds like a true statement, but it doesn’t reveal any truth of what it means to be strong. What if you give me 200 – .001 lbs, would I still be strong? How many times can I remove .001 lbs before I am no longer strong? No matter what proposition I fill in for P and Q, there will always be an undefined answer.
Even the mapping of mathematical equations to the natural world proves inadequate in revealing truths. We find the equation 2+2=4 as quite useful, but what does that reveal about truth or certainty in the real world? If I have two pairs of shoes, I'll get four shoes total. But what is a shoe? And what does combining this vague definition of a shoe with our equation even mean? The only thing we can know for certain is the syntactical manipulation in accordance with our predefined connectives.
But lets not forget:
“When one admits that nothing is certain one must, I think, also admit that some things are much more nearly certain than others.” - Bertrand Russell
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